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# canonicalUnitNormal¶
The class of all integral domains such that we can choose a canonical representative for each class of associate elements, that is associates?(a, b) returns true if and only if unitCanonical(a) = unitCanonical(b).
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# Define differential analysis, differential revenue, differential
Define differential analysis, differential revenue, differential cost, and differential income.
<p><!----><!----><!----></p> <p class="MsoNormal" style="text-align: justify;">Differential Analysis is decision making instrument in which the evaluation is restricted only to those factors which are different or unique among possible course of actions. It is also called as incremental analysis or relevant cost analysis. Differential Revenue can be defined as the expected increase or decrease in revenue that arises from one course of action in comparison to an alternative plan that the business is considering. Differential...
## Related Questions in Managerial Accounting - Decision Making
• ### When, if ever, are fixed costs differential?
(Solved) March 08, 2013
When, if ever, are fixed costs differential?
Differential cost is the cost that differs among alternatives. These costs differ on the basis of the course of action selected by the firm. The differential cost can be variable or fixed....
• ### A proper evaluation of any project using differential analysis r
(Solved) March 05, 2013
A proper evaluation of any project using differential analysis requires the consideration of all relevant costs —past, present, and future. Comment.
Answer: All the costs incurred or to be incurred in a project are considered to be relevant under differential analysis . The consideration of all types of cost and even cost of past ,...
• ### What is a differential cost? Give an example of how
(Solved) February 15, 2013
What is a differential cost ? Give an example of how differential costs are used by managers making product and process decisions.
Differential cost is the cost which is different for different alternatives. It is the cost which may be incurred in one alternative and may not be incurred in another alternative result...
• ### Distinguish between variable costs and differential costs. Why i
(Solved) February 15, 2013
Distinguish between variable costs and differential costs . Why is the distinction important?
Differential cost is the cost which is different for different alternatives. Differential cost is the cost which is used interchangeably with the term relevant cost, incremental cost, and...
• ### Using differential analysis—special customer order Dribble, Inc., manufactures basketballs. The company’s forecasted income statement for
(Solved) November 10, 2014
Using differential analysis—special customer order Dribble, Inc., manufactures basketballs. The company’s forecasted income statement for the year, before any special orders, is as follows: Amount Per Unit Sales $8,000,000$10.00 Manufacturing cost of goods sold 6
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# TraditionalForm with function names non-italic [closed]
I'm almost certain that there is no (simple) way to achieve this as a user, but I'll ask anyway: What has always bothered the heck out of me is that Mathematica's TraditionalForm just doesn't look quite right, and does not follow some of the widespread traditions for mathematical typesetting. I'm not even talking about the poor spacing of objects overall; Mathematica just isn't TeX/LaTeX, and there's probably no hope it ever will be, even though in principle this should be possible, but I digress...
What I have in mind here is the time-honored law that says that names of functions should not be italicized (which is why LaTeX provides things like \sin, \cos, \tan, etc., etc.). Mathematica and its frontend know exactly what objetcs are defined as functions, so it should be able to follow tradition and print function names in upright fonts.
Is there any way for the user to achieve this? Is there any way to get the powers that be at Mathematica do this for us?
## closed as off-topic by WReach, m_goldberg, Mr.Wizard♦Aug 6 '16 at 6:26
This question appears to be off-topic. The users who voted to close gave this specific reason:
• "This question cannot be answered without additional information. Questions on problems in code must describe the specific problem and include valid code to reproduce it. Any data used for programming examples should be embedded in the question or code to generate the (fake) data must be included." – Mr.Wizard
If this question can be reworded to fit the rules in the help center, please edit the question.
• I don't see this if I evaluate TraditionalForm[3 Sin[x] + 2 Cos[2 x]]. I have "sin" and "cos" in a Roman font. – mikado Aug 5 '16 at 19:43
• I'm voting to close this question as off-topic because the problem the user is experiencing can not be reproduced by others. – m_goldberg Aug 6 '16 at 0:03
• Did the OP simply pick a poor example? Trig functions are converted to lowercase roman font in traditional form, but this is not the case generically: TraditionalForm[3 f[x]+2 g[x] ] has italicized f and g. Perhaps the OP is asking that for anything of the form h_[ ___ ], h be printed in non-italicized font? @m_goldberg – jjc385 Aug 6 '16 at 2:10
• @jjc385. See my answer – m_goldberg Aug 6 '16 at 5:28
• Pirx, please edit your question to include some images of what you are describing, as well as the code used to produce it. – Mr.Wizard Aug 6 '16 at 6:19
It is traditional in math notation to italicize the names of functions when they are a single letter and to display them non-italicized when multi-letter. Mathematica follows this convention with user-defined functions or functional forms when displaying them in traditional form.
For example
f[x] + func[x] // TraditionalForm
One may use SingleLetterItalics to control this behavior:
noitalic = Style[#, SingleLetterItalics -> False]&;
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# Fourier Transform Doubt!
1. Mar 24, 2012
### salil87
Hi
Do Fourier Transforms give us actual amplitude/phase of the particular frequency (ejωt) just like Fourier series?
Thanks
Salil
2. Mar 24, 2012
### rbj
sorta, yes. but the inverse continuous Fourier transform is an integral not a summation like in the Fourier series. so the actual amplitude is proportional to the product of $X(f)$ and the width of the sliver of spectrum $df$.
to compare, give the (inverse) Fourier integral a finite width (with the limits of the integral) and then represent that finite width integral with a Riemann summation and then you will be able to see the relationship between the inverse Fourier transform and the Fourier series. in a loose sense, they are the same thing.
3. Mar 26, 2012
### sophiecentaur
The series is a Discrete process where the Transform is Continuous. The series can yield 'wrong' / misleading results if you ignore the basic rules.
4. Mar 31, 2012
### Anitha Sankar
what is the fourier transform of sum( Vhcos(hwt)) where h varies from 1 to infinity
5. Mar 31, 2012
### sophiecentaur
Hi
I assume that when you write Vh , the h is a suffix.
The transform will be a regular 'comb' of components at frequency w, hw, 2hw etc. with amplitdes given by the coefficients V. In fact, the original function is of a form that tells you the frequency spectrum just by 'observation'.
6. Mar 31, 2012
### Cecilia48
http://www.infoocean.info/avatar2.jpg [Broken]The series is a Discrete process where the Transform is Continuous.
Last edited by a moderator: May 5, 2017
7. Apr 1, 2012
### sophiecentaur
I guess I meant "sum' as against 'integral'.
Is that better?
Last edited: Apr 1, 2012
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# BilevelMeasurementsConfiguration
Measure transitions, aberrations, and cycles of bilevel signals
Since R2022a
## Description
Use the BilevelMeasurementsConfiguration object to measure transitions, aberrations, and cycles of bilevel signals. You can also specify the bilevel settings such as high-state level, low-state level, state-level tolerance, upper-reference level, mid-reference level, and lower-reference level.
You can control bilevel measurements from the toolstrip or from the command line. To modify bilevel measurements from the toolstrip, in the Measurements tab, click Bilevel Settings and select the measurements you want to display. A panel appears at the bottom of the Time Scope window showing all the measurements you enabled.
## Creation
### Syntax
bilevelMeas = BilevelMeasurementsConfiguration()
### Description
example
bilevelMeas = BilevelMeasurementsConfiguration() creates a bilevel measurements configuration object.
## Properties
expand all
All properties are tunable.
Automatic detection of high- and low-state levels, specified as true or false. Set this property to true so that the scope automatically detects high- and low-state levels in the bilevel waveform. When you set this property to false, you can specify values for the high- and low- state levels manually using the HighStateLevel and LowStateLevel properties.
#### Scope Window Use
On the Measurements tab, in the Measurements section, click Bilevel Settings. Under State Level, and select Auto State Level.
Data Types: logical
High-state level, specified as a nonnegative scalar. The high-state level denotes a positive polarity.
If the initial transition of a pulse is positive-going, the pulse has positive polarity. The terminating state of a positive-polarity (positive-going) pulse is more positive than the originating state.
This figure shows a positive-polarity pulse.
#### Dependency
To enable this property, set AutoStateLevel to false.
#### Scope Window Use
On the Measurements tab, in the Measurements section, click Bilevel Settings. Under State Level, clear Auto State Level and specify a nonnegative scalar in the High box.
Data Types: double
High-state level, specified as a nonnegative scalar. The low-state level denotes a negative polarity.
If the initial transition of a pulse is negative-going, the pulse has negative polarity. The terminating state of a negative-polarity (negative-going) pulse is more negative than the originating state.
This figure shows a negative-polarity pulse.
#### Dependency
To enable this property, set AutoStateLevel to false.
#### Scope Window Use
On the Measurements tab, in the Measurements section, click Bilevel Settings. Under State Level, clear Auto State Level and specify a nonnegative scalar in the Low box.
Data Types: double
Tolerance level of the state, specified as a positive scalar in the range (0 100).
This value determines how much a signal can deviate from the low- or high-state level before it is considered to be outside that state. Specify this value as a percentage of the difference between the high- and low-state levels. For more details, see State-Level Tolerances.
#### Scope Window Use
On the Measurements tab, in the Measurements section, click Bilevel Settings. Under State Level, specify a positive scalar less than 100 in the State Level Tol. (%) box.
Data Types: double
Upper-reference level, specified as a positive scalar in the range (0 100). The scope uses the upper-reference level to compute the start of a fall time or the end of a rise time. Specify this value as a percentage of the difference between the high- and low-state levels.
If S1 is the low-state level, S2 is the high-state level, and U is the upper-reference level, the waveform value corresponding to the upper-reference level is
${S}_{1}+\frac{U}{100}\left({S}_{2}-{S}_{1}\right).$
#### Scope Window Use
On the Measurements tab, in the Measurements section, click Bilevel Settings. Under Reference Level, specify a positive scalar less than 100 in the Upper Ref. Level (%) box.
Data Types: double
Mid-reference level, specified as a positive scalar in the range (0 100). The scope uses the mid-reference level to determine when a transition occurs. Specify this value as a percentage of the difference between the high- and low-state levels.
The mid-reference level in a bilevel waveform with low-state level S1 and high-state level S2 is
${S}_{1}+\frac{1}{2}\left({S}_{2}-{S}_{1}\right)$
This figure shows the mid-reference level as a horizontal line, and shows its corresponding mid-reference level instant as a vertical line.
#### Scope Window Use
On the Measurements tab, in the Measurements section, click Bilevel Settings. Under Reference Level, specify a positive scalar less than 100 in the Mid Ref. Level (%) box.
Data Types: double
Lower-reference level, specified as a positive scalar in the range (0 100). The scope uses the lower-reference level to compute the end of a fall time or the start of a rise time. Specify this value as a percentage of the difference between the high- and low-state levels.
If S1 is the low-state level, S2 is the high-state level, and L is the lower-reference level, the waveform value corresponding to the lower-reference level is
${S}_{1}+\frac{L}{100}\left({S}_{2}-{S}_{1}\right).$
#### Scope Window Use
On the Measurements tab, in the Measurements section, click Bilevel Settings. Under Reference Level, specify a positive scalar less than 100 in the Lower Ref. Level (%) box.
Data Types: double
Time duration over which the scope searches for a settling time, specified as a positive scalar in seconds.
#### Scope Window Use
On the Measurements tab, in the Measurements section, click Bilevel Settings. Under Reference Level, specify a positive scalar in the Settle Seek (s) box.
Data Types: double
Enable transition measurements, specified as true or false. For more information on the transition measurements that the scope displays, see Transitions Pane (Simulink).
#### Scope Window Use
On the Measurements tab, in the Measurements section, click Bilevel Settings and select Transitions. A Transitions pane opens at the bottom of the Time Scope window to show the transition measurements.
Data Types: logical
Enable aberration measurements, specified as true or false. Aberration measurements include distortion and damping measurements such as preshoot, overshoot, and undershoot. For more information on the aberration measurements that the scope displays, see Overshoots / Undershoots Pane (Simulink).
#### Scope Window Use
On the Measurements tab, in the Measurements section, click Bilevel Settings and select Aberrations. An Aberrations pane opens at the bottom of the Time Scope window to show the aberration measurements.
Data Types: logical
Enable cycle measurements, specified as true or false. These measurements are related to repetitions or trends in the displayed portion of the input signal. For more information on the cycle measurements, see Cycles Pane (Simulink).
#### Scope Window Use
On the Measurements tab, in the Measurements section, click Bilevel Settings and select Cycles. A Cycles pane opens at the bottom of the Time Scope window to show the cycle measurements.
Data Types: logical
## Examples
collapse all
Create a sine wave and view it in the Time Scope. Programmatically compute the bilevel measurements related to signal transitions, aberrations, and cycles.
Initialization
Create the input sine wave using the sin function. Create a timescope MATLAB® object to display the signal. Set the TimeSpan property to 1 second.
f = 100; fs = 1000; swv = sin(2.*pi.*f.*(0:1/fs:1-1/fs)).'; scope = timescope(SampleRate=fs,... TimeSpanSource="property",... TimeSpan=1);
Transition Measurements
Enable the scope to show transition measurements programmatically by setting the ShowTransitions property to true. Display the sine wave in the scope.
Transition measurements such as rise time, fall time, and slew rate appear in the Transitions pane at the bottom of the scope.
scope.BilevelMeasurements.ShowTransitions = true; scope(swv); release(scope);
Aberration Measurements
Enable the scope to show aberration measurements programmatically by setting the ShowAberrations property to true. Display the sine wave in the scope.
Aberration measurements such as preshoot, overshoot, undershoot, and settling time appear in the Aberrations pane at the bottom of the scope.
scope.BilevelMeasurements.ShowAberrations = true; scope(swv); release(scope);
Cycle Measurements
Enable the scope to show cycles measurements programmatically by setting the ShowCycles property to true. Display the sine wave in the scope.
Cycle measurements such as period, frequency, pulse width, and duty cycle appear in the Cycles pane at the bottom of the scope.
scope.BilevelMeasurements.ShowCycles = true; scope(swv); release(scope);
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# Impossible Problem?
1. Sep 16, 2010
### Ch3st3r
Impossible Problem?????????
Can anyone solve this problem.....
The age of a machine, x, in years, is related to the probability of breakdown, y, by the formula...
x = 3 + 1n [y / 1 - y]
Determine the probability of breakdown for 1, 3 and 10 years.
You need to explain what you did to acheive each out come.
2. Sep 16, 2010
Re: Impossible Problem?????????
In each case you are given a value of $$x$$ and asked to solve for the corresponding value of $$y$$. You need to rearrange the equation you're provided to be able to do that. By the way, parentheses can help you give a clear presentation of your formula:
x = 3 + ln(y/(1-y))
is a better way to write your formula if you don't use the latex feature here in this post. written with latex
$$x = 3 + \ln \left(\frac y{1-y}\right)$$
3. Sep 16, 2010
### snipez90
Re: Impossible Problem?????????
Uh no, this is basic algebra, and you should give it an attempt first.
4. Sep 16, 2010
### Staff: Mentor
Re: Impossible Problem?????????
It's not at all impossible. What you need to do is to solve the equation for y in terms of x; i.e., find the inverse relationship.
BTW, it's not 1n; it's ln, short for logarithmus naturalis.
Also, you need another pair of parentheses in your equation, like so: x = 3 + ln [y / (1 - y)]
5. Sep 16, 2010
### Ch3st3r
Re: Impossible Problem?????????
I know i'm supposed to rearrange the equation , but from there on i'm stuck.... can anyone give me a hint or two?
6. Sep 16, 2010
### HallsofIvy
Re: Impossible Problem?????????
x is the time in years and y is the probability of break down. To find "the probability of breakdown for 1, 3 and 10 years", set x equal to 1, 3, and then 10 and solve for y in each equation:
$$x= 3+ ln\left(\frac{y}{1- y}\right)$$
so you need to solve
$$3+ ln\left(\frac{y}{1- y}\right)= 1$$
$$3+ ln\left(\frac{y}{1- y}\right)= 3$$
and
$$3+ ln\left(\frac{y}{1- y}\right)= 10$$
I would start, in each equation by subtracting 3 from both sides. And you invert ln(x) by using its inverse function $e^x$, the exponential function: if ln(y)= x, then $y= e^x$.
7. Sep 16, 2010
### Ch3st3r
Re: Impossible Problem?????????
Ok, so now I've got e^-2 [y / 1 - y] = -2
How do i get a value for y?
8. Sep 16, 2010
### zgozvrm
Re: Impossible Problem?????????
What happened to X?
Subtracting 3 from both sides gives you:
$$x-3 = ln \left( \frac{y}{1-y} \right)$$
Last edited: Sep 17, 2010
9. Sep 22, 2010
### Ch3st3r
Re: Impossible Problem?????????
So here it is........
The age of a machine, x, in years, is related to the probability of breakdown, y, by the formula...
x = 3 + 1n [y / 1 - y]
Determine the probability of breakdown for 1, 3 and 10 years.
We start off with :- x = 3 + 1n [y / 1 - y]
Using Age of machine is 1 Year x = 1 , we get...
1 = 3 + ln [y / 1 - y]...............
Using Exponential e, we get.... 1 - 3 (and Exchange Exponential e for + ln..
= e^-2 = [ y / 1 - y ]........ (Exponential (e) -2 = 0.135)
Now here's the 'Magic'...
We need to make 'y' the subject so we need to rearrange the equation...
So the Equation becomes.... y = 0.135 / 1 + 0.135
Which = y = 0.135 / 1.135 = 0.1189............
The probability of breakdown for 1 year is................ 0.1189
Have a go at 3 years and 10 years and see if you get the same Answers as I did...
The probability of breakdown for 3 years is............... 0.5
The probability of breakdown for 10 years is............. 0.999
10. Sep 23, 2010
### zgozvrm
Re: Impossible Problem?????????
This is correct. But why not just solve for Y first, then enter the X values as needed?
You should come up with
$$y = \frac{e^{x-3}}{1+e^{x-3}} = \frac{e^x}{e^3 + e^x}$$
11. Sep 23, 2010
### Ch3st3r
Re: Impossible Problem?????????
Yeah, I like your way of thinking, I 'll keep a note of that. Because up until now I didn't know it could be solved that way. Thanks For the Heads Up.
12. Sep 23, 2010
### Ch3st3r
Re: Impossible Problem?????????
But looking at your idea......it's another way.... But, I get to thinking my way is a lot Simpler. (Algebra is all about reversing the equasion anyway).
i.e........
3x + 4 = 19
3x = 19 - 4
...and so on.
13. Sep 23, 2010
### zgozvrm
Re: Impossible Problem?????????
No problem.
Of course, what's simple for one person, isn't necessarily simple for another.
Knowing that this is a homework forum, I'm apt to think that the question you posted might not have been stated exactly as it was given to you. Or, that the instructor may have wanted to see the equation solved for "y" instead.
Also, If you needed to find the value of y for many different values of x, it would be much easier to enter my version into a calculator or spreadsheet. Then, all you would need to do is enter new values of x to get corresponding values of y. No extra algebra necessary!
14. Sep 23, 2010
### Ch3st3r
Re: Impossible Problem?????????
It's all part of my Mechanical Engineering HNC, and I know a few people I'm studying with used MS Excel...... but come on, using a spreadsheet isn't really showing that you can do the Math, is it. It's not getting the grey matter working.
But like you said it's easier for some than it is others... but like Esther Rantzen used to say, 'That's Life'. Thanks again for your input, Keep up the good work, Cheers.
15. Oct 7, 2010
### Ch3st3r
Re: Impossible Problem?????????
Hi, What do I do to rearragne this Equation to make 'I' the subject.....
144 x 15.71 + I x 15.71 = (144 + I) 14.05
16. Oct 7, 2010
### Ch3st3r
Re: Impossible Problem?????????
What's the Difference between Sine and arcsin? Can I still work out an arcsin problem on my calculator using the sin key?
17. Oct 7, 2010
### zgozvrm
Re: Impossible Problem?????????
First of all, you should start a new post, since this is a new, unrelated question.
Arcsine is the inverse of Sine. It finds the angle given a ratio, whereas Sine finds the ratio given an angle. (The ratio being the length of the side opposite the angle divided by the length of the hypotenuse of a right triangle).
Most calculators use [itex]sin^{-1}[/tex] for the Arcsine function, and is usually a 2nd function above the "sin" key.
18. Oct 7, 2010
### Redbelly98
Staff Emeritus
Re: Impossible Problem?????????
zgozvrm is correct. Please post new & unrelated questions by starting a new thread.
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# Math Help - Calculus proof methods...
1. ## Calculus proof methods...
Maybe in the wrong forum...
I was just curious as to how everyone here approaches rigorous calculus proofs, I'm thinking more specifically about convergence and related topics. I find that no matter how many examples I do I always find myself lost on the next Q. Here's an example...
Let $(a_n)$ and $(b_n)$ be two sequences of real numbers such that $a_n -> 0$ and $(b_n)$ is bounded. Show that $a_n b_n -> 0$.
My first thought was that since $b_n$ is bounded then there must exist a k such that $|b_n| < k$, and so $|a_n b_n| -> 0k = 0$..? But the proof was...
=> We have M such that $|b_n| \le M$ for all n. Let $\epsilon > 0$. Then we can find m such that n>m implies $|a_n| < \frac{\epsilon}{M}$. Then for n>m we have $|a_n b_n| \le M|a_n| < M\frac{\epsilon}{M} = \epsilon$ as required.
Is there a way to learn these methods other than doing lots of examples which, i feel aren't really helping me... About to start subsequential limits and every Q scares the hell out o me.
So basically, strange post i know but does anyone have any methods they use for proofs?
2. I hope someone replies to this post so bump. I'm have the same reasoning as you and could use some help in understanding all this.
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iPQF
0th
Percentile
iPQF: iTRAQ (and TMT) Protein Quantification based on Features
The iPQF spectra-to-protein summarisation method integrates peptide spectra characteristics and quantitative values for protein quantitation estimation. Spectra features, such as charge state, sequence length, identification score and others, contain valuable information concerning quantification accuracy. The iPQF algorithm assigns weights to spectra according to their overall feature reliability and computes a weighted mean to estimate protein quantities. See also combineFeatures for a more general overview of feature aggregation and examples.
Usage
iPQF(object, groupBy, low.support.filter = FALSE, ratio.calc = "sum", method.combine = FALSE, feature.weight = c(7, 6, 4, 3, 2, 1, 5)^2)
Arguments
object
An instance of class MSnSet containing absolute ion intensities.
groupBy
Vector defining spectra to protein matching. Generally, this is a feature variable such as fData(object)$accession. low.support.filter A logical specifying if proteins being supported by only 1-2 peptide spectra should be filtered out. Default is FALSE. ratio.calc Either "none" (don't calculate any ratios), "sum" (default), or a specific channel (one of sampleNames(object)) defining how to calculate relative peptides intensities. method.combine A logical defining whether to further use median polish to combine features. feature.weight Vector "numeric" giving weight to the different features. Default is the squared order of the features redundant -unique-distance metric, charge state, ion intensity, sequence length, identification score, modification state, and mass based on a robustness analysis. Value A matrix with estimated protein ratios. References iPQF: A new peptide-to-protein summarization method using peptide characteristics to improve iTRAQ quantification Martina Fischer and Bernhard Y. Renard, in prep. Aliases • iPQF Examples data(msnset2) head(exprs(msnset2)) prot <- combineFeatures(msnset2, groupBy = fData(msnset2)$accession,
fun = "iPQF")
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Open access peer-reviewed chapter
# Bioresources for Third-Generation Biofuels
By Rafael Picazo-Espinosa, Jesús González-López and Maximino Manzanera
Submitted: October 19th 2010Reviewed: March 30th 2011Published: August 1st 2011
DOI: 10.5772/17134
## 1. Introduction
Modern societies’ welfare relies greatly on fossil fuels. The current energy model, based on the extensive utilization of fossil fuels, is affected by economic and environmental problems. The United States Department of Energy 2009 report estimates that, within the next two decades, global energy consumption will double (Conti, 2009). On the other hand, the European Commission 2009 report indicates that the management of climate change problems in Europe, since 2000, has been globally unfavourable. Nevertheless, there are some positive signs, such as the 1.4% reduction in 2007 of CO2 emissions with respect to the figures obtained from 2000 to 2004 in the European Union of Fifteen (E-15). However, considering the 27 European states (E-27), and paying attention to the consumption and production of renewable energy and biofuels, the reduction in emissions has not fulfilled the European Union objectives. Among the motives of this negative evaluation, the fall in the companies’ productivity, increased transport and industry emissions and the reduction in research and development areas can be cited (Radermacher, 2009). First- and second-generation biofuels could ameliorate or solve the associated fossil fuel depletion problems, although their recent implantation has raised some doubts. The main problems associated with biofuels are the food vs. fuel controversy; the agricultural and forestry land usage and the actual sustainability of biofuels’ production. Third-generation biofuels, based on the microbiological processing of agricultural, urban and industrial residues, could be a possible solution. However, several technical problems must be solved to make them economically viable and easily affordable for the industry (Robles-Medina et al., 2009).
## 2. First-generation biofuels
The parallel progression in energy demands over depleting oil reserves and rising greenhouse gas emissions entails a high risk of severe impacts on biodiversity, humankind food security and welfare. Thus, a new energy model is needed, based on greener and renewable energy sources, and cleaner as well as more sustainable fuel technology (Fortman et al., 2008; Jegannathan et al., 2009).
### 2.1. Biogas, syngas, vegetable oils blends and Fischer Tropsch liquids
The first response of heavy industry to the current energy and environmental problems includes some old systems, such as syngas and Fischer Tropsch liquids. Current advances in technology and engineering could bring new opportunities to these classical chemistry and biochemistry solutions, associated with fuel shortage situations such as the Arab oil embargo of the 1970s, or the Second World War. Some of these will be detailed below.
#### 2.1.1. Biogas
Biogas is an attractive source of energy primarily because it is renewable and enables the recycling of organic waste. The production of biogas from manure can help to manage the problems associated with this residue, contributing to the reduction of the greenhouse gas methane. Besides, biomethanation is not only useful for energy production, but also for cleaning up solid waste in urban areas. Compared with bioethanol from wheat and biodiesel from rapeseed, biogas production based on energy crops could generate about twice the net energy yield per hectare per year. Furthermore, biogas could be produced from the by-products generated by the current bioethanol and biodiesel industries (Jegannathan et al., 2009).
Biogas production is based on bacterial methanogenesis in the absence of air of organic matter in a water solution. The process occurs in three steps. The first, hydrolysis, is carried out by strict anaerobes such as Bacteroides or Clostridia, and facultative anaerobes such as Streptococci. It involves the enzymatic transformation of insoluble organic material and higher molecular mass compounds such as lipids, polysaccharides, proteins, nucleic acids etc. into soluble organic materials — energy and cell carbon sources such as monosaccharides and amino acids, among others. In the second step, acidogenesis, other types of microorganisms ferment the mentioned products to acetic acid, hydrogen, carbon dioxide and other lower weight simple volatile organic acids, such as propionic and butyric acid, which are converted to acetic acid. Finally, organic acids, hydrogen and carbon dioxide are converted into a mixture of methane and carbon dioxide by the methanogenic bacteria such as Methanosarcina spp. or Methanothrix spp. (consuming acetate), as well as microorganisms such as Methanobacterium sp. and Methanococcus sp., or others that consume hydrogen and formate to yield methane (Jegannathan et al., 2009).
In spite of its attractions, biogas has only been used in rural areas of developing countries and has received investment from governmental and non-profit organizations. The absence of private investment is due to some technical limitations that hamper its economic viability. The process is relatively slow and unstable, and requires large volumes of digester. The decrease in gas generation during the winter season is a serious problem, and can lead to the clogging of the reactor. Other causes for the reduction in gas production are pH and temperature variations, so the loading rate and solid concentration have to be continuously maintained (Jegannathan et al., 2009).
#### 2.1.2. Syngas, biosyngas and Fischer-Tropsch derivatives
Synthetic gas, known as syngas, is a mixture of H2, CO and CO2 in different proportions. Traditionally, syngas was produced through gasification of coal at high temperatures, but it can also be produced by methane reformation (submitting the methane to a high temperature water steam stream, or hydrocracking) or by gasification of biomass. In the latter case, the obtained gas is called biosyngas. Syngas and biosyngas can be used directly as fuel, but they also can serve as precursors for other fuels, such as hydrogen, obtained by the compression of carbon monoxide and dioxide. Also, by Fischer-Tropsch synthesis (FTS), short and long chain hydrocarbons can be obtained from the aforementioned H2, CO and CO2 mixture (Srinivas et al., 2007). Fischer-Tropsch synthesis was discovered in the first half of the twentieth century and developed for large-scale production during the Second World War. It is based on the polymerization, through successive stages, of H2 with CO and CO2, yielding linear hydrocarbons. Iron, cobalt or ruthenium can be used as catalysts (Huber et al., 2006). FTS can be developed at high or low temperature. The high temperature FTS is performed at 330–350ºC yielding mostly short-chain hydrocarbons (gasolines) and light olefins in a fluidized-bed reactor. On the other hand, low temperature FTS develops at 220–250ºC in a slurry bubble column reactor, and waxes and long-chain hydrocarbons are obtained (Bludowsky & Agar, 2009). As FTS is an extremely exothermic reaction, it can be coupled with biomass gasification. However, FTS has some drawbacks, such as the fact that complex mixtures of different chain lengths are always obtained. Thus, FTS products have to be separated prior to subsequent processes (Huber et al., 2006).
#### 2.1.3. Vegetable oil blends
The direct usage of crude or filtered vegetable oils for diesel engine fuel is possible by blending them with conventional diesel fuels in a suitable ratio. These blends are easy to obtain and keep stable for short-term use. But vegetable oils present high viscosity, acid contamination and free fatty acids that lead to gum formation by oxidation, polymerization and carbon deposition (Ranganathan, 2008). Thus, the long-term utilization of vegetable oils for fuel leads to filter clogging, nozzle blockage and deposits in the combustion chamber (Sidibé et al., 2010). Alongside the long-term problems in injection systems, filters and combustion chamber, doubts about the sustainability of using crude vegetable oil for fuels have to be considered. Vegetable oils are expensive, and their direct use in engines or as feedstock to produce petro-diesel substitutes would encounter the same economic and environmental problems that affect the conventional biodiesel and bioethanol industries (UNCTAD, 2010).
A more interesting solution is the usage of waste cooking oil (WCO; also called waste frying oil, WFO). Waste cooking oil is widely produced, inedible, and could serve as a low-cost and almost ready-to-use substitute for fossil origin diesel. As crude vegetable oil, waste cooking oil has a high viscosity. Besides, it is enriched with free fatty acids and, hence, can generate clogging problems in unmodified diesel vehicles, especially in temperate climates and during the ignition of the engine. Viscosity problems are usually bypassed by blending WCO with petrol diesel or by using transesterification to produce biodiesel (Pugazhvadivu et al., 2005; Al-Zuhair et al., 2009; Chen et al., 2009). Al-Zuhair et al. studied the production of biodiesel with lipases from Candida antarctica and Burkholderia cepacia, both free and immobilized in ceramic beads, with or without solvents. They found that clay micro-environments protected immobilized B. cepacia lipase from methanol damage (Al-Zuhair et al., 2009). Also, Pugazhvadivu et al. proposed solving the injection and filter-clogging problems by preheating the waste cooking oil (Pugazhvadivu et al., 2005), by comparing the performance of a diesel engine when using conventional diesel and waste frying oil, preheated at different temperatures, as fuel. They found that preheating the waste frying oil to 135ºC improved the overall yield of the engine. In particular, the brake specific energy consumption and brake thermal efficiency were improved, and the engine exhaust CO and smoke density were reduced considerably compared to WFO preheated at 75ºC. They concluded that WFO could be used as a diesel fuel by preheating it to 135ºC.
### 2.2. Bioethanol and biodiesel
Bioethanol and biodiesel are frequently claimed as the most realistic alternatives to fossil fuels. These renewable fuels can be extensively produced, and both the fossil fuel distribution and engines can be easily adapted to work with blends of ethanol and gasoline, diesel and biodiesel, or even pure ethanol and pure biodiesel (Da Costa et al., 2010). But, in order to play a significant role in fossil fuel substitution, these renewable fuel industries should overcome technical limitations in production process efficiency and feedstock-related issues (UNCTAD, 2010). Decisions about feedstock election, catalysis technology or energy gain along the production process are of paramount importance for proper biodiesel and bioethanol production.
#### 2.2.1. Bioethanol and biodiesel production
Bioethanol is produced from simple sugar-rich raw materials or from starchy feedstock, from which simple sugars can be easily processed and released, which are fermented to produce ethanol. Bioethanol production comprises three steps. Firstly, the complex sugars are hydrolysed to release glucose. Subsequently, the glucose is subjected to a second fermentation step carried out by yeasts such as Saccharomyces cerevisiae; for example, yielding ethanol and carbon dioxide. The third step consists of a thermochemical process and is based on the distillation of the diluted ethanol to obtain highly concentrated ethanol. When using lignocellulosic raw materials such as agricultural residues (corn stover, straw, sugar cane bagasse), forestry waste, wastepaper and other cellulosic residues, a chemical or enzymatic hydrolysis pretreatment to degrade the lignin is needed. This additional step reduces the efficiency of the process. Some improvements have been achieved by the engineering of cellulases from the Trichoderma genus fungi (Fukuda et al., 2006) and the utilization of microorganisms able to simultaneously express the cellulase and enzymes needed for the ethanol fermentation pathway, such as piruvate descarboxilases and alcohol dehydrogenases (Lu et al., 2006; van Zyl et al., 2007; Jegannathan et al., 2009; Rahman et al., 2009; van Dam et al., 2009). However, these improvements have still not generated an efficient and economically affordable process.
With regard to biodiesel, it consists of a mixture of fatty acid alkyl esters (FAAE) obtained by the transesterification of fatty acids and straight chain alcohols (generally ethanol or methanol), mainly from vegetable oils. When methanol is the alcohol of choice, the term used to refer to the biodiesel is fatty acid methyl esters (FAME), while the ethanol-derived biodiesel is known as fatty acid ethyl esters (FAEE). The properties of the biodiesel obtained from ethanol or methanol are very similar, but methanol is the preferred alcohol in spite of its toxicity and fossil fuel origin because of its low cost and wide availability (Ranganathan et al., 2008; Fjerbaek et al., 2009).
The commercially delivered biodiesel is mainly obtained by the chemical transesterification of the triglycerides contained in sunflower, rapeseed or palm oil. This process can be carried out by acid and alkaline liquid catalysts (Kawahara & Ono, 1979; Jeromin et al., 1987; Aksoy et al., 1988; Fukuda et al., 2001), or heterogeneous solid catalysts such as supported metals, basic oxides or zeolites (Cao et al., 2008). The preferred catalysts are the liquid ones, particularly the alkaline ones, because these catalysts are cheap, very versatile and yield less corrosive fuel than the acid catalysts. Also, liquid catalysts are preferred because the reusable solid catalysts are still withdrawn with mass transfer and reactant diffusion problems. However, the alkaline catalysis has several limitations, especially the futile consumption of the catalyst, problems of viscosity, mass transfer and recovery of biodiesel and by-products owing to the saponification of the catalyst and free fatty acids in the presence of water (Freedman et al., 1984; Zhang et al., 2003; Jaruwat et al., 2010). These problems are bypassed by high temperature reaction conditions, addition of organic solvents to manage the water presence or enhance the interface formation, or increase of the alcohol:catalysts ratio (Kawahara & Ono, 1979; Fukuda et al., 2001). Thus, the process requires high energy inputs to maintain high temperatures conducive to viable transesterification rates, and to separate methanol. Besides, the process generates alkaline waste water that requires treatment prior to its disposal (Jaruwat et al., 2010). Jointly, all these negative factors raise doubts about the sustainability and environmental benefits of the biodiesel industry.
#### 2.2.2. Bioethanol and biodiesel advantages and drawbacks
Extensive bioethanol and biodiesel implantation has been followed by a panoply of economic, sociopolitical and environmental issues (Guerrero-Compeán, 2008). It is worth noting the strong dependency of these biofuels industries on crops used for human nourishment and the feeding of livestock (UNCTAD, 2010). Although a large number of patents have been proposed to solve many technical problems, the sudden peak in demand for biofuels has uncovered serious technical limitations of the currently used production systems. As a consequence, a growing controversy about the real sustainability and environmental friendliness of the actual biofuels industry has been generated (Fortman et al., 2008; Abdullah et al., 2009; Demirbaş, 2009; Yee et al., 2009; Jaruwat et al., 2010).
In addition, the consequences of biofuel production for farming practices or food markets, as well as real greenhouse gases (GHG) emission reduction along the biofuel life cycle, represent an important issue that, frequently, is not clearly treated. Parameters such as the kind of biofuel under study, feedstock, and energy inputs needed to maintain the process of transformation need to be taken into account. Also, the possibility of cogeneration of electricity or the exchange of energy between the biofuel synthesis and the feedstock transformation processes must be added to the model. Thus, wide variations in the net energy gain and consumption of resources can occur owing to the different assumptions made to calculate the overall benefits and drawbacks. Timilsina and collaborators draw a general picture of this issue over the OECD estimations. According to these authors, the most efficient biofuel production scheme is represented by sugarcane-based bioethanol in Brazil, with a 90% GHG reduction with respect to the gasoline equivalent. This high efficiency relies mainly on the high yield of this crop and the usage of sugarcane as an energy source for production plants and the cogeneration of electricity. Second-generation biofuels based on cellulosic feedstocks present a 70–90% GHG reduction relative to gasoline or diesel. Combined with electricity cogeneration, this kind of biofuel could have an even greater effect on GHG reduction, but they are still under development. Ethanol from sugar beet GHG reduction ranges from 40 to 60%, while wheat-based ethanol presents a 30–50% GHG reduction. The corn-based production of bioethanol is the least GHG-reducing biofuel and presents a low efficiency at GHG reductions varying from 0 (even negative in some cases) to 50% compared to gasoline (OECD, 2008; Timilsina & Shrestha, 2010).
## 3. Second-generation biofuels
Theoretically, biofuel implantation in transport and industry should solve, or at least improve, the ecological and economic problems derived from the unsustainability of the fossil fuel-based energy model.
However, recent field experiences indicate a much more complex scenario. The market economy and unbalanced relations between different sectors of the economy and national markets generate unpredictable dynamics of fuels’ raw material prices. In this context, the development of subsequent new commercial and industrial opportunities has altered the already unstable behaviour of the agricultural international markets. The sudden peak in demand for grain, owing to its usage as a raw material for the production of ethanol, has abruptly increased the prices of corn (Fischer et al., 2009). The demand pressure has operated similarly in the palm oil market, generating a palm oil tree and soy culture surface expansion in several regions, with spectacular dimensions in South-East Asia (Abdullah et al., 2009; Jaruwat et al., 2010), where the biofuels fever threatens biodiversity and has a deep social impact because of the proliferation of unregulated, intensive, agricultural practices and the switching of oil usage for traditional human nutrition, housekeeping and livestock feed (Fortman et al., 2008; Guerrero-Compeán, 2008; Demirbaş, 2009; UNCTAD, 2010; Yee et al., 2009).
### 3.1. Feedstock costs and biofuel competition
Biodiesel usually costs over 0.5 US$/l, compared to 0.35 US$/l for petroleum-based diesel (Demirbaş et al., 2009). It is reported that the high cost of biodiesel is mainly due to the cost of virgin vegetable oil (Krawczyk, 1996; Connemann & Fischer, 1998). For example, the soybean oil price is currently 1.27 $/l while the palm oil price is 1.18$/l (World-Bank, 2011). Biodiesel from animal fat is currently the cheapest option (0.4–0.5 US$/l), while the traditional transesterification of vegetable oil is, at present, around 0.6–0.8 US$/l (Bender, 1999). Zhang et al. (2007) stated that there is no global market for ethanol. Within the reasons for this, crop types, agricultural practices, land labour costs, production plant sizes, processing technologies and government policies can be cited. The cost of ethanol production in a dry mill plant currently totals 0.44 US$/l. Corn represents 66% of operating costs while energy (electricity and natural gas) to fuel the production plant represents nearly 20% of operating costs. Nevertheless, ethanol from sugar cane, produced mainly in developing countries with warm climates, is generally much cheaper to produce than ethanol from grain or sugar beet (Bender, 1999). For this reason, in countries like Brazil and India, sugar cane-based ethanol is becoming an increasingly cost-effective alternative to petroleum fuels. On the other hand, ethanol derived from cellulosic feedstock using enzymatic hydrolysis requires much greater processing than from starch or sugar-based feedstock, but feedstock costs for grasses and trees are generally lower than for grain and sugar crops. If targeted reductions in conversion costs are achieved, the total cost of producing cellulosic ethanol in EOCD countries could fall below that of grain ethanol. Estimates show that ethanol in the EU becomes competitive when the oil price reaches 70 US$/barrel, while in the USA it becomes competitive at 50–60 US$/barrel. For Brazil and other efficient sugar producing countries such as Pakistan, Swaziland and Zimbabwe, the competitive ethanol price is much cheaper, between 25–30 US$/barrel. However, anhidrous ethanol, blendable with gasoline, is still more expensive, although prices in India have declined and are approaching the price of gasoline. Although the feedstock costs represent the majority of biofuels’ cost, the production plant size can reduce the final cost of the fuel. Thus, the generally larger USA conversion plants produce biofuels, particularly ethanol, at lower cost than plants in Europe. Production costs are much lower in countries with a warm climate such as Brazil, with less than half the costs of Europe. But, in spite of the reduced costs of production, ethanol from Brazil is competitive with gasoline owing to the huge sugar cane production and the cogeneration of electricity (Demirbaş et al., 2009).
### 3.2. Brazilian and USA models of implementation for the bioethanol industry
Since the Arab oil embargo of the 1970s, Brazil has made an incomparable effort in the reduction of its energy dependency by intensifying and extending sugar cane-based bioethanol production. Although the alternative periods of scarcity and abundance of oil have marked fluctuations in the strength of the Brazilian Alcohol National Programme (Proalcool), the global trend has been an ascending progression in the total production of alcohol, as well as in the yield per hectare of sugar cane, and the implantation of this alcohol as transportation fuel. Today, Brazil is the second largest worldwide ethanol producer. In this way, Brazil has reduced its energy dependency, and has become the first ethanol exporter. According to Brazilian Government data, this milestone has been achieved on the basis of rural employment and welfare improvement. The key aspects of the Proalcool programme are a combination of technological advances, social planification and projection of the bioethanol industry. According to the Brazilian Government (Da Costa et al., 2010), owing to the high productivity of sugar cane, Brazil has expanded ethanol production and use without a significant increment in the fertile land surface used to cultivate sugar cane, or a food vs. fuel competition. However, there are several authors who are not so enthusiastic with the success of the Brazilian model, and point to the sugar cane industry as one of the reasons for the losses in biodiversity and the expansion of agricultural land over doubtfully catalogued marginal land, which is more relevant and dangerous than the Brazilian Government data indicates (Coelho et al., 2008; Gauder et al., 2011).
On the other hand, the American bioethanol industry choice of corn grain as its raw material has been followed by a dramatic rise in the prices of corn derivatives. Although the USA production of bioethanol supersedes the Brazilian one, the production:consumption ratio of the former (1:3) is much smaller than the latter (8:3). Despite its commercial orientation, the global efficiency of the USA model is low compared with the Brazil system and relies on the high importation taxes that protect the American industry from foreign ethanol inputs (Da Costa et al., 2010). Finally, the narrow margin of the USA production:consumption ratio suggests that the model has reached a production glass ceiling that blockades the medium-term implantation of biofuels in American society and hampers their exportation (UNCTAD, 2010; Da Costa et al., 2010).
### 3.3. Europe and Asia: Chemically catalyzed biodiesel
The European and Asian strategy to improve climate change and fossil fuel depletion problems is based mainly on the chemically catalyzed biodiesel obtained from vegetable oils. There is a variety of feedstocks for the production of this biofuel, from inedible oils, (mainly rapeseed oil in Europe or jatropha oil in Asia), to edible oils (principally sunflower oil in Europe and palm oil or soybean oil in Asia, although corn, peanut, cotton seed or canola oil can also be cited) (Ranganathan et al., 2008; Abdullah et al., 2009). As the elected method for industrial biodiesel production is chemical catalysis, these vegetable oils are preferred to other heterogeneous lipids sources. These other lipids need pretreatment prior to their use (Peterson, 1986; Fortman et al., 2008), and include waste frying oils, waste-activated bleaching earth from the oil refinery industry, and even animal origin lipids such as beef tallow, lard, yellow grease and poultry grease or fat from fat traps, septic tanks, or waste water sludges. The need for economically viable vegetable oils for biodiesel production implies the cultivation of greater areas with oil-producing crops such as sunflowers or palm oil trees. Thus, the previously mentioned rising corn prices, owing to the derivation of huge amounts of grain for the industrial production of bioethanol, is neither an isolated case in developing biofuel industries nor the only aspect of the biofuel industry issue. Like the bioethanol industry, the European and Asian biodiesel industries have the energy and chemical problems associated with the current biofuels model. These limitations can be summarized according to nearly obsolete technology, being strongly dependent on chemical catalysis, non-renewable materials and promotion of non-sustainable market and farming practices (Guerrero-Compeán, 2008; Demirbaş, 2009; UNCTAD, 2010).
### 3.4. Technical aspects of biodiesel production
The industrial production of biodiesel needs to solve several technical problems in order to obtain this kind of biofuel in an efficient and sustainable way. The physical factors to consider can be summarized by pH, temperature, hydric activity, solvents and supports. Depending on the catalyst used to drive the transesterification reaction, some of the cited factors have different impacts on the global efficiency and feasibility of the process. A non-optimal configuration of the system can reduce significantly the biodiesel yield and compromise the viability of the production plant, especially if the upstream by-products, excess catalyst or auxiliary devices for solvent recovery hinder an easy, clean and rapid downstream processing of the biofuel.
#### 3.4.1. pH, temperature and hydric activity
As mentioned above, the chemical catalysis of the transesterification reaction requires high temperatures to achieve an acceptable reaction rate. In the case of the alkaline catalysis, the minimal temperature to produce conventional biodiesel is 60ºC, while in the acid catalysis the temperature ranges from 50 to 80ºC (Robles-Medina et al., 2009). Acid catalysis is slower than the alkaline one and generates a more corrosive fuel, so alkaline catalysts are preferred by the industry. It incurs a great energy cost in order to initiate and maintain the reaction (Kawahara & Ono, 1979; Aksoy et al., 1988; Cao et al., 2008). However, the utilization of sodium hydroxide as a catalyst has a serious limitation in the form of saponification of free fatty acids if water is present. This drives the increased consumption of the catalyst and downstream processing problems, such as the separation of glycerol and unreacted precursors. The solutions to manage this problem include using only virgin oils, often edible vegetable oils, instead of oils with high free fatty acids and water content, such as waste cooking oils or animal origin fats, as well as other residual fats. Higher temperatures, up to 120ºC, and the addition of organic solvents, or additional steps for free fatty acids esterification with sulphuric acid before performing the alkali-catalyzed transesterification are quite common as well (Jeromin et al., 1987).
When lipases are used as catalysts, it is possible to get over the saponification problems owing to their ability to transesterificate alcohols with both triacylglycerols and free fatty acids. Besides, lipases work as well in the presence of water. In fact, they need a certain hydric activity to maintain their tridimensional structure, so the presence of water is not a problem with this kind of catalyst — although excessive hydric activity affects the transesterification reaction because the substrates are water insoluble (Jaeger & Eggert, 2002; Shah et al., 2004; Gilham & Lehner, 2005; Fjerbaek et al., 2009). Lipases can operate at low or relatively low temperatures in the range of 20 to 70ºC, and at even lower temperatures if the enzyme has been obtained from psycrophilic microorganisms (Dabkowska & Szewczyk, 2009). Depending on the chosen lipase and preparation (free, immobilized or whole cell catalyst), lower temperatures (below 65ºC) can be applied to avoid the thermal denaturation of the enzyme, thus saving in production costs (Fukuda et al., 2008). Within the thermostable lipases, we can cite Burkholderia cepacia lipase (Amano PS lipase, from Amano Pharmaceutical Co., Japan), that reaches its highest activity at 60ºC (Dabkowska & Szewczyk, 2009), and the lipases obtained from Thermoanaerobacter thermohydrosulfuricus SOL1 and Caldanaerobacter subterraneous subsp. tengcongensis, which show their activity maximum at 75ºC and tolerate temperatures as high as 95ºC (Royter et al., 2009).
On the other side of the spectrum, the lipase from Bacillus sphaericus MTCC 7526 presents its optimal temperature at 15ºC, keeping stable until 30ºC, and the Microbacterium phyllosphaerae lipase presents the optimal temperature at 20ºC and deactivates when the temperature exceeds 35ºC, with the pH value fixed at 8 for both psycrophilic enzymes (Joseph et al., 2006; Srinivas et al., 2009). Therefore, pH plays an important role in the enzymatic production of biodiesel because it influences both the reaction rate and the thermal stability or solvents’ susceptibility of the lipases. An adequate pH can facilitate the optimization of the operation temperature and improve the activity of the enzyme. Gutarra and collaborators reported a high stability of the Penicillium simplicissimum lipase in the pH range 4.0–6.0, that showed the maximal activity at 50ºC and remained stable and active (although with a lower activity) even at 70ºC (Gutarra et al., 2009).
#### 3.4.2. Heterogeneous catalysts and immobilized enzymes
An alternative to the chemical transesterification of low quality oils with a relatively high concentration of water or free fatty acids consists of heterogeneous catalysis using acidic cation-exchange resins, supported metals (Zabeti et al., 2009), basic oxides or zeolites (Knezevic et al., 1998; Suppes et al., 2004). Even low cost alternatives such as waste eggshell have been proposed as well (Wei et al., 2009). These kind of catalysts are considered as an intermediate and relatively low-cost solution between the traditional homogeneous catalysts and the lipases. However, the cited heterogeneous catalysts are affected by the slow diffusion of the triglycerydes through their pores and require a higher alcohol:oil ratio to accelerate the reaction, in order to increase the production (Zabeti et al., 2009). Nevertheless, the heterogeneous catalysts can serve to improve the reusability and efficiency of immobilized enzymes and whole cell catalysts. Immobilization of enzymes on inert materials such as porous ceramic beads (Iso et al., 2001) or polymeric resins (Dizge et al., 2008; Dizge et al., 2009) can improve their performance. This improvement is owing to the protection that the pores’ microenvironment brings to the enzyme, avoiding the inhibition or damage of the enzyme caused by methanol or solvents. Another attractive approach to the immobilization is the so-called protein-coated microcrystals technology (PCMC). PCMC is based on the use of crystalized proteins as a support to the lipases, or in the direct use of crystalized lipases as solid catalysts (Raita et al., 2010). However, the real increase in reaction rate and enzyme stability with these immobilization techniques is usually lower than the theoretically expected. One of the reasons for these lower rate issues responds to the blockage of the pores of the used material as support because of the precipitation of glycerol or the insufficient circulation of substrates around the enzyme (Zabeti et al., 2009). The knowledge generated by the intense research on production and use of supports, resins and porous metallic alloys can be useful for enzymatic production of biodiesel. With this comparative approach, the optimization of the immobilized enzyme technology could be a reality in the short rather than medium term.
#### 3.4.3. Alcohol to oil ratio and solvents
Depending on the kind of catalyst used and the selected operation conditions in the biodiesel production plant, the alcohol to oil molar ratio will present a wide variation. Adding excess alcohol is a common practice, and could serve as reference. However, excess alcohol use implies higher reactant associated costs, especially when the alcohol of choice is ethanol, which is more expensive than methanol. Thus, a more detailed approach to the system optimization in terms of minimal alcohol consumption is needed. Besides, a fine adjustment of the alcohol to oil ratio allows the maximal biodiesel production in the shortest possible time span and with the lowest energy input (Shieh et al., 2003).
The optimization is a relatively simple task when homogeneous catalysts such as sulphuric acid or sodium hydroxide are used to perform the conventional transesterification of vegetable oils with methanol. High yields are achieved with a methanol to oil ratio of 1:1 with an alkaline catalyst (although to improve the yield this proportion rises to 6:1) and a 30:1 ratio when an acid catalyst is used (Zhang et al., 2003).
However, in the case of lipase-catalyzed biodiesel, the situation is more complex and the molar ratio of alcohol to oil varies depending on the type of lipase, the use of an immobilized or free enzyme, and the alcohol used. Similar to the chemical catalysts, an increase of the molar alcohol:oil ratio elevates the efficiency of the reaction, but an excessive alcohol content inhibits and even damages the enzyme, especially when using methanol and free enzymes. Although the lipase-based solvent-free systems are under intensive research, owing to advantages such as the direct saving in solvents and the indirect cost reductions in downstream processes, the utilization of lipases does not necessary mean abandoning the use of a certain amount of solvents. The addition of solvents like t-butanol, diesel oil, hexane or dioxane to the precursors of biodiesel usually allows a better mixing of the reactants. Thus, solvents relieve the problems associated with the different water solubility of lipids and alcohols. In addition, solvents provide a more durable interaction between the enzyme and its substrates, and can favour the circulation of reactants through resins and support pores in immobilized enzyme systems. This improved circulation confers some protection to the lipases against inhibition by substrates and damages by excessive alcohols. However, solvents’ addition has to be carefully studied, since an excess of solvent or an inadequate amount of solvent can affect the enzyme activity and stability. For example, Shieh et al. studied the optimal operation conditions to transesterificate soybean oil with methanol by Rhizomucor miehei lipase immobilized on macroporous weak anionic resin beads. They found that the best transesterification rate was obtained when the methanol:oil molar proportion was 3.4:1 at 36.5ºC (Shieh et al., 2003). Raita et al. studied the transesterification of palm oil with ethanol by Thermomyces lanuginosa lipase-coated microcrystals in the presence of t-butanol. In this case, the optimal conditions were ethanol to fatty acids 4:1 molar ratio and t-butanol:tryacylclycerides 1:1 molar ratio, at 45ºC (Raita et al., 2010. However, Tongboriboon et al. worked on the solvent-free transesterification of used palm oil with Thermomyces lanuginosa and Candida antarctica lipases immobilized in porous polypropylene powder, reporting that the best yield was achieved at an ethanol to oil ratio of 3:1, and the yield decreased when the molar ratio was increased to 4:1 at 45ºC (Tongboriboon et al., 2010). These authors pointed to the inhibition of the enzymes by an excessive amount of ethanol, although it is worth emphasizing that they worked on a solvent-free system, so the enzyme was relatively vulnerable to alcohol-driven damage. On the other hand, Shah et al used 4:1 ethanol to oil molar ratio as standard reaction settings in their study about the transesterification of jatropha oil with ethanol at 40ºC. The experimental design consisted of a solvent-free system and three different lipases (free and immobilized on Celite), namely Chromobacterium viscosum, Candida rugosa and Porcine pancreas lipases, although they did not try different alcohol to oil molar ratios (Shah et al., 2004).
## 4. Third-generation biofuels
As a response to the problems associated with the recent worldwide implantation of second-generation biofuels, some authors propose focusing on the processes involved in the production of such biofuels. This new approach consists of the utilization of microbial enzymes to achieve the current chemical pretreatment steps of cellulosic or starchy raw materials (Carere et al., 2008). Microorganisms deal with the degradation of lignocellulose, hemicellulose or lipid-rich materials by means of enzyme catalyzed processes at near to room temperature. Therefore, microbial enzymes could be used to make the current biofuels industry cleaner and greener. Furthermore, the production of biofuels would be coupled with the management of woody and oily wastes, converting these residues into suitable and cheap raw materials (Steen et al., 2010).
### 4.1. Microalgae-based biodiesel production
Another promising lipids source, still not implemented but currently being studied worldwide, is represented by microalgae. Microalgae have a high potential as biodiesel precursors because many of them are very rich in oils, sometimes with oil contents over 80% of their dry weight, although not all species are suitable as biodiesel production oils (Chisti, 2008; Manzanera, 2011). Besides, these microorganisms are able to double their biomass in less than 24 hours, achieving a reduction between 49 and 132 fold in the medium culture time required by a rapeseed or soybean field. Furthermore, microalgae cultures require low maintenance and can grow in wastewaters, non-potable water or water unsuitable for agriculture, as well as in seawater (Mata et al., 2010). The production of microalgae biodiesel could be combined with the CO2 removal from power generation facilities (Benemann, 1997), the treatment of waste water from which microalgae would remove NH4+, NO3- and PO43- (Aslan & Kapdan, 2006), or the synthesis of several valuable products, from bioethanol or biohydrogen to organic chemicals and food supplements (Banerjee et al., 2002; Chisti, 2007; Rupprecht, 2009; Harun et al., 2010). However, microalgae biomass-based biofuels have several problems ranging from the optimization of high density and large surface units of production to the location of the microalgae production unit. Anyway, the main decisions to take are the adoption of open or closed systems, and the election of batch or continuous operation mode. As will be discussed below, depending on the system and mode of operation choice, there will be different advantages and drawbacks.
#### 4.1.1. Open vs. closed systems
Microalgae can be cultivated in open-culture systems such as lakes or (raceway) ponds, and in closed-culture systems called photobioreactors (PBRs). Open-culture systems are normally cheaper to build and operate, more durable and have a higher production capacity than PBRs. However, open systems are more energy expensive in terms of nutrient distribution owing to mass transfer problems, and have their depth limited to 15 cm, to ensure that the microalgae receive enough light to grow. Moreover, ponds are more sensitive to weather changes, and temperature, evaporation and light intensity controls are not feasible. Furthermore, these open systems require more land area than PBRs, and are more susceptible to contamination, both from bacteria and from microalgae present in the surroundings of culture installations (Manzanera, 2011).
In contrast, PBRs are more flexible and are intensive land-usage systems that can be configured according to the specific physical-chemical requirements of the algae of choice, allowing the cultivation of species unsuited to open ponds. Nutrient homogenization, light distribution, pH, temperature, CO2 and O2 control can be achieved in photobioreactors. Thus, closed systems provide more stable and appropriate growing conditions, allowing higher cell densities and minimizing contamination. Nevertheless, PBRs have several technical problems that make them non-competitive in applications that can be achieved in raceway ponds. Such problems are overheating, bio-fouling, shearing stress, oxygen accumulation, scaling-up difficulties and the high costs of building, operation and maintenance (Chen et al., 2011).
Within these problems, it is worth highlighting capital building investment and high operation costs. PBRs biomass production costs may be one order of magnitude higher than in open systems. If the biomass added value is high, PBRs can be competitive. Otherwise, open ponds will be the preferred option. However, the evaluation of performance of open and closed systems is complex and depends on several factors, such as algal species or productivity computation method. Three parameters are commonly used to evaluate productivity in microalgae cultivation installations. Firstly, volumetric productivity (VP), that is, productivity per unit of reactor volume (g/l d). The second parameter is area productivity (AP), defined as productivity per unit of ground area occupied by the reactor (g/m2 d). The third one is illuminated surface productivity (ISP), namely the productivity per unit of reactor illuminated surface area (g/m2 d). Nevertheless, the election of closed or open systems relies on more aspects apart from productivity, as will be discussed below (Richmond, 2010).
#### 4.1.2. Continuous vs. batch operation mode
PBRs can be operated in batch or continuous mode. There are several advantages when using them in continuous mode. Firstly, continuous culture provides a higher control than batch mode. Secondly, growth rates can be regulated and keep in a steady state for long periods, and the biomass concentration can be modulated by dilution rate control. In addition, results are more reliable and reproducible owing to the steady state of continuous reactors, and the system yields better quality production (Molina et al., 2001).
However, there are limitations that can make the continuous process unsuitable for some cases. One of these limitations is the difficulty in controlling the production of some non-growth-related products. For instance, the system often requires feed-batch culturing and continuous nutrient supply that can lead to wash-out. Filamentous organisms can be difficult to grow in continuous PBRs because of the viscosity and heterogeneity of the culture medium. Another problem is that the original strain can be lost if it is displaced by a faster-growing contaminant. The contamination risk and loss of reliability of the bioreactor becomes more relevant when long incubation periods are needed, so the potential initial investment in necessary better quality equipment could rise and hamper the economic viability of the production unit (Mata et al., 2010).
The possible coproduction of high value chemicals could lead to the solution of the above problems, but it implies taking multiple parameters and options into consideration. The microalgae production units will suffer drastic changes, both in the operational aspect (temperature, insolation, wind, microalgal and bacterial or fungical contaminations etc.) and in the commercial one (oscillations in value of by-products, improvements in centrifugation or extraction strategies or development of non-algal biofuels, etc). Taking into consideration all the above mentioned parameters, it can be ascertained that any microalgae-based biodiesel project is unique. Hence, such projects must be designed by thinking in terms of a flexible or even multipurpose and adaptable installation (Richmond, 2010).
### 4.2. Biodiesel production from oily biomass
Microalgae are not the only option to produce biofuels from oily biomass. Multiple prokaryotes and eukaryotes can accumulate high amounts of lipids. But, as occurred with microalgae, not all species are suitable for biodiesel production owing to differences in the kind of storage lipids. Thus, as stated by Waltermann & Steinbüchel (2010), many prokaryotes synthesize polymeric compounds such as poly(3-hydroxybutyrate) (PHB) or other polyhydroxyalkanoates (PHAs), whereas only a few genera show accumulation of triacylglycerols (TAGs) and wax esters (WEs) in the form of intracellular lipid bodies. On the other hand, storage TAGs are often found in eukaryotes, while PHAs are absent, and WE accumulation has only been reported in jojoba (Simmondsia chinensis). All these lipids are energy and carbon storage compounds that ensure the metabolism viability during starvation periods. Similar to the formation of PHAs, TAGs and WE, synthesis is promoted by cellular stress and during imbalanced growth; for instance, by nitrogen scarcity alongside the abundance of a carbon source (Kalscheuer et al., 2004).
The most interesting prokaryote genera in terms of accumulation of TAGs are nocardioforms such as Mycobacterium sp., Nocardia sp., Rhodococcus sp., Micromonospora sp., Dietzia sp., and Gordonia sp, alongside streptomycetes, which accumulate TAGs in the cells and the mycelia. TAGs storage is also frequently shown by members of the gram-negative genus Acinetobacter (although, in this case, WE are the dominant inclusion bodies components) (Waltermann & Steinbüchel, 2010). Within eukaryotes, with the exception of algae, yeasts of the genera Candida (non albicans) (Amaretti et al., 2010), Saccharomyces (Kalscheuer et al., 2004; Waltermann & Steinbüchel, 2010) and Rhodotorula (Cheirsilp et al., 2011) are the most interesting ones to produce biodiesel feedstocks.
Steinbüchel and collaborators have worked on the heterologous expression of the non specific acyl transferase WS/DGAT from Acinetobacter calcoaceticus ADP1 in Saccharomyces cerevisiae H1246 (a mutant strain unable of accumulating TAGs) (Kalscheuer et al., 2004). These authors found that the yeast recovered the ability to accumulate TAGs, as well as fatty acid ethyl esters and fatty isoamyl esters. This finding showed that the Acinetobacter calcoaceticus transferase had a high potential for biotechnological production of a large variety of lipids, either in prokaryotic and eukaryotic hosts. From this basis, as will be discussed in detail in Section 4.3, they worked on Escherichia coli TOP 10 (Invitrogen) and obtained an engineered strain able to produce fatty acid ethyl esters (biodiesel) directly from oleic acid and glucose (Kalscheuer et al., 2006).
Another possibility is combining the biomass obtained from microalgae and yeast, as recently proposed by Cheirsilp et al. (2011). These authors studied a mixed culture of oleaginous yeast Rhodotorula glutinis and microalga Chlorella vulgaris in industrial wastes. The used effluents, including both a seafood processing wastewater and molasses from a sugar cane plant. They found a synergistic effect in the mixed culture. R. glutinis grew faster and accumulated more lipids in the presence of C. vulgaris, that acted as an oxygen generator for yeast, while the microalgae obtained surplus CO2 from yeast. The optimal conditions for lipid production were 1:1 microalga to yeast ratio initial pH of 5.0, molasses concentration at 1%, 200 rpm shaking, and light intensity at 5.0 klux under 16:8 hours light and dark cycles (Cheirsilp et al., 2011).
### 4.3. Whole cell catalysts
Pure or immobilized enzymes obtained from microorganisms could reduce the energy costs of industrial ethanol and biodiesel production. Nevertheless, the cellulases used to treat (ligno)cellulosic materials such as forestry residues, waste paper or straw are difficult to purify, like the lipases used for the transesterification of lipids yielding biodiesel. Hence, their price is still too high to make their usage economically viable (Shieh et al., 2003; Ranganathan et al., 2008). Another limiting factor for the use of enzymes is the inactivation and inhibition by reactants and substrates. These drawbacks are the object of an intensive effort to make possible the reutilization of enzymes through protein engineering (Ebrahimpour et al., 2008), in order to increase their stability and activity. Research interest is also targeted on immobilization in different supports or the usage of genetically engineered microorganisms, called whole cell catalysts, which carry the necessary enzymes, avoiding their exposure to inhibiting substrates and operating as microrefineries (Kalscheuer et al., 2006). In the case of biodiesel microbiological production that will be revealed in detail below, the authors proposing and developing this technology refer to this third-generation biofuel as ‘Microdiesel’. The microbial production of biodiesel requires the construction of genetically modified microorganisms, able to transesterificate ethanol with lipids and, if possible, able to produce it by themselves to optimize the whole process. Since their 2006 work on microdiesel production on the laboratory scale using an engineered Escherichia coli strain, Steinbüchel and collaborators have established the guidelines of microdiesel industry development. Their approach consisted of expressing heterologously in E. coli the genes from Zymomonas mobilis, encoding for piruvate decarboxylase (pdc) and alcohol dehydrogenase (adhB), as well as the Acinetobacter baylyi non specific acyl transferase ADP1 (atfA). The obtained strain was able to carry out the aerobic ethanol fermentation from sugars, as well as the enzymatic transesterification of this alcohol with the fatty acids derived from the lipidic metabolism, yielding FAEE, referred to as ‘microdiesel’ by the authors (Kalscheuer et al., 2006). Recently, Elbahloul and Steinbüchel have used the aforementioned microdiesel producing E. coli at a pilot plant scale, using glycerol and sodium oleate as carbon and fatty acids sources respectively, with promising results (Elbahloul & Steinbüchel, 2010). Nevertheless, their conclusions for both studies indicate that there is still a long way to go to the industrial application of their findings, and that the technique needs to be modified to make the engineered strains adaptable to different lipids rich sources and to lignocellulosic raw materials. These modifications would allow the usage of forestry and agricultural wastes, making the biodiesel production process at least as versatile as chemical transesterification.
### 4.4. Microdiesel production from residues
Vegetable oils are expensive and require large areas of farmland for their production, so the direct usage of these oils for biodiesel production is expensive and unsustainable. However, there are multiple and as yet unexploited alternative fatty acid sources. Similarly, bioethanol production for its direct use as a biofuel or as a biodiesel precursor requires huge amounts of corn grain or sugar cane. Nevertheless, industrial residues such as the vegetable oil refinery waste, as well as farming, forestry, livestock and domestic solid and liquid waste (Chen et al., 2009; Dizge et al., 2009) are widespread and huge sources of lipids and carbon. Wang et al. proposed the soybean oil deodorizer distillate (SODD), a by-product from the soybean oil refineries that represents 0.3–0.5% of the soybean oil processed, to produce biodiesel. With 45–55% of triglycerides and 25–35% of free fatty acids, these authors estimated that around 80% of the SODD can be transformed into biodiesel in a transesterification with methanol by the Thermomyces lanuginosa and Candida antarctica lipases in the presence of tertbutanol and 3Å molecular sieve (Wang et al., 2006). Park et al. used waste-activated bleaching earth (ABE), a residue of the rapeseed or palm oil refinery industry that stores 35–40% of oil and can be used to synthesize multiple bulk chemicals, including biodiesel. As in the Wang example, these authors chose methanol as alcohol, but their solvent choice was fuel oil and kerosene, the catalyst was Candida cylindracea lipase and the obtained FAME was extracted with a filter press (Park et al., 2008). Al-Zuhair and colleagues studied the production of biodiesel from simulated waste cooking oil (SWCO) with free- and immobilized- on ceramic beads Candida antarctica and Burkholderia cepacia lipases, with or without organic solvent. They obtained the best yield when they used B. cepacia without organic solvent, and observed that the system worked better when the enzymes were immobilized, probably because the clay structural microenvironments offered the lipases protection against the methanol derived denaturation (Al-Zuhair et al., 2009). Recently, Steen et al., among others, have proposed the direct fermentation of cellulosic biomass to produce biodiesel, fatty alcohols, waxes and other valuable chemicals (Steen et al., 2010). Their approach combines the waste management and the guidelines defined by Steinbüchel et al. with the new trends in synthetic biology and consolidated bioprocesses. This multidisciplinary approach brings a new flexible, easy-to-modify toolbox, composed of genetically modified FAEE synthetic strains, harbouring the enzymatic apparatus needed to produce ethanol from raw (hemi)cellulosic materials, to transesterificate it with fatty acids, or to synthesize both the fatty acids and the ethanol directly from the cellulose (Steen et al., 2010).
### 4.5. Wastewater sludges-based microdiesel
The microdiesel concept initiated by Steinbüchel et al. can be combined with the management and reutilization of waste waters by the application of microbial lipases to transesterificate the lipids present in the dairy industry or urban wastewater sludges. The lipidic fraction of sludges from urban wastewater treatment represents between 17 and 30% of the dry weight. This lipidic fraction is formed by direct absorption of fats present in the water by the sludge particles and by the phospholipids released from the cell membranes of micro-organisms, as well as from metabolites and cell lysis by-products (Boocock et al., 1992; Shen & Zhang, 2003; Jardé et al., 2005).
Lipid-rich wastewaters require pretreatment in order to reduce the amount of lipids and ease the subsequent conventional treatment. The pretreatment is usually based on physical processes, the most common of which are fat traps, tilted plate separators (TPS), and dissolved air flotation (DAF) units. In addition, centrifuges and electroflotation systems are used occasionally (Willey, 2001). Fat traps are rectangular or circular vessels through which the wastewater passes under laminar-flow conditions, at a rate that allows the lipids to rise to the surface near to the outlet end of the trap. The separation principle is based on Stoke's law, relating rising velocity of a particle to its diameter, so the theoretical separation efficiency is dependent on depth. In practice, fat traps have a depth of 1.5 m, although if the accumulation of a bottom sludge is expected, then an additional 0.5 m would be added to the total liquid depth. Gravity flow is preferred to pumping when feeding the trap, in order to minimize the wastewater emulsification. Fat traps are used in the food industry and in restaurants (Willey, 2001).
Meanwhile, tilted plate separators were developed in the petrochemical industry and are based on the fact that surface area, rather than depth, determines the oil separation. The introduction of tilted plates into a vessel provides many parallel gravity separators with a high surface to volume ratio in a shallow tank. Typically, TPS can occupy less than 10% of the area needed to install a conventional fat trap, although they have some disadvantages. They are susceptible to fouling if solid or semi-solid fat is present in the effluent and a crane is required to remove the plate pack for cleaning. Besides, the pumping systems have to be carefully selected and controlled to avoid surging and liquid depth fluctuations (Zeevalkink & Brunsmann, 1983; Willey, 2001). Finally, dissolved air flotation units are based on the flotation of lipids by means of microbubble clouds (60-70 μm bubble diameter) created by the injection into water of 6 bar pressure air through nozzles. Microbubbles attach to the surface of the fat and oil particles, increasing their rise rate. These systems are used both in the food industry (Willey, 2001) and in the mining wastewater treatment (Tessele, 1998). Once the pre-treatment has finished, wastewater can receive further treatment prior to its disposal or biological treatment. Thus, chemical treatment may be used to reduce the total fatty matter in wastewater. Such treatment uses aluminium sulphate, ferric chloride, or more usually, lime, to break the emulsion and coagulate the fat particles. Subsequently, the fats can be separated by flotation or sedimentation. The rate of sedimentation can be improved by a second-stage flocculation, involving the addition of low levels of polyelectrolyte (0.5-5.0 mg/l) to the wastewater once coagulation has taken place (Willey, 2001).
The use of sludges to produce biofuels is not a new idea itself, but the available literature focuses mainly on the methane production by anaerobic fermentation, currently applied in the majority of waste water treatment plants (WWTP) to provide energy to these installations, or for fermentative biohydrogen production, which is still not industrially available (van Groenestijn et al., 2002; Wang et al., 2003). Several groups have studied the in situ transesterification of WWTP sludges, but have focused on the chemical catalysis of the transesterification with methanol (Haas & Foglia, 2003; Mondala et al., 2009). However this method still presents the same limiting factors that affect the chemical transesterification of edible vegetable oils (Freedman et al., 1984). In spite of their chemical approach, these works provide useful information about several aspects of the biodiesel production process, especially at the first stages of the process. Thus, one common problem of chemical and enzymatic biodiesel production is the need for the pretreatment of the feedstock to make its lipids easily available to the catalyst. In the case of wastewater treatment sludge, this pretreatment step usually implies the use of organic or non-polar solvents to release the lipids from the organic matter (Antczak et al., 2009; Siddiquee & Rohani, 2011).
The most extended protocols rely on chloroform:methanol mixtures, as used in the Folch's method (Folch, 1957), in which a 2:1 chloroform:methanol reactant is mixed with the sample, where water acts as ternary component to form an emulsion. After equilibration with a fourth volume in saline solution, the emulsion separates in two phases: the lower one containing chloroform:methanol:water in the proportions 86:14:1 alongside the lipids; and the upper one containing the same solvents in proportions 3:48:47 and carrying the non-lipidic components of the sample. Bligh and Dyer's method is a simplified variant of the former, but requires the re-extraction of the sample residue with chloroform (Bligh & Dyer, 1959). Nevertheless, there are some methods with near to Folch's reagent yielding which use less toxic reagents, such as pure hexane or different combinations of hexane and other solvents, such as the hexane-isopropanol (3:2) blend proposed by Hara and Radin (Hara & Radin, 1978), or the ethyl acetate-ethanol (2:1) mixture used by Lin et al. (Lin et al., 2004). For a detailed revision of the solvents based extraction protocols, see Kuksis, 1994; Murphy, 1994; Kates, 1996.
In spite of being slightly less toxic than chloroform, the cited solvents are hazardous and present enough management risks to consider other extraction strategies. Several authors propose solvent-free methods based on ionic liquids (Ha et al., 2007), boiling the sludge or subjecting it to supercritical gases, mainly t-butanol (Wang et al., 2006; Royon et al., 2007), propane (Rosa et al., 2008), syngas (Tirado-Acevedo et al., 2010) and CO2 (Helwani et al., 2009), or even to extreme pressures and temperatures (cracking) (Saka & Kusdiana, 2001). All of them are costly and not feasible with the current technology (Siddiquee et al., 2011). A more realistic and ready-to-use option is extraction using hot ethanol, which can be used to perform the lipids’ extraction without using coadyuvant solvents. This approach to extraction can be illustrated with the works developed by Holser and Akin (2008) or Nielsen and Shukla (2004), among others. Although these authors have focused on the ethanol-based extraction of high value lipids from flax processing wastewater and egg yolk powder, respectively, their findings could be scaled and applied to biodiesel production from wastewater sludges. Nielsen and Shukla found that the use of ethanol at room temperature led to the extraction of nearly all the phospholipids, together with cholesterol and a minor part of the triacylglycerols, without special extraction and filtration devices. On the other hand, Holser and Akin performed a serial extraction of the lipids present in flax wastewater in three steps, under different temperature values (50, 80, 90 and 100ºC). They found that the most efficient extraction was achieved when the sample-ethanol mixture was heated to 90ºC and the reaction time was 15 minutes (Holser & Akin, 2008).
Considering the above findings, and taking into account the fact that the enzymatic production of biodiesel generally requires high alcohol to oil ratios, to improve the solubilization of the lipids and the formation of water-oil, enzyme-oil and enzyme-alcohol-oil interfaces, we propose that a suitable scheme for the production of biodiesel from WWTP sludge could be as simple as using a pressurized pretreatment tank, where the sludge is soaked in ethanol, kept at 90ºC under stirring and refluxed to subject the mixture to three extraction cycles. This is followed by incubation in a reaction tank where the extracted lipids, alongside with part of the ethanol used in the previous step, are added to a reaction mix containing the enzyme (free, immobilized or whole cell catalyst) and kept at the optimal temperature and pH conditions, to ensure both enzyme stability and an acceptable microdiesel production rate. Heat exchangers between the two tanks could serve to save energy, using the heat released before entering the second tank to preheat the sludge before entering the first one.
The system could even be autonomous in terms of ethanol requirements if the engineered microorganism used to produce the lipase was able to produce ethanol simultaneously, or if the cited tanks were coupled with a third reactor where bioethanol was produced from sugars present in the non-lipidic products obtained in the pretreatment tank by means of ethanol-producing yeast or bacteria strains. In the case of economic restrictions, some short-term cost reduction could be achieved by replacing the pretreatment pressurized tank with a non-pressurized unit, and keeping the temperature of the extraction mix below 79ºC, although it would imply medium-term economic losses because the lower extraction efficiency must be compensated by performing more extraction cycles at a higher reflux rate and a greater ethanol volume in the pretreatment tank, or even by the use of at least two serial pretreatment tanks.
## 5. Conclusion
As a short-term response to the consequences of greenhouse gas emissions and the unsustainability of the fossil fuel-based energy model, the industry has developed ready-to-use substitutes for traditional fossil fuels, delivered generally and ambiguously under the commercial ‘bio’ denomination. However, the first- and second-generation of so-called biofuels are neither of completely biological origin nor based on renewable and environmentally friendly feedstocks. In addition, the production techniques rely on high energy inputs, both in feedstock production (as is the case for rapeseed, soybean or palm oil) and in the biofuel synthesis (acid catalyzed biodiesel or corn bioethanol perfectly illustrate the neat energy gain problems). Alongside these problems, new and complex problems have emerged. Firstly, the increase in the prices of grain and vegetable oils used both to produce biofuels and for human nourishment and livestock feeding; and secondly, the expansion of agricultural land to increase production of sugar cane or vegetable oils to satisfy the huge demand for these sugar and lipid sources, generated by the abrupt increase in biofuels production. Thus, the development of cleaner and more sustainable biofuels is required to achieve the challenge to totally replace traditional fossil fuels by third-generation biofuels, independent of non-renewable precursors or inefficient industrial processes, that damage the environment directly and indirectly and threaten biodiversity and food security (UNCTAD, 2010).
A great variety of domestic, agricultural and industrial residues, from lignocellulosic forestry and agriculture waste to fatty acid rich waste waters, generated by the dairy, poultry or vegetable oil refinery industries, as well as the sludges from urban waste waters, can be used as precursors of biofuels. The treatment of these residues could be combined with the production of third-generation biofuels by enzymatic catalysis because the high cost of enzymes could be compensated by the low cost of the residues (or even the presence of incentives for residue reduction and management). But the massive application of these concepts requires a series of technical and biotechnological improvements, such as the optimization of lipids and sugars extraction, feedstock pretreatment processes, biofuels production plant design, heterogeneous catalysts and enzyme immobilization techniques, protein engineering of lipases, alcohol dehydrogenases or hydrolases to increase their activity and reusability, genetic engineering of microbes to facilitate both the pretreatment of precursors, and the synthesis and purification of the biofuels.
## Acknowledgments
We thank the Junta de Andalucía (Spain) for funding this study through project reference P08-RNM-04180 and the Spanish Ministry of Science and Technology for funding through project reference CTM2009-09270. M. Manzanera received grants from the Programa Ramon y Cajal, (Ministerio de Educacion y Ciencia MEC, Spain, and ERDF, European Union).
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Rafael Picazo-Espinosa, Jesús González-López and Maximino Manzanera (August 1st 2011). Bioresources for Third-Generation Biofuels, Biofuel's Engineering Process Technology, Marco Aurélio dos Santos Bernardes, IntechOpen, DOI: 10.5772/17134. Available from:
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Wolfgang Koenig 氏 (Weierstrass Institute Berlin)
Eigenvalue order statistics and mass concentration in the parabolic Anderson model (ENGLISH)
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We consider the random Schr\\"odinger operator on the lattice with i.i.d. potential, which is double-exponentially distributed. In a large box, we look at the lowest eigenvalues, together with the location of the centering of the corresponding eigenfunction, and derive a Poisson process limit law, after suitable rescaling and shifting, towards an explicit Poisson point process. This is a strong form of Anderson localization at the bottom of the spectrum. Since the potential is unbounded, also the eigenvalues are, and it turns out that the gaps between them are much larger than of inverse volume order. We explain an application to concentration properties of the corresponding Cauchy problem, the parabolic Anderson model. In fact, it will turn out that the total mass of the solution comes from just one island, asymptotically for large times. This is joint work in progress with Marek Biskup (Los Angeles and Budweis).
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Roman Kotecky 氏 (Charles University Prague/University of Warwick)
Gradient Gibbs models with non-convex potentials (ENGLISH)
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A motivation for gradient Gibbs measures in the study of macroscopic elasticity and in proving the Cauchy-Born rule will be explained. Results concerning strict convexity of the free energy will be formulated and discussed. Based on joint works with S. Adams and S. Mueller and with S. Luckhaus.
#### GCOEセミナー
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Einstein relation and linear response for random walks in random environment (ENGLISH)
### 2011年12月08日(木)
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18:30-19:30 数理科学研究科棟(駒場) 056号室
Gerd Faltings 氏 (Max Planck Institute for Mathematics, Bonn)
Nonabelian p-adic Hodge theory and Frobenius (ENGLISH)
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Some time ago, I constructed a relation between Higgs-bundles and p-adic etale sheaves, on curves over a p-adic field. This corresponds (say in the abelian case) to a Hodge-Tate picture. In the lecture I try to explain one way to introduce Frobenius into the theory. We do not get a complete theory but at least can treat p-adic sheaves close to trivial.
(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)
### 2011年12月07日(水)
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16:00-18:00 数理科学研究科棟(駒場) 122号室
Michel Cristofol 氏 (マルセイユ大学) 16:00-17:00
"Inverse problems associated with linear and non-linear parabolic systems " (ENGLISH)
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In this talk, I present several inverse reconstruction results for linear and non linear parabolic systems with different coupling terms : for linear systems with reaction-convection terms and for cooperative systems like Lotka Volterra systems with strong coupling terms. I will show different approaches to prove uniqueness of the coefficients via Carleman inequalities or via regularities properties of the solutions.
Guillaume Olive 氏 (マルセイユ大学) 17:00-18:00
"Hautus test for the approximate controllability of linear systems" (ENGLISH)
[ 講演概要 ]
We will introduce some generalization of the Hautus test to linear parabolic systems and give some applications to the distributed and boundary approximate controllability of such systems.
### 2011年12月06日(火)
#### 数値解析セミナー
16:30-18:00 数理科学研究科棟(駒場) 002号室
http://www.ms.u-tokyo.ac.jp/gcoe/index.html
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http://www.infsup.jp/saito/
### 2011年12月05日(月)
#### 代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 122号室
Obstructions to deforming curves on a uniruled 3-fold (JAPANESE)
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1. a generalization of Mumford's example of a non-reduced component of the Hilbert scheme, and
2. a sufficient condition for a first order deformation of a curve on a uniruled 3-fold to be obstructed.
As a sequel of the study, we will discuss some obstructed deformations of degenerate curves on a higher dimensional scroll.
### 2011年12月01日(木)
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16:30-18:00 数理科学研究科棟(駒場) 117号室
Spyridon Michalakis 氏 (Caltech)
Stability of topological phases of matter (ENGLISH)
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16:30-18:00 数理科学研究科棟(駒場) 002号室
Dmitry Kaledin 氏 (Steklov Mathematics Institute/ KIAS)
Cyclic K-theory (ENGLISH)
[ 講演概要 ]
Cyclic K-theory is a variant of algebraic K-theory introduced by Goodwillie 25 years ago and more-or-less forgotten by now. I will try to convince the audience that cyclic K-theory is actually quite useful -- in particular, it can be effectively computed for varieties over a finite field.
### 2011年11月30日(水)
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15:00-16:10 数理科学研究科棟(駒場) 002号室
Information criteria for parametric and semi-parametric models (JAPANESE)
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Since Akaike proposed an Information Criteria, this approach to
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Since then many Information Criteria have been proposed and it is still
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topic, we have not have proper Information Criteria for semiparametric
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for semiparametric models.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/05.html
### 2011年11月29日(火)
#### 講演会
16:30-18:00 数理科学研究科棟(駒場) 126号室
Spyridon Michalakis 氏 (Caltech)
Stability of topological phases of matter (ENGLISH)
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17:00-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:40 - 17:00 コモンルーム
Athanase Papadopoulos 氏 (IRMA, Univ. de Strasbourg)
Mapping class group actions (ENGLISH)
[ 講演概要 ]
I will describe and present some rigidity results on mapping
class group actions on spaces of foliations on surfaces, equipped with various topologies.
#### Lie群論・表現論セミナー
16:30-18:00 数理科学研究科棟(駒場) 002号室
Daniel Sternheimer 氏 (Rikkyo Univertiry and Université de Bourgogne)
Symmetries, (their) deformations, and physics: some perspectives and open problems from half a century of personal experience (ENGLISH)
[ 講演概要 ]
This is a flexible general framework, based on quite a number of papers, some of which are reviewed in:
MR2285047 (2008c:53079) Sternheimer, Daniel. The geometry of space-time and its deformations from a physical perspective. From geometry to quantum mechanics, 287–301, Progr. Math., 252, Birkhäuser Boston, Boston, MA, 2007
http://monge.u-bourgogne.fr/d.sternh/papers/PiMOmori-DS.pdf
### 2011年11月28日(月)
#### 代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 122号室
Comparison with Gieseker stability and slope stability via Bridgeland's stability (JAPANESE)
[ 講演概要 ]
In this talk we compare two classical notions of stability (Gieseker stability and slope stability) for sheaves on K3 surfaces by using stability conditions which was introduced by Bridgeland. As a consequence of this work, we give a classification of 2 dimensional moduli spaces of sheaves on K3 surface depending on the rank of the sheaves.
#### 複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
An ampleness criterion with the extendability of singular positive metrics (JAPANESE)
[ 講演概要 ]
Coman, Guedj and Zeriahi proved that, for an ample line bundle $L$ on a projective manifold $X$, any singular positive metric on the line bundle $L|_{V}$ along a subvariety $V \subset X$ can be extended to a global singular positive metric of $L$. In this talk, we prove that the extendability of singular positive metrics on a line bundle along a subvariety implies the ampleness of the line bundle.
### 2011年11月25日(金)
#### 談話会・数理科学講演会
16:30-17:30 数理科学研究科棟(駒場) 002号室
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。
[ 講演概要 ]
### 2011年11月24日(木)
#### 講演会
16:30-18:00 数理科学研究科棟(駒場) 117号室
Spyridon Michalakis 氏 (Caltech)
Stability of topological phases of matter (ENGLISH)
### 2011年11月22日(火)
#### 作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 126号室
Spyridon Michalakis 氏
( Institute for Quantum Information and Matter (Caltech))
Stability of topological phases of matter (ENGLISH)
[ 講演概要 ]
The first lecture will be an introduction to quantum mechanics and a proof of Lieb-Robinson bounds for constant range interaction Hamiltonians. The second lecture will build on the first to prove a powerful lemma on the transformation of the interactions of generic gapped Hamiltonians to a new set of rapidly-decaying interactions that commute with the groundstate subspace. I call this "The Energy Filtering Lemma". Then, the third lecture will be on the construction of the Spectral Flow unitary (Quasi-adiabatic evolution) and its properties; in particular, the perfect simulation of the evolution of the groundstate subspace within a gapped path. I will end with a presentation of the recent result on the stability of the spectral gap for frustration-free Hamiltonians, highlighting how the previous three lectures fit into the proof.
#### トポロジー火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Quantum and homological representations of braid groups (JAPANESE)
[ 講演概要 ]
Homological representations of braid groups are defined as
the action of homeomorphisms of a punctured disk on
the homology of an abelian covering of its configuration space.
These representations were extensively studied by Lawrence,
Krammer and Bigelow. In this talk we show that specializations
of the homological representations of braid groups
are equivalent to the monodromy of the KZ equation with
values in the space of null vectors in the tensor product
of Verma modules when the parameters are generic.
To prove this we use representations of the solutions of the
KZ equation by hypergeometric integrals due to Schechtman,
Varchenko and others.
In the case of special parameters these representations
are extended to quantum representations of mapping
class groups. We describe the images of such representations
and show that the images of any Johnson subgroups
contain non-abelian free groups if the genus and the
level are sufficiently large. The last part is a joint
work with Louis Funar.
#### Lie群論・表現論セミナー
16:30-18:00 数理科学研究科棟(駒場) 002号室
Smallest complex nilpotent orbit with real points (JAPANESE)
[ 講演概要 ]
Let $\\mathfrak{g}$ be a non-compact simple Lie algebra with no complex
structures.
In this talk, we show that there exists a complex nilpotent orbit
$\\mathcal{O}^{G_\\mathbb{C}}_{\\text{min},\\mathfrak{g}}$ in
$\\mathfrak{g}_\\mathbb{C}$ ($:=\\mathfrak{g} \\otimes \\mathbb{C}$)
containing all of real nilpotent orbits in $\\mathfrak{g}$ of minimal
positive dimension.
For many $\\mathfrak{g}$, the orbit
$\\mathcal{O}^{G_\\mathbb{C}}_{\\text{min},\\mathfrak{g}}$ is just the
complex minimal nilpotent orbit in $\\mathfrak{g}_\\mathbb{C}$.
However, for the cases where $\\mathfrak{g}$ is isomorphic to
$\\mathfrak{su}^*(2k)$, $\\mathfrak{so}(n-1,1)$, $\\mathfrak{sp}(p,q)$,
$\\mathfrak{e}_{6(-26)}$ or $\\mathfrak{f}_{4(-20)}$,
the orbit $\\mathcal{O}^{G_\\mathbb{C}}_{\\text{min},\\mathfrak{g}}$ is not
the complex minimal nilpotent orbit in $\\mathfrak{g}_\\mathbb{C}$.
We also determine $\\mathcal{O}^{G_\\mathbb{C}}_{\\text{min},\\mathfrak{g}}$
by describing the weighted Dynkin diagrams of these for such cases.
### 2011年11月21日(月)
#### 複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
Techniques of computations of Dolbeault cohomology of solvmanifolds (JAPANESE)
#### 諸分野のための数学研究会
13:30-14:30 数理科学研究科棟(駒場) 056号室
Ernie Esser 氏 (University of California, Irvine)
A convex model for non-negative matrix factorization and dimensionality reduction on physical space (ENGLISH)
[ 講演概要 ]
A collaborative convex framework for factoring a data matrix X into a non-negative product AS, with a sparse coefficient matrix S, is proposed. We restrict the columns of the dictionary matrix A to coincide with certain columns of the data matrix X, thereby guaranteeing a physically meaningful dictionary and dimensionality reduction. We focus on applications of the proposed framework to hyperspectral endmember and abundances identification and also show an application to blind source separation of NMR data.
This talk is based on joint work with Michael Moeller, Stanley Osher, Guillermo Sapiro and Jack Xin.
#### Kavli IPMU Komaba Seminar
16:30-18:00 数理科学研究科棟(駒場) 002号室
Siu-Cheong Lau 氏 (IPMU)
Enuemerative meaning of mirror maps for toric Calabi-Yau manifolds (ENGLISH)
[ 講演概要 ]
For a mirror pair of smooth manifolds X and Y, mirror symmetry associates a complex structure on Y to each Kaehler structure on X, and this association is called the mirror map. Traditionally mirror maps are defined by solving Picard-Fuchs equations and its geometric meaning was unclear. In this talk I explain a recent joint work with K.W. Chan, N.C. Leung and H.H. Tseng which proves that mirror maps can be obtained by taking torus duality (the SYZ approach) and disk-counting for a class of toric Calabi-Yau manifolds in any dimensions. As a consequence we can compute disk-counting invariants by solving Picard-Fuchs equations.
### 2011年11月19日(土)
#### 保型形式の整数論月例セミナー
10:15-12:30 数理科学研究科棟(駒場) 117号室
[ 講演概要 ]
この微分方程式の基本解が超楕円積分と超幾何関数を使って表示できることを示しさらに関連した話題を説明する。
[ 講演概要 ]
### 2011年11月18日(金)
#### 講演会
15:00-16:00 数理科学研究科棟(駒場) 052号室
Inverse problems for heat equations with discontinuous conductivities
(JAPANESE)
[ 講演概要 ]
In a bounded domain $\\Omega \\subset {\\bf R}^n$, consider the heat
equation $\\partial_tu = \\nabla(\\gamma(t,x)\\nabla u)$. The heat
conductivity is assumed to be piecewise constant : $\\gamma = k^2$ on
$\\Omaga_1(t) \\subset\\subset \\Omega$, $\\gamma(t,x) = 1$ on
$\\Omega\\setminus\\Omega_1(t)$. In this talk, we present recent results
for the inverse problems of reconstructing $\\gamma(t,x)$ from the
Dirichlet-to-Neumann map :
$u(t)|_{\\partial\\Omega} \\to$\\partial_{\\nu}u|_{\\partial\\Omega}$for a time interval$(0,T)\$. These are the joint works with P.Gaitan, O.Poisson,
S.Siltanen, J.Tamminen.
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Replacing resistors with equivalent resistor
This is somewhat a homework assignment, but please bear with me. Given the following schematic, I want to know the overall resistance when measured from node A to node B.
simulate this circuit – Schematic created using CircuitLab
First of all, I'm not sure whether the order of calculations is important. Here's what I did: R3 and R4 are in series, so they add up to 500 Ohm. R2 is in parallel to those two, so (1/500+1/500)^-1 = 250 Ohm. Now I add R1 and my previous result because they are in series and thus get 1250 Ohm.
Is this way of calculating correct? If I, for example, first calculate R2 and R3 in parallel, and then in series with R4, I get a completely different result, which confuses me a lot.
• +1 If only all homework questions were as well-stated. – JYelton Aug 28 '13 at 1:01
• The way you did it is correct. And no, you cant switch the order. R2 and R3 are not in parallel by themselves, R3 and R4 are in series with one another and together they are in parallel with R2. If you pretend R2 and R3 are in parallel, how do you factor in R4? Its in series with R3 but not with R2. – CogitoErgoCogitoSum Jul 26 '17 at 22:51
The first calculation you did is correct, R3 and R4 are in series, the combination is in parallel with R2 and when combined it is in series with R1.
The second method of trying to combine R3 and R2 in parallel results in an incorrect answer because they are not in parallel. Devices are in parallel if they have the same voltage across them. The voltage across R2 is split between R4 and R3, thus the voltage across R2 and R3 is not the same, which means they are not parallel.
The second calculation is wrong because that R3 is NOT in parallel with R2.
A component is considered to be in parallel with another component only if you can say that different currents flows through them.
(Not necessarily a different value, both currents may have the same exact value, but you define it as a different current because that it's in a different branch.)
R2 and R3 are not in parallel. Two resistors are in parallel only if they connect to the same two nodes.
Similarly, two resistors are in series only if they are the only two elements connecting to a single central node.
The initial calculation steps you described are correct.
Hint:
You need to do this in stages
R3 and R4 are in series so you can replace them one resistor R5
$$R5 = R3 + R4 = 500 \Omega$$
Now: R2 and the new R5 are in parallel so you replace them with R6
$$R6 = \frac{R2 \times R5}{R2 + R5} = 250 \Omega$$
There is one more step to get the final answer is R1 and the new R6 a series or parallel circuit?
It may help to redraw the circuit at each stage until you get used to simplifying this type of circuit in your head.
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Existence of Taut Foliations on Seifert Fibered Homology $3$-spheres This paper concerns the problem of existence of taut foliations among $3$-manifolds. Since the contribution of David Gabai, we know that closed $3$-manifolds with non-trivial second homology group admit a taut foliation. The essential part of this paper focuses on Seifert fibered homology $3$-spheres. The result is quite different if they are integral or rational but non-integral homology $3$-spheres. Concerning integral homology $3$-spheres, we can see that all but the $3$-sphere and the Poincaré $3$-sphere admit a taut foliation. Concerning non-integral homology $3$-spheres, we prove there are infinitely many which admit a taut foliation, and infinitely many without taut foliation. Moreover, we show that the geometries do not determine the existence of taut foliations on non-integral Seifert fibered homology $3$-spheres. Keywords:homology 3-spheres, taut foliation, Seifert-fibered 3-manifoldsCategories:57M25, 57M50, 57N10, 57M15
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# Area of projection on a plane?
• January 18th 2010, 03:08 AM
fishlord40
Area of projection on a plane?
what is the area of the projection on a plane of an equilateral triangle 10 cm on a side, if one side is parallel to the plane and the other sides form an angle of 30° with the plane?
*** the answer to this problem is approximately 35.35 sq. cm but i need the DIAGRAM/FIGURE of this problem and please explain the steps to solve this problem. thanks!!!
• January 18th 2010, 03:55 AM
Garas
delete
• January 18th 2010, 05:23 AM
earboth
Quote:
Originally Posted by fishlord40
what is the area of the projection on a plane of an equilateral triangle 10 cm on a side, if one side is parallel to the plane and the other sides form an angle of 30° with the plane?
*** the answer to this problem is approximately 35.35 sq. cm but i need the DIAGRAM/FIGURE of this problem and please explain the steps to solve this problem. thanks!!!
Let e denote the side of the isoceles triangel which is the projection of the equilateral triangle. Let h denot the height in the isoceles triangel.
1. $e = 10\cdot \cos(30^\circ) = 5 \cdot \sqrt{3}$
2. To calculate the height h use Pythagorean theorem:
$h^2+5^2 = e^2~\implies~h^2 = (5 \cdot \sqrt{3})^2-5^2 = 50$
Thus $h = 5 \cdot \sqrt{2}$
3. The area of the projection is
$A = \frac 12 \cdot 10 \cdot 5 \cdot \sqrt{2} \approx 35.355339...$
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# Tip on how to make a visually good table
I'm using booktabs to make most of the tables in my thesis. However, I'm not sure if that is the best solution for tables with more than 6-7 rows, as it can be difficult to read (there is no line seperating the rows).
If you feel you are good at making visually good tables, I'd like you to make a proposal for the following table (made in Word to illustrate the content and size):
The table is meant to illustrate different simulation cases. The Y illustrates that the specific case make use of the method mentioned in the first row in each column.
• If you've already made it with booktabs, why not provide that code as a minimal working example (MWE) to save us the typing? – Paul Gessler Apr 14 '15 at 12:36
• Once you got rid of the lines and the huge horizontal spacing, make the cells centered. You can add a bit of whitespace using \addlinespace to group items. – Johannes_B Apr 14 '15 at 12:42
• This is a gif I like to reference for table design imgur.com/gallery/ZY8dKpA – DavidTheWin Apr 14 '15 at 14:33
• – morbusg Apr 15 '15 at 9:20
• You (and all people who answered this question) could use \checkmark (or \checked from wasysym) instead of Y. – Martin Thoma Apr 15 '15 at 18:59
I suggest you read the booktabs package documentation. Very good advices are given in there about table formatting and I think it is a good introduction on the subject.
1. Never, ever use vertical rules.
2. Never use double rules.
You may also add some zebra stripes to guide the eye horizontally with the command rowcolors using the package xcolor. This practice is however often unnecessary for tables that are completely filled with values. There is an interesting discussion on Edward Tufte’s Web forum about this subject as well as in this thread on TeX.SX.
When dealing with float numbers instead of letters, they should be align with the decimal using either the dcolumn or siunitx package. The precision of the float numbers within a same column should be kept as consistent as possible.
Here is proposition of a MWE for the example you provided :
\documentclass{article}
\usepackage{booktabs}
\usepackage[svgnames,table]{xcolor}
\usepackage[tableposition=above]{caption}
\usepackage{pifont}
\newcommand*\CHECK{\ding{51}}
\begin{document}
\begin{table}
\centering
\caption{MWE of a table using booktabs}
\rowcolors{5}{}{gray!10}
\begin{tabular}{*4c}
\toprule
& \multicolumn{3}{c}{methods tested} \\
\cmidrule(lr){2-4}
Case & Heat & Exhaust & Outdoor \\
\# & Wheel & Air & Air \\
\midrule
1 & & \CHECK & \\
2 & & & \CHECK \\
3 & & \CHECK & \CHECK \\
4 & \CHECK & & \\
5 & \CHECK & \CHECK & \\
6 & \CHECK & & \CHECK \\
7 & \CHECK & \CHECK & \CHECK \\
\bottomrule
\end{tabular}
\end{table}
\end{document}
Which results in this table:
• I've broken the column titles in two lines to reduce the width of the columns. In addition to make the table looks better, it also helps the horizontal readability.
• I replaced the horizontal lines by light toned zebra lines. In my opinion, for this example, this is totally acceptable to add zebra lines since rows are independent from each other.
• I replaced the 'Y' symbol by a checkmark symbol as suggested by @moose.
• I removed the word 'Case' before each number to avoid unecessary repetition of the information.
• I added the meta-title 'methods tested' and the title 'Case' for the first column. I believe that a table should be relatively standalone. A reader should be able to grasp the structure and have an idea of the meaning of every elements of the table just by looking at it. Details could be added in the title or as a table note. If the reader have to go within the text to understand the table, it is a no-go in my opinion. This practice also allows to more easily refer to the various elements of the table in the text.
Here is another example of a table I have produced for my thesis that gives an example with float numbers using the siunitx package:
\documentclass{article}
\usepackage{booktabs, siunitx}
\usepackage[svgnames,table]{xcolor}
\usepackage[tableposition=above]{caption}
\begin{document}
\begin{table}
\centering
\caption{MWE of a table using booktabs and siunitx with floats}
\begin{tabular}{
l
S[table-format = 3]
S[table-format = 2]
S[table-format = 1.3]
S[table-format = -2.2]
S[table-format = 1.3]
S[table-format = 1.3]
S[table-format = 2.2]
}
\toprule
\multicolumn{3}{c}{} &
\multicolumn{5}{c}{Brooks-Corey model parameters}\\
\cmidrule(lr){4-8}
& {Sand} & {Clay} & {$\lambda$} & {$\psi_e$} & {$\theta_r$} & {$\theta_{sat}$} & {$K_{sat}$} \\
Texture Class & {(\si{\percent})} & {(\si{\percent})} & {(-)} & {(\si{cm})} & {(\si{m^3/m^3})} & {(\si{m^3/m^3})} & {(\si{cm/h})} \\
\midrule
Sand & 100 & 0 & 0.592 & -7.26 & 0.020 & 0.437 & 21.00 \\
Loamy Sand & 85 & 5 & 0.474 & -8.69 & 0.035 & 0.437 & 6.11 \\
Sandy Loam & 65 & 10 & 0.322 &-14.66 & 0.041 & 0.453 & 2.59 \\
\bottomrule
\end{tabular}
\end{table}
\end{document}
Which results in this table:
• Here's the same example without the \rowcolors command. Personally, I think the zebra striping is superfluous (or at least far too strong there). But that's a matter of taste and could also depend on the actual table content. – wchargin Apr 14 '15 at 14:06
• Two additions: use \captionsetup[table]{postion=above} to get proper spacing between the caption and the table. Mention, that package siunitx provides the feature of package dcolumn as well. – Johannes_B Apr 14 '15 at 15:34
• I believe Edward Tufte recommends to color every 3 rows rather than every other row using the following argument: it is less noisy, and reading a row one recognises whether the row is at top, middle, or bottom of such a colouring. – Christian Lindig Apr 14 '15 at 20:31
• Please note that I'm not attacking, I am genuinely curios to know: Where did you/they come by those three rules? I.e., no vertical rule, no double rule and alignment on decimal point. Are there any graphic design discipline for that? I am also curios to know about the decimal alignment when the numbers have different precision (e.g. how would it look like to align 123.45 and 3.141596 at the decimal point.). – Pouya Apr 15 '15 at 9:41
• @Pouya The no-vertical-line guideline is discussed in the booktabs documentation, which I found very useful as an introductory read on the subject. – Jean-Sébastien Apr 15 '15 at 13:43
I would swap columns and rows -- at least if the content of the cell are so short as shown in your example. And I would also try to avoid "rules" in the form of color backgrounds -- in most cases a bit more space is enough. And I would always try to have column titles which are not much longer than the content of the cells.
\documentclass{scrartcl}
\usepackage{booktabs}
\begin{document}
\begin{table}\centering
\caption{Use of xxxx methods in simulation cases 1--7}
\begin{tabular}[t]{lccccccc}\toprule
& 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \midrule
Heat wheel & & & & Y & Y & Y & Y \\\addlinespace
Exhaust air & Y & & Y & & Y & & Y \\\addlinespace
Outside air & & Y & Y & & & Y & Y \\
\bottomrule
\end{tabular}
\end{table}
\end{document}
• Although this is a nice approach for the example as given it will rapidly fall down if the cases are identified by name rather than a single-character index, as the table will be too wide for the page. It may be appropriate to define the cases nearby to allow the use of an index, but not always. – Chris H Apr 14 '15 at 20:52
• @ChrisH sure, other content will perhaps need another layout. There is no general solution that works in all cases. – Ulrike Fischer Apr 14 '15 at 21:06
• @ChrisH You could also rotate the cases name as demonstrated here tex.stackexchange.com/questions/98388/… – Jean-Sébastien Apr 15 '15 at 14:38
• @UlrikeFischer Adding a title Cases over the numbers and maybe a title Processes next to the methods could maybe improve further the design. See the link I've posted in my comment above. – Jean-Sébastien Apr 15 '15 at 14:42
• @JSGosselin: I would avoid (full) rotation, and I would rotate the other way round: people tend to hold books in the left hand to switch pages with the right one and so clockwise rotation is more natural. And I wouldn't add unneeded noise like "cases". – Ulrike Fischer Apr 15 '15 at 14:43
I'd use booktabs together with xcolor to shade alternating rows:
The code:
\documentclass{article}
\usepackage[svgnames,table]{xcolor}% note the table option
\usepackage{booktabs}
\begin{document}
\rowcolors{2}{White}{LightBlue!30}% colors to shade rows withs
\begin{tabular}{*4c}\toprule
& \textbf{Heat Wheel} & \textbf{Exhaust air} & \textbf{Outdoor air}\\\midrule
Case 1& & Y & \\
Case 2& & & Y \\
Case 3& & Y & Y \\
Case 4& Y & & \\
Case 5& Y & Y & \\
Case 6& Y & & Y \\
Case 7& Y & Y & Y \\\bottomrule
\end{tabular}
\end{document}
Btw, a mwe would have been helpful, with or without booktabs.
• Thank you for your answer. Will this change the layout for all tables in the report, or only the ones having \rowcolors{2}{White}{LightBlue!30}% colors to shade rows withs in front of it? – ROLF Apr 14 '15 at 13:32
• @ROLF A \rowcolors command will change all subsequent tables. Of course, you can write \rowcolors{2}{}{} to turn off the row colouring. – user30471 Apr 15 '15 at 3:39
Coding for beauty is not always easy and is time-consuming, but I think using booktabs is very sufficient and its output is decent. You can also consider using colortbl if you want some colors. Here I initially post the first solution using booktabs to give you some insight.
\documentclass{article}
\usepackage{booktabs}
\begin{document}
\begin{table}\centering
\begin{tabular}{cccc}\toprule
& Heat wheel & Exhaust air & Outside air \\ \midrule
Case 1 & & Y & \\
Case 2 & & & Y \\
Case 3 & & Y & Y \\
Case 4 & Y & & \\
Case 5 & Y & Y & \\
Case 6 & Y & & Y \\
Case 7 & Y & Y & Y \\
\bottomrule
\end{tabular}
\end{table}
\end{document}
If you decide to go the second approach, you may try this:
\documentclass{article}
\usepackage{booktabs}
\usepackage{colortbl}
\begin{document}
\begin{table}\centering
\begin{tabular}{cccc}\toprule
& \bf{Heat wheel} & \bf{Exhaust air} &\bf{Outside air} \\ \midrule \rowcolor[gray]{.95}
Case 1 & & Y & \\
Case 2 & & & Y \\ \rowcolor[gray]{.95}
Case 3 & & Y & Y \\
Case 4 & Y & & \\ \rowcolor[gray]{.95}
Case 5 & Y & Y & \\
Case 6 & Y & & Y \\ \rowcolor[gray]{.95}
Case 7 & Y & Y & Y \\ \bottomrule
\end{tabular}
\end{table}
\end{document}
Which gives:
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# Mutation and crossover operations in discrete differential evolutionary operations?
I need to use discrete differential evolutionary algorithm for assigning discrete values from set size $L$ to vectors of size $D$ where $L$ could be smaller, equal or larger than $D$. Elements of vector $X$ could take the same values of other elements. My question is if we have a population of size $NP$ with each vector $X$ in the population of size $D$. How do we actually apply the mutation operand:
$$V_{j,i}^{G+1} = X_{j, r_1}^{G} + F\cdot (X_{j, r_2}^{G}-X_{j, r_3}^{G})$$
where $i$, $r_1$, $r_2$, $r_3$ are references to vectors in $NP$ and none is equal to the other, $J$ is an index in vector $X$, and $F$ is a random number between $0$ and $1.2$.
Suppose $X_{r_1}^{G}$ is equal to $\{4, 1, 3, 2, 2, 0\}$ and $X_{r_2}^{G}$ is equal to $\{2, 2, 3, 0, 4, 2\}$ and $X_{r_3}^{G}$ is equal to $\{1, 2, 3, 3, 0, 1\}$ Could anyone explain in detail the steps (through example if possible) on how to get the mutant vector $V_{j,i}^{G+1}$
There isn't a single way in which one can approach a discrete optimization problem using Differential Evolution (DE).
Widespread techniques listed under the Discrete Differential Evolution label aren't DE-specific.
You can allow variables to take values in a continuous range and use penalty functions to enforce integer values:
$$\bar{f}(w) = f(w) - \sum_i{k_i \cdot (w_i - \operatorname{round}(w_i))^2}$$
$w$ is the vector of parameters (chromosome values), $f: \mathbb R^n \rightarrow \mathbb R$ the basic fitness function (here assuming "greater is better"), $k$ a problem-specific scaling vector, $\bar{f}(\cdot)$ the "penalized" fitness function.
In this way the DE algorithm (DE/rand/1) stays the same:
\begin{align} X_{j,r2}^G - X_{j,r3}^G & = \{2,2,3,0,4,2\} - \{1,2,3,3,0,1\} = \{1,0,0,-3,4,1\} \\ F \cdot (X_{j,r2}^G - X_{j,r3}^G) & = 0.5 \cdot \{1,0,0,-3,4,1\} = \{0.5,0,0,-1.5,2,0.5\} \\ V_{j,i}^{G+1} & = \{4,1,3,2,2,0\} + \{0.5,0,0,-1.5,2,0.5\} = \{4.5,1,3,0.5,4,0.5\} \end{align}
The trial vector $U$ is obtained via crossover between the donor vector $V_{j,i}^{G+1}$ and a target vector $X$:
$$U_{j,i}^{G+1} = \operatorname{crossover}(V_{j,i}^{G+1}, X_{j,i}^{G})$$
The target vector is compared with the trial vector and the best one is admitted to the next generation.
This is the recommended procedure with R DEOptim Package (via the optional fnMap parameter).
You can round all the real-valued parameters before evaluating the fitness function:
$$\bar{f}(w) = f(\operatorname{round}(w))$$
(round acts as a repair operator)
This is the technique used by Mathematica's functions NMinimize / NMaximize with the options Method → "DifferentialEvolution" and Element[w,Integers]
There are also many variations of DE named something-Discrete-DE:
• Binary Discrete Differential Evolution: the solution of a problem is presented as a binary string instead of a real-valued vector
• Real Value based Discrete Differential Evolution introduces forward/backward transformations to map integer into real number and viceversa
• Exchange based Discrete Differential Evolution: here the crossover operator doesn't change but mutation, being the primary operator acting on elements of vector in continuous space, is replaced.
• ...
So you should specify what form of Discrete DE you're interested in for a step by step example.
Meanwhile A Comparative Study of Discrete Differential Evolution on Binary Constraint Satisfaction Problems by Qingyun Yang (2008 IEEE Congress on Evolutionary Computation) is a good starting point with many references.
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Question
# How many numbers lie between squares of the following numbers?${\text{(i)}}$12 and 13${\text{(ii)}}$25 and 26${\text{(iii)}}$ 99 and 100
Hint:- Find squares of given numbers.
As, we know that,
Total numbers lying between two numbers a and b,
is given as $b - a - 1$, where $b > a$.
So, here we had to find total numbers lying between squares of two numbers.
So, solving all the parts.
${\text{(i)}}$So, a will be ${(12)^2}$
$\Rightarrow a = {(12)^2} = 144$
And, b will be ${(13)^2}$
$\Rightarrow b = {(13)^2} = 169$
So, total numbers lying between the squares of 12 and 13 will be,
$\Rightarrow b - a = 169 - 144 - 1 = 24$
$\Rightarrow$Hence, the total numbers lying between squares of 12 and 13 is 24.
${\text{(ii)}}$So, a will be ${(25)^2}$
$\Rightarrow a = {(25)^2} = 625$
And, b will be ${(26)^2}$
$\Rightarrow b = {(26)^2} = 676$
So, total numbers lying between the squares of 25 and 26 will be,
$\Rightarrow b - a = 676 - 625 - 1 = 50$
$\Rightarrow$Hence, the total numbers lying between squares of 25 and 26 is 50.
${\text{(iii)}}$So, a will be ${(99)^2}$
$\Rightarrow a = {(99)^2} = 9801$
And, b will be${\text{ }}{(100)^2}$
$\Rightarrow b = {(100)^2} = 10000$
So, total numbers lying between the squares of 99 and 100 will be,
$\Rightarrow b - a = 10000 - 9801 - 1 = 198$
$\Rightarrow$Hence, the total numbers lying between squares of 99 and 100 is 198.
Note:- Whenever we came up with this type of problem then remember that,
for any two numbers a and b such that $b > a$. Total numbers lying between
them will be $b - a - 1$. But if the given two numbers are consecutive and we
had to find total numbers lying between their squares then we can also directly
say that numbers lying between them is $2*a$.
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234: TZ Discussion – Death by iPad
1. Richard says:
I don’t know about a marathon podcast but this must be some kind of record for show notes length! Sounds like a lot of good stuff, looking forward to listening.
2. Hey, great episode. Long and interesting!
1. Percona – it was an awesome talk with Alexander from Percona.
All the “Aha” moments we could’ve get for the next few months were squeezed into the single expert session. I honestly wanted to replicate he’s brain.
2. @Jason – the accountability website for public influencers – I thought about something like that for a while, but I found out that most of the public is losing interest quickly.
Usually public issues touch closely only a small group of people. Something might get millions of people involved at first, but the real problem is – how many people will actually care enough 6 months after the election? 6 months after someone promised to change something? to fix something? I believe the people that will actually care is a small group that feel strongly about the issue.
About 2 years ago, during the Arab spring, million Israelis demonstrated against the expensive living in Israel (population is 7 mil, 1 mil demonstrating is a lot). Since then – no real issue was resolved, its getting worse for a lot of families to survive, and the recent demonstration about the subject (the “reorganization” of the parties involved) was few thousands of people only.
In Israel we have a website maintained by a public org. (not the government) with issues and responsibilities of public figures. Anyone rarely looks at it and asks “So what’s going on with X?”. The media is trying, but as long as the public doesn’t care enough itself, the media won’t cover it.
I guess if most of us had less crazy life perhaps we could “afford” to care more.
3. Israel-Iran-Nuclear weapon issue – the information about it is so conflicted. There are many reports that state Iran is actually developing a nuclear weapon (or at least trying to).
Frankly, I don’t trust the media much especially if the source of the information is a government.
I believe that Iran is building a nuclear weapon to be at the same status like Pakistan and North Korea. That’s its biggest goal.
Problem is, Iran is responsible for many terror organizations, weaponizing and training them.
Iran may not actually bomb Israel with nuclear rockets, and Iran may not give nuclear weapons to terror org. – but is it a chance we (Israelis) should take? is it a chance the entire world should take (US and Europe suffer from terror attacks as well)?
Many say that Iran won’t bomb Israel because we have Syria, Lebanon, Jordan and Egypt around us. True. But Hamas bombed Jerusalem recently, a city they feel so strongly about and call it their sacred place (in their bombing of Jerusalem they actually hit an area populated with Palestinians without any remorse) so how much can you really trust their love for each other?
Bottom line, I don’t think that a government like Iran should have a nuclear power. The implications (or possible implications) of nuclear Iran are so great and scary that the world should seriously consider putting an end to it. I know how awful a war is, that’s the last thing I want, but when you allow the violent kid at school to walk around with a rock, he will make more damage next time he’s getting pissed at someone (sounds better in Hebrew).
3. Jason says:
Marathon TV Show similar to your Marathon Podcast idea
http://www.reuters.com/article/2013/04/15/us-nepal-tv-record-idUSBRE93E0SJ20130415
4. Craig says:
Jason does a Jim Carrey laugh at 38:20.
5. Jason says:
@Craig – Actually, after listening to it I think it might be more of an old man laugh. 😉
6. Jason says:
@Richard – Yeah, dude, writing up those notes was a nightmare. It took forever!
7. Jason says:
@Jason – A 62 hour show?! We may need to scale back our ambitions a bit. 😉
8. Jason says:
@Udi Mosayev – I promise I’m not ignoring your comment, but I’m going to have to find some time to respond to it. 😉
9. Justin says:
@Udi – holy cr*p that’s the longest comment we’ve ever had… ;
10. This is what you get for a 2.5 hours long episode 🙂
11. Tony says:
I’ve listened to every episode, and have complimented it in the past, but you’re losing me with the weekly Tesla stock story rehashing and price movement talk. To my ears, it’s getting a bit boorish. Sorry.
12. Love the show, but very long.
Have you thought about recording a long show, but splitting it in two so you can make the show weekly again?
13. P.S. How do we kick start this ice cream truck?
14. Tom says:
Hey guys,
Long time fan of the show. I really enjoy the discussion every week.
Thought I would provide an insight into concerns about sharing. I work for a competitor to Uber in Sydney, Australia (goCatch.com). We are approaching the problem from the taxi end (as opposed to limos), but we are definitely in the same space.
I agree with Jason on this. I have found Jason’s insights on technical challenges and solutions at Uber interesting, but at no point have I caught myself thinking “WOW! We can use that”. Comparing architectures and approaches is interesting from an academic perspective, but that is all.
Just my two cents.
15. Funny, since I have to walk 3 times 20 mn a day (as part of my post-surgery plan) it took me up to yesterday to finish the show! 🙂 That was perfect for me!
I enjoyed the discussion on database server scaling and TL;DR the most.
I also updated quite a few pages on the TechzingWiki – just check out the Recent Changes page for details.
I invite more listeners to register an account, I will then make them members (with edit rights) so they can update any content. Here are a couple “easy things” folks could do:
– Find and rate the “best of Techzing”
– Add your own review of the show
16. Len Jaffe says:
When did we start writing to slaves?
17. Justin says:
@Lenn – I have my reasons, that I don’t want to talk about on air. Wink wink, nudge nudge.
18. Jason says:
@Udi Mosayev – In regards to whether Iran is developing a nuclear weapon and whether they should be bombed just in case they are, I’d just like to point you to some additional sources.
1. It is the consensus view of the 16 U.S. intelligence agencies that Iran halted it’s nuclear weapons program in 2003.
http://articles.latimes.com/2012/feb/23/world/la-fg-iran-intel-20120224
2. In 1992, Netanyahu, claimed that Iran was three to five years from developing a nuclear bomb. It was a false statement then, and it’s a false statement now.
http://www.csmonitor.com/layout/set/print/World/Middle-East/2011/1108/Imminent-Iran-nuclear-threat-A-timeline-of-warnings-since-1979/Earliest-warnings-1979-84
3. While Israel refuses to confirm or deny anything about it’s nuclear weapons program, it is widely believed that Israel now has as many as 200 atomic warheads. Irony…?
http://www.haaretz.com/news/diplomacy-defense/barak-no-threat-to-israel-s-policy-of-nuclear-ambiguity-1.289438
4. Israel, like North Korea and Pakistan, is not a signatory of the NPT (Treaty on the Non-Proliferation of Nuclear Weapons). Iran, on the other hand, is a signatory of the NPT.
https://en.wikipedia.org/wiki/Treaty_on_the_Non-Proliferation_of_Nuclear_Weapons
5. Not only is Iran a signatory of the NPT, but in 2003 they signed the Additional Protocol on Nuclear Safeguards treaty. IAEA inspectors are all over Iran inspecting their nuclear material and facilities on a weekly basis. Even if Iranian leadership wanted to begin working on a nuclear bomb, they would have to kick the IAEA out of the country, which would obviously alert the world.
http://www.iaea.org/newscenter/news/2003/iranap20031218.html
6. Mohamed ElBaradei, the Nobel Peace Prize laureate who spent more than a decade as the director of the IAEA, said he had not “seen a shred of evidence” that Iran was pursuing the bomb, “I don’t believe Iran is a clear and present danger,” he said. “All I see is the hype about the threat posed by Iran.”
7. If Israel were to attempt to destroy Iran’s nuclear facilities, or somehow manage to head fake the U.S. into doing it for them, it would likely result in the deaths of hundreds of thousands of Iranian men, women and children. And if Israel decided to use nukes to achieve this (or if it escalated to that), those numbers would likely be in the millions. Israel, incidentally, would take quite a hit as well.
http://www.alternet.org/world/unimaginable-destruction-if-israel-did-attack-iran-nuclear-weapons
http://www.conflictandhealth.com/content/pdf/1752-1505-7-10.pdf
8. Don’t allow yourself to fall victim to the politics of fear. It’s how the US congress and population was manipulated into supporting an aggressive war against Iraq, which resulted in the deaths of over a million Iraqis and thousands of American and coalition soldiers, not to mention an unimaginable cost of $6 trillion dollars. http://en.wikipedia.org/wiki/Casualties_of_the_Iraq_War http://en.wikipedia.org/wiki/Financial_cost_of_the_Iraq_War 19. @Jason – I have little faith for world-wide organizations such as the UN and the committees it has, and IAEA.. its full of politics and it doesn’t reflect the truth at all. The fact Iran signed NPT means nothing to me, when time comes I’m sure Iran won’t care much. In 73′, Yom Kippur war, Egypt and Syria broke cease-fire agreements and crossed the line. They were signed on some peace of paper as well at that time. 2008: “…Today the reason for the Zionist regime’s existence is questioned, and this regime is on its way to annihilation 2011, “..like a cancer cell that spreads through the body, this regime infects any region. It must be removed from the body..” The guy who said it, and has many more statements against Israel and US, he may be “peaceful” regarding his nuclear activities now, maybe, but what makes you so sure that he won’t flip at the end? When he does, and he’ll use his weapons, how many will die then? Israel may or may not have nuclear weapon, but I’ve never heard any threats made by Israeli government officials to annihilate anyone. I have a feeling that if this nuclear yes/no rumor wasn’t out there, we would see more of what we had in 48′, 67′ and 73′. Sadly, I agree that having a bigger stick is the ultimate defense. Up until the point where the world believed Israel has nuclear power, israel suffered many annihilation attempts by its neighbors (although now we have much more terrorists to worry about and less wars, but still its an improvement of some sort). This situation reminds me a little on Yom Kippur war in 73′: In 73′, if Israel would attack first it won’t get any aid from US, Kissinger said so himself (Israel already had intel about the Egypt and Syria plans). Yom Kippur war is by far one of the most tragic wars to Israel. Another interesting fact about 73′ war: US plains were not allowed to land in any european country because the europeans were worried about their oil deals with Arab countries, lucky us… If this time is like back in 1973, the consequences are far grater and affect the entire world. For me the bottom line is that the small chance you’re wrong, we all pay the price. You have any doubts about Iran’s involvement in terror around the world? what do you think will happen once they’ll have their friendly peaceful nuclear power? For people who live in Israel this is a serious chance to take. Even if Iran won’t attack Israel, it’ll drag the entire region to nuclear armsrace (Iran has strong grip on Syria and Lebanon) and we’ll have a mexican standoff. I’ll look into the links you sent, thanks. 20. Jason says: @Tony – I don’t know what to tell you, man. 😉 Tesla is one of our story lines and when there’s a lot going on with the company, we’ll most likely talk about it. Also, in line with our radical transparency DNA, we’ll talk about it as if it was just the two of us discussing it over lunch, and that includes how our personal investments in the company have fared. 21. Jason says: @Udi Mosayev – This discussion has clearly devolved beyond the question of whether Iran is developing a nuclear weapon and into the realm of Israeli politics and belief. Since I can’t afford to get sucked into that debate and since I’m pretty sure that no one reading these comments (other than the two of us) is remotely interested in this subject, I think it’s best we drop it. We can take it up over lunch the next time you come to Pasadena. 😉 22. Jason says: @Philippe Monnet – Again, thanks so much for your help with the TechZing wiki. We really appreciate it. 23. Jason says: @Richard Garside – Yeah, it was too long for us as well. Did you see how long of a description I had to write? Screw that! For now on we’ll be sticking to the 90 minute format. 24. @Jason – yep, I was just telling Justin that its kinda useless, usually people waste a lot of energy and don’t convince each other anyway 🙂 25. Aaron says: Jason, glad the subdomains worked out as a clean solution for your secret project. Be on the look out for a sweet new app from your friend Mark (via me)! We’re getting started in the next few days. Thanks again for the recommendation, much appreciated. Aaron 26. Danilo Celic says: Feature creep for AnyFu based on your conversation about recording the conversation. Perhaps in addition to recommending recording, how about AnyFu facilitating the recording. Maybe you could use the Twilio API to initiate calls beween the expert and the customer and record the conversation and send the file (or provide a link, add to DropBox, whatever). Maybe even as a value-add:$1-5 to record to conversation added to your bill depending on the length of the call.
27. Hey Justin and Jason,
Could you do an episode where you go into detail about the do’s and don’t of an api that is going to be used for web and mobile applications.
I believe you are envisaging a series of ajax calls that return json. I know in a previous episode you debated how to handle security (does a user object get provided with every call ?)
A single discussion introducing the concept and main dos and don’ts would really interest me.
Do you know anyone on anyfu who would be good to talk to about this ? I have created my webapp without a documented, consistent api and I want to create one before I start mobile development.
Cheers
Sam
28. Jason says:
@Sam Howley – I don’t know if I could say much beyond what you might find from a Google search on the subject, but we can give it a shot.
We don’t have an API specific expert on AnyFu yet, but that’s a great idea!
29. You could also have a regular expression expert on AnyFu, he could even be available in 1/2 or even 1/4 hour increments 🙂
30. Jason says:
@Sam Howley – A 15-minute session just isn’t enough time to get much done, plus it doesn’t represent enough money to incentivize an expert to switch context, much less to rearrange their schedule.
31. Tony says:
@Tony – I don’t know what to tell you, man. 😉 Tesla is one of our story lines and when there’s a lot going on with the company, we’ll most likely talk about it
Jason, I enjoy “Tesla, the story” and all the company does. I’m specifically speaking to the weekly rehash of explaining to Justin where you bought in, where the stock is relevant to your average price, etc. Maybe it would be a good Wiki entry. lol 😉
32. @Tony, I just created an entry on the TechzingWiki for Tesla Motors: http://techzingwiki.com/doku.php?id=tesla_motors
33. Jason says:
@Philippe Monnet – You are the man! Thanks again for all of your work on the show wiki. 😉
34. Hey guys, good show for a relaxing drive to work (and back 😉 ) …
After hearing your plea for review contribution I decided to do it (“It will take 5 minutes…” I thought to myself…).
Can I just say that I now hate Itunes even more then before!
Here are couple of things that irritated me:
1. You got to have Itunes application to register an account in order to give a review…
I don’t use apple products, I don’t use Itunes, had to download huge Itunes application…
2. As I don’t won’t to do anything with Itunes (besides giving a review) I don’t want to give them my credit card info… -> Search google for “Creating Itunes Store account without a credit card”… Turnes out you need multi-step tutorial just for registering… Talk about customer satisfaction based user interface…
3. Won’t even get deeper into why I searched on Google for “example UK phone number…” and “example UK zip code…”. I know Apple is US company, but making so much obstacles just for an online account in 2013 is just ‘broken’…
At least I learned something from Itunes and apple – “How not to iritate users of your application”…
Ordeal lasted for almost half hour but I got my review in and I wish you guys all the best !
ps. Only 22 reviews ? I thought you would have hundreds by now ? You should beg for more every episode 😉
35. rou1i says:
@Jason
Mohamed ElBaradei, the Nobel Peace Prize laureate who spent more than a decade as the director of the IAEA …
Just find it funny that you of all people would fall for a plead to authority 🙂
(full disclosure – I’m an Israeli, but this doesn’t matter, I think …)
36. Alfie says:
@rou1i: Mohamed ElBaradei was the Directors General of the IAEA. One of their jobs is to find evidence of nuclear weapons. They didn’t find any. If there are others who say they have an expansive program, the onus is on them. You know, with proof and stuff.
As for the fallacy, it would have been a plead to authority if Michael Jordan said Iran doesn’t have nuclear weapons.
37. rou1i says:
@Alfie
I fully agree with your first point (onus and such).
Not sure if it isn’t an appeal to authority (https://yourlogicalfallacyis.com/appeal-to-authority). Otherwise, I could have said that top Israeli generals believe that Iran has a military nuclear program, and it is also their job to find such evidence (well, in a less diplomatic way :)).
38. Matt S says:
Tech….zing…..withdrawl…..
Must….have…..new…..episode…….
;-D
39. Jason says:
@rou1i – For all practical purposes it’s virtually impossible to make any kind of a judgement about a geopolitical issue without relying on the opinions of experts simply due to the sheer vastness and inaccessibility of the primary source data. And yes, while citing an expert’s opinion is technically a logical fallacy in the context of a deductive argument, it is entirely proper to use it in the context of an inductive argument. In other words, while relying on an expert doesn’t guarantee that an argument is correct it is a question of probabilities. The expert is far more likely to be correct than the layperson.
So, the question then becomes – who’s an expert on the existence, or non-existence, of an Iranian nuclear weapons program? I would claim that a man who served as the director of the IAEA for over a decade clearly qualifies as such, while an Israeli military general (as you suggest), whose primary expertise is the prosecution of war and not the analysis of nuclear material and facilities, clearly does not. But then I’m also stacking the odds by not resting my argument purely on ElBaradei’s conclusion, but also on the conclusion of other experts, like that of the 16 U.S. intelligence agencies whose consensus view is that Iran halted it’s nuclear weapons program in 2003. http://articles.latimes.com/2012/feb/23/world/la-fg-iran-intel-20120224.
Now that I’ve wasted even more time (which I don’t have) on an argument that hardly anyone is going to read and even fewer people are going to care about, I’m going to end it here. Any additional comments on this subject will not be approved. Let’s get back to work, people!! 😉
40. Jason says:
@Vladimir Janković – Thanks so much for going to all the trouble. You’re right, we really do need to beg for some more reviews. 😉
41. Jason says:
@Matt S – We should have it posted tomorrow. I just need to finish up the notes.
42. Andrea says:
I think I speak for all the listeners when I say
:””””””””””””””””””””””””(
43. Jason says:
@Andrea The new show is live! The delay in posting was my fault. Sorry guys.
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# Limits preserve weak inequalities
Does anyone have a quick way to show that if $f(x)$ tends to a limit A as $x$ tends to $0$, and $f(x) \geq 0$ then $A \geq 0$?
Thanks
$|f(x)-A|<\epsilon \Rightarrow A-\epsilon < f(x) < A+\epsilon$
If $A<0$ then choose $\epsilon$ less than $|A|$ which forces $f(x)<0$.
Let if possible $A<0$
Then $-A>0$
As $f(x)\to A$ as $x\to 0$ so $\forall \epsilon>0 \exists \delta>0$ such that $|f(x)-A|<\epsilon$ for all $x$ with$|x|<\delta$
Take $\epsilon=-A/2$
Then we have $|f(x)-A|<-A/2\Rightarrow 3A/2<f(x)<A/2<0$ for all $|x|<\delta_A$ This is a contradiction.So $A\ge 0$
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# HD 206860
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Spectral synthesis analysis and radial velocity study of the northern F-, G- and K-type flare starsIn this paper, we present a study of the general physical and chemicalproperties and radial velocity monitoring of young active stars. Wederive temperatures, logg, [Fe/H], v sini and Rspec valuesfor eight stars. The detailed analysis reveals that the stars are nothomogeneous in their principal physical parameters or in the agedistribution. In 4/5, we found a periodic radial velocity signal whichoriginates in surface features; the fifth is surprisingly inactive andshows little variation. The Nearest Young Moving GroupsThe latest results in the research of forming planetary systems have ledseveral authors to compile a sample of candidates for searching forplanets in the vicinity of the Sun. Young stellar associations areindeed excellent laboratories for this study, but some of them are notclose enough to allow the detection of planets through adaptive opticstechniques. However, the existence of very close young moving groups cansolve this problem. Here we have compiled the members of the nearestyoung moving groups, as well as a list of new candidates from ourcatalog of late-type stars that are possible members of young stellarkinematic groups, studying their membership through spectroscopic andphotometric criteria. IRS Spectra of Solar-Type Stars: A Search for Asteroid Belt AnalogsWe report the results of a spectroscopic search for debris diskssurrounding 41 nearby solar-type stars, including eight planet-bearingstars, using the Infrared Spectrometer (IRS) on the Spitzer SpaceTelescope. With the accurate relative photometry of the IRS between 7and 34 μm we are able to look for excesses as small as ~2% ofphotospheric levels, with particular sensitivity to weak spectralfeatures. For stars with no excess, the 3 σ upper limit in a bandat 30-34 μm corresponds to ~75 times the brightness of our zodiacaldust cloud. Comparable limits at 8.5-13 μm correspond to ~1400 timesthe brightness of our zodiacal dust cloud. These limits correspond tomaterial located within the <1 to ~5 AU region that, in our solarsystem, originates predominantly from debris associated with theasteroid belt. We find excess emission longward of ~25 μm from fivestars, of which four also show excess emission at 70 μm. Thisemitting dust must be located in a region starting around 5-10 AU. Onestar has 70 μm emission but no IRS excess. In this case, the emittingregion must begin outside 10 AU; this star has a known radial velocityplanet. Only two stars of the five show emission shortward of 25 μm,where spectral features reveal the presence of a population of small,hot dust grains emitting in the 7-20 μm band. One of these stars, HD72905, is quite young (300 Myr), while the other, HD 69830, is olderthan 2 Gyr. The data presented here strengthen the results of previousstudies to show that excesses at 25 μm and shorter are rare: only 1out of 40 stars older than 1 Gyr or ~2.5% shows an excess. Asteroidbelts 10-30 times more massive than our own appear are rare amongmature, solar-type stars. Frequency of Debris Disks around Solar-Type Stars: First Results from a Spitzer MIPS SurveyWe have searched for infrared excesses around a well-defined sample of69 FGK main-sequence field stars. These stars were selected withoutregard to their age, metallicity, or any previous detection of IRexcess; they have a median age of ~4 Gyr. We have detected 70 μmexcesses around seven stars at the 3 σ confidence level. Thisextra emission is produced by cool material (<100 K) located beyond10 AU, well outside the habitable zones'' of these systems andconsistent with the presence of Kuiper Belt analogs with ~100 times moreemitting surface area than in our own planetary system. Only one star,HD 69830, shows excess emission at 24 μm, corresponding to dust withtemperatures >~300 K located inside of 1 AU. While debris disks withLdust/L*>=10-3 are rare around oldFGK stars, we find that the disk frequency increases from 2%+/-2% forLdust/L*>=10-4 to 12%+/-5% forLdust/L*>=10-5. This trend in thedisk luminosity distribution is consistent with the estimated dust inour solar system being within an order of magnitude greater or less thanthe typical level around similar nearby stars. Although there is nocorrelation of IR excess with metallicity or spectral type, there is aweak correlation with stellar age, with stars younger than a gigayearmore likely to have excess emission. Spectroscopic Properties of Cool Stars (SPOCS). I. 1040 F, G, and K Dwarfs from Keck, Lick, and AAT Planet Search ProgramsWe present a uniform catalog of stellar properties for 1040 nearby F, G,and K stars that have been observed by the Keck, Lick, and AAT planetsearch programs. Fitting observed echelle spectra with synthetic spectrayielded effective temperature, surface gravity, metallicity, projectedrotational velocity, and abundances of the elements Na, Si, Ti, Fe, andNi, for every star in the catalog. Combining V-band photometry andHipparcos parallaxes with a bolometric correction based on thespectroscopic results yielded stellar luminosity, radius, and mass.Interpolating Yonsei-Yale isochrones to the luminosity, effectivetemperature, metallicity, and α-element enhancement of each staryielded a theoretical mass, radius, gravity, and age range for moststars in the catalog. Automated tools provide uniform results and makeanalysis of such a large sample practical. Our analysis method differsfrom traditional abundance analyses in that we fit the observed spectrumdirectly, rather than trying to match equivalent widths, and wedetermine effective temperature and surface gravity from the spectrumitself, rather than adopting values based on measured photometry orparallax. As part of our analysis, we determined a new relationshipbetween macroturbulence and effective temperature on the main sequence.Detailed error analysis revealed small systematic offsets with respectto the Sun and spurious abundance trends as a function of effectivetemperature that would be inobvious in smaller samples. We attempted toremove these errors by applying empirical corrections, achieving aprecision per spectrum of 44 K in effective temperature, 0.03 dex inmetallicity, 0.06 dex in the logarithm of gravity, and 0.5 kms-1 in projected rotational velocity. Comparisons withprevious studies show only small discrepancies. Our spectroscopicallydetermined masses have a median fractional precision of 15%, but theyare systematically 10% higher than masses obtained by interpolatingisochrones. Our spectroscopic radii have a median fractional precisionof 3%. Our ages from isochrones have a precision that variesdramatically with location in the Hertzsprung-Russell diagram. We planto extend the catalog by applying our automated analysis technique toother large stellar samples. Stellar Coronal Abundances at Intermediate-Activity Levels: ξ UMaWe present an analysis of Chandra High Energy Transmission Grating(HETG) spectra of the corona of the critical intermediate-activity,quadruple stellar system ξ UMa. Using the maximum A/B subsystemseparation in 2001, we attempted to resolve for the first time in X-raysthe two components using the HETG Medium Energy Grating (MEG). We foundthe Aa component of the system to be at least 2 orders of magnitudefainter than the Bb component. We used the Markov Chain Monte Carlomethod to reconstruct differential emission measures (DEMs) andabundances and discuss first ionization potential (FIP) issues. Thereconstructed DEMs showed two pronounced peaks at logT~6.5 and logT~7.0K, respectively, similar to brighter solar active regions. A plot ofcoronal abundances, with respect to stellar photospheric, versus FIPreveals that the FIP behavior of ξ UMa is intermediate between lessand more active stars, commensurate with its X-ray luminosity. Theabundances of Mg, Fe, and Si are just subsolar, with Fe having thelowest abundance of these. The low-FIP elements Na and Al have similarabundances, and they are both higher than the Mg, Fe, and Si group. Theabundances show a minimum at S, rising gradually to Ne, which is higherthan photospheric, as has been seen by other authors on similar stars.Some of the FIP behavior seen here is predicted by the new ponderomotiveforce model of Laming. The Planet-Metallicity CorrelationWe have recently carried out spectral synthesis modeling to determineTeff, logg, vsini, and [Fe/H] for 1040 FGK-type stars on theKeck, Lick, and Anglo-Australian Telescope planet search programs. Thisis the first time that a single, uniform spectroscopic analysis has beenmade for every star on a large Doppler planet search survey. We identifya subset of 850 stars that have Doppler observations sufficient todetect uniformly all planets with radial velocity semiamplitudes K>30m s-1 and orbital periods shorter than 4 yr. From this subsetof stars, we determine that fewer than 3% of stars with-0.5<[Fe/H]<0.0 have Doppler-detected planets. Above solarmetallicity, there is a smooth and rapid rise in the fraction of starswith planets. At [Fe/H]>+0.3 dex, 25% of observed stars have detectedgas giant planets. A power-law fit to these data relates the formationprobability for gas giant planets to the square of the number of metalatoms. High stellar metallicity also appears to be correlated with thepresence of multiple-planet systems and with the total detected planetmass. This data set was examined to better understand the origin of highmetallicity in stars with planets. None of the expected fossilsignatures of accretion are observed in stars with planets relative tothe general sample: (1) metallicity does not appear to increase as themass of the convective envelopes decreases, (2) subgiants with planetsdo not show dilution of metallicity, (3) no abundance variations for Na,Si, Ti, or Ni are found as a function of condensation temperature, and(4) no correlations between metallicity and orbital period oreccentricity could be identified. We conclude that stars with extrasolarplanets do not have an accretion signature that distinguishes them fromother stars; more likely, they are simply born in higher metallicitymolecular clouds.Based on observations obtained at Lick and Keck Observatories, operatedby the University of California, and the Anglo-Australian Observatories. Search for Variability in the Equivalent Width of the HeI D3 Spectrum Line in Several Stars of Later Spectral TypeHigh resolution spectra with a high signal/noise ratio have beenobtained in the region of the HeI D line for 13 dwarfs of spectral typesA5 through K0. The variability in the equivalent width of this spectrumline was studied for five of these stars over a period of severalhundred days. Significant variability was observed for only one of thesestars, θ Cyg. Abundance trends in kinematical groups of the Milky Way's diskWe have compiled a large catalogue of metallicities and abundance ratiosfrom the literature in order to investigate abundance trends of severalalpha and iron peak elements in the thin disk and the thick disk of theGalaxy. The catalogue includes 743 stars with abundances of Fe, O, Mg,Ca, Ti, Si, Na, Ni and Al in the metallicity range -1.30 < [Fe/H]< +0.50. We have checked that systematic differences betweenabundances measured in the different studies were lower than randomerrors before combining them. Accurate distances and proper motions fromHipparcos and radial velocities from several sources have been retreivedfor 639 stars and their velocities (U, V, W) and galactic orbits havebeen computed. Ages of 322 stars have been estimated with a Bayesianmethod of isochrone fitting. Two samples kinematically representative ofthe thin and thick disks have been selected, taking into account theHercules stream which is intermediate in kinematics, but with a probabledynamical origin. Our results show that the two disks are chemicallywell separated, they overlap greatly in metallicity and both showparallel decreasing alpha elements with increasing metallicity, in theinterval -0.80 < [Fe/H] < -0.30. The Mg enhancement with respectto Fe of the thick disk is measured to be 0.14 dex. An even largerenhancement is observed for Al. The thick disk is clearly older than thethin disk with tentative evidence of an AMR over 2-3 Gyr and a hiatus instar formation before the formation of the thin disk. We do not observea vertical gradient in the metallicity of the thick disk. The Herculesstream has properties similar to that of the thin disk, with a widerrange of metallicity. Metal-rich stars assigned to the thick disk andsuper-metal-rich stars assigned to the thin disk appear as outliers inall their properties. Photometric periods of HN Peg from multichannel analysisWe applied the method of three-stage weighted multichannel periodanalysis (MPA) to photometric observations of HN Peg obtained in1992-99. We detected two periods: the longer one stayed almost constantnear 5.5 d but appeared only during the observing seasons in 1993-98,while the shorter one was present for all observing seasons, havingfluctuations within . If the two periods are interpreted as caused bydifferential rotation, we may have detected two distinct latitude zonesof spot activity, one where spots were confined to within a very narrowrange of latitude, and another where the latitude range may be somewhatbroader. The existence of two latitude zones of activity in this youngsolar analogue closely matches what is seen in the Sun. However, thepresence of two periods may also be caused by long-lived active areasmoving in longitude. We use HN Peg as a test case for our new MPAstatistical method. Because of the limited quality of the data and thecomplexity of stellar activity our results are tentative, leaving spacealso for other interpretations.Based on observations collected at the Mt. Maidanak (Uzbekistan) andFairborn (USA) observatories. Lithium abundances of the local thin disc starsLithium abundances are presented for a sample of 181 nearby F and Gdwarfs with accurate Hipparcos parallaxes. The stars are on circularorbits about the Galactic centre and, hence, are identified as belongingto the thin disc. This sample is combined with two published surveys toprovide a catalogue of lithium abundances, metallicities ([Fe/H]),masses, and ages for 451 F-G dwarfs, almost all belonging to the thindisc. The lithium abundances are compared and contrasted with publishedlithium abundances for F and G stars in local open clusters. The fieldstars span a larger range in [Fe/H] than the clusters for which [Fe/H]~=0.0 +/- 0.2. The initial (i.e. interstellar) lithium abundance of thesolar neighbourhood, as derived from stars for which astration oflithium is believed to be unimportant, is traced from logɛ(Li) =2.2 at [Fe/H]=-1 to logɛ(Li) = 3.2 at +0.1. This form for theevolution is dependent on the assumption that astration of lithium isnegligible for the stars defining the relation. An argument is advancedthat this latter assumption may not be entirely correct, and, theevolution of lithium with [Fe/H] may be flatter than previouslysupposed. A sharp Hyades-like Li dip is not seen among the field starsand appears to be replaced by a large spread among lithium abundances ofstars more massive than the lower mass limit of the dip. Astration oflithium by stars of masses too low to participate in the Li dip isdiscussed. These stars show little to no spread in lithium abundance ata given [Fe/H] and mass. Synthetic Lick Indices and Detection of α-enhanced Stars. II. F, G, and K Stars in the -1.0 < [Fe/H] < +0.50 RangeWe present an analysis of 402 F, G, and K solar neighborhood stars, withaccurate estimates of [Fe/H] in the range -1.0 to +0.5 dex, aimed at thedetection of α-enhanced stars and at the investigation of theirkinematical properties. The analysis is based on the comparison of 571sets of spectral indices in the Lick/IDS system, coming from fourdifferent observational data sets, with synthetic indices computed withsolar-scaled abundances and with α-element enhancement. We useselected combinations of indices to single out α-enhanced starswithout requiring previous knowledge of their main atmosphericparameters. By applying this approach to the total data set, we obtain alist of 60 bona fide α-enhanced stars and of 146 stars withsolar-scaled abundances. The properties of the detected α-enhancedand solar-scaled abundance stars with respect to their [Fe/H] values andkinematics are presented. A clear kinematic distinction betweensolar-scaled and α-enhanced stars was found, although a one-to-onecorrespondence to thin disk'' and thick disk'' components cannot besupported with the present data. Nearby stars of the Galactic disk and halo. III.High-resolution spectroscopic observations of about 150 nearby stars orstar systems are presented and discussed. The study of these and another100 objects of the previous papers of this series implies that theGalaxy became reality 13 or 14 Gyr ago with the implementation of amassive, rotationally-supported population of thick-disk stars. The veryhigh star formation rate in that phase gave rise to a rapid metalenrichment and an expulsion of gas in supernovae-driven Galactic winds,but was followed by a star formation gap for no less than three billionyears at the Sun's galactocentric distance. In a second phase, then, thethin disk - our familiar Milky Way'' - came on stage. Nowadays ittraces the bright side of the Galaxy, but it is also embedded in a hugecoffin of dead thick-disk stars that account for a large amount ofbaryonic dark matter. As opposed to this, cold-dark-matter-dominatedcosmologies that suggest a more gradual hierarchical buildup throughmergers of minor structures, though popular, are a poor description forthe Milky Way Galaxy - and by inference many other spirals as well - if,as the sample implies, the fossil records of its long-lived stars do notstick to this paradigm. Apart from this general picture that emergeswith reference to the entire sample stars, a good deal of the presentwork is however also concerned with detailed discussions of manyindividual objects. Among the most interesting we mention the bluestraggler or merger candidates HD 165401 and HD 137763/HD 137778, thelikely accretion of a giant planet or brown dwarf on 59 Vir in itsrecent history, and HD 63433 that proves to be a young solar analog at\tau200 Myr. Likewise, the secondary to HR 4867, formerly suspectednon-single from the Hipparcos astrometry, is directly detectable in thehigh-resolution spectroscopic tracings, whereas the visual binary \chiCet is instead at least triple, and presumably even quadruple. Withrespect to the nearby young stars a complete account of the Ursa MajorAssociation is presented, and we provide as well plain evidence foranother, the Hercules-Lyra Association'', the likely existence ofwhich was only realized in recent years. On account of its rotation,chemistry, and age we do confirm that the Sun is very typical among itsG-type neighbors; as to its kinematics, it appears however not unlikelythat the Sun's known low peculiar space velocity could indeed be thecause for the weak paleontological record of mass extinctions and majorimpact events on our parent planet during the most recent Galactic planepassage of the solar system. Although the significance of thiscorrelation certainly remains a matter of debate for years to come, wepoint in this context to the principal importance of the thick disk fora complete census with respect to the local surface and volumedensities. Other important effects that can be ascribed to this darkstellar population comprise (i) the observed plateau in the shape of theluminosity function of the local FGK stars, (ii) a small thoughsystematic effect on the basic solar motion, (iii) a reassessment of theterm asymmetrical drift velocity'' for the remainder (i.e. the thindisk) of the stellar objects, (iv) its ability to account for the bulkof the recently discovered high-velocity blue white dwarfs, (v) itsmajor contribution to the Sun's 220 km s-1 rotationalvelocity around the Galactic center, and (vi) the significant flatteningthat it imposes on the Milky Way's rotation curve. Finally we note ahigh multiplicity fraction in the small but volume-complete local sampleof stars of this ancient population. This in turn is highly suggestivefor a star formation scenario wherein the few existing single stellarobjects might only arise from either late mergers or the dynamicalejection of former triple or higher level star systems. Stellar Chemical Signatures and Hierarchical Galaxy FormationTo compare the chemistries of stars in the Milky Way dwarf spheroidal(dSph) satellite galaxies with stars in the Galaxy, we have compiled alarge sample of Galactic stellar abundances from the literature. Whenkinematic information is available, we have assigned the stars tostandard Galactic components through Bayesian classification based onGaussian velocity ellipsoids. As found in previous studies, the[α/Fe] ratios of most stars in the dSph galaxies are generallylower than similar metallicity Galactic stars in this extended sample.Our kinematically selected stars confirm this for the Galactic halo,thin-disk, and thick-disk components. There is marginal overlap in thelow [α/Fe] ratios between dSph stars and Galactic halo stars onextreme retrograde orbits (V<-420 km s-1), but this is notsupported by other element ratios. Other element ratios compared in thispaper include r- and s-process abundances, where we find a significantoffset in the [Y/Fe] ratios, which results in a large overabundance in[Ba/Y] in most dSph stars compared with Galactic stars. Thus, thechemical signatures of most of the dSph stars are distinct from thestars in each of the kinematic components of the Galaxy. This resultrules out continuous merging of low-mass galaxies similar to these dSphsatellites during the formation of the Galaxy. However, we do not ruleout very early merging of low-mass dwarf galaxies, since up to one-halfof the most metal-poor stars ([Fe/H]<=-1.8) have chemistries that arein fair agreement with Galactic halo stars. We also do not rule outmerging with higher mass galaxies, although we note that the LMC and theremnants of the Sgr dwarf galaxy are also chemically distinct from themajority of the Galactic halo stars. Formation of the Galaxy's thickdisk by heating of an old thin disk during a merger is also not ruledout; however, the Galaxy's thick disk itself cannot be comprised of theremnants from a low-mass (dSph) dwarf galaxy, nor of a high-mass dwarfgalaxy like the LMC or Sgr, because of differences in chemistry.The new and independent environments offered by the dSph galaxies alsoallow us to examine fundamental assumptions related to thenucleosynthesis of the elements. The metal-poor stars ([Fe/H]<=-1.8)in the dSph galaxies appear to have lower [Ca/Fe] and [Ti/Fe] than[Mg/Fe] ratios, unlike similar metallicity stars in the Galaxy.Predictions from the α-process (α-rich freeze-out) would beconsistent with this result if there have been a lack of hypernovae indSph galaxies. The α-process could also be responsible for thevery low Y abundances in the metal-poor stars in dSph's; since [La/Eu](and possibly [Ba/Eu]) are consistent with pure r-process results, thelow [Y/Eu] suggests a separate r-process site for this light(first-peak) r-process element. We also discuss SNe II rates and yieldsas other alternatives, however. In stars with higher metallicities([Fe/H]>=-1.8), contributions from the s-process are expected; [(Y,La, and Ba)/Eu] all rise as expected, and yet [Ba/Y] is still muchhigher in the dSph stars than similar metallicity Galactic stars. Thisresult is consistent with s-process contributions from lower metallicityAGB stars in dSph galaxies, and is in good agreement with the slowerchemical evolution expected in the low-mass dSph galaxies relative tothe Galaxy, such that the build-up of metals occurs over much longertimescales. Future investigations of nucleosynthetic constraints (aswell as galaxy formation and evolution) will require an examination ofmany stars within individual dwarf galaxies.Finally, the Na-Ni trend reported in 1997 by Nissen & Schuster isconfirmed in Galactic halo stars, but we discuss this in terms of thegeneral nucleosynthesis of neutron-rich elements. We do not confirm thatthe Na-Ni trend is related to the accretion of dSph galaxies in theGalactic halo. The Brown Dwarf Desert at 75-1200 AUWe present results of a comprehensive infrared coronagraphic search forsubstellar companions to nearby stars. The research consisted of (1) a178-star survey at Steward and Lick observatories, with opticalfollow-up from Keck Observatory, capable of detecting companions withmasses greater than 30 MJ, and semimajor axes between about140 to 1200 AU; (2) a 102-star survey using the Keck Telescope, capableof detecting extrasolar brown dwarfs and planets typically more massivethan 10 MJ, with semimajor axes between about 75 and 300 AU.Only one brown dwarf companion was detected, and no planets. Thefrequency of brown dwarf companions to G, K, and M stars orbitingbetween 75 and 300 AU is measured to be 1%+/-1%, the most precisemeasurement of this quantity to date. The frequency of massive (greaterthan 30 MJ) brown dwarf companions at 120-1200 AU is found tobe f=0.7%+/-0.7%. The frequency of giant planet companions with massesbetween 5 and 10 MJ orbiting between 75 and 300 AU ismeasured here for the first time to be no more than ~3%. Together withother surveys that encompass a wide range of orbital separations, theseresults imply that substellar objects with masses between 12 and 75MJ form only rarely as companions to stars. Theories of starformation that could explain these data are only now beginning toemerge. Erratum: Magnetic activity of six young solar analogues II. Surface Differential Rotation from long-term photometryNot Available On the determination of oxygen abundances in chromospherically active starsWe discuss oxygen abundances derived from [O I] λ6300s and the OI triplet in stars spanning a wide range in chromospheric activitylevel, and show that these two indicators yield increasingly discrepantresults with higher chromospheric/coronal activity measures. While theforbidden and permitted lines give fairly consistent results forsolar-type disk dwarfs, spuriously high O I triplet abundances areobserved in young Hyades and Pleiades stars, as well as in individualcomponents of RS CVn binaries (up to 1.8 dex). The distinct behaviour ofthe [O I]-based abundances which consistently remain near-solar suggeststhat this phenomenon mostly results from large departures from LTEaffecting the O I triplet at high activity level that are currentlyunaccounted for, but also possibly from a failure to adequately modelthe atmospheres of K-type stars. These results suggest that some cautionshould be exercised when interpreting oxygen abundances in activebinaries or young open cluster stars.Based on observations collected at the European Southern Observatory,Chile (Proposals 64.L-0249 and 071.D-0260).Table \ref{tab_data} is only available in electronic form athttp://www.edpsciences.org Chemical enrichment and star formation in the Milky Way disk. III. Chemodynamical constraintsIn this paper, we investigate some chemokinematical properties of theMilky Way disk, by using a sample composed by 424 late-type dwarfs. Weshow that the velocity dispersion of a stellar group correlates with theage of this group, according to a law proportional to t0.26,where t is the age of the stellar group. The temporal evolution of thevertex deviation is considered in detail. It is shown that the vertexdeviation does not seem to depend strongly on the age of the stellargroup. Previous studies in the literature seem to not have found it dueto the use of statistical ages for stellar groups, rather thanindividual ages. The possibility to use the orbital parameters of a starto derive information about its birthplace is investigated, and we showthat the mean galactocentric radius is likely to be the most reliablestellar birthplace indicator. However, this information cannot bepresently used to derive radial evolutionary constraints, due to anintrinsic bias present in all samples constructed from nearby stars. Anextensive discussion of the secular and stochastic heating mechanismscommonly invoked to explain the age-velocity dispersion relation ispresented. We suggest that the age-velocity dispersion relation couldreflect the gradual decrease in the turbulent velocity dispersion fromwhich disk stars form, a suggestion originally made by Tinsley &Larson (\cite{tinsley}, ApJ, 221, 554) and supported by several morerecent disk evolution calculations. A test to distinguish between thetwo types of models using high-redshift galaxies is proposed.Full Table 1 is only available in electronic form at the CDS viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/423/517 The Geneva-Copenhagen survey of the Solar neighbourhood. Ages, metallicities, and kinematic properties of 14 000 F and G dwarfsWe present and discuss new determinations of metallicity, rotation, age,kinematics, and Galactic orbits for a complete, magnitude-limited, andkinematically unbiased sample of 16 682 nearby F and G dwarf stars. Our63 000 new, accurate radial-velocity observations for nearly 13 500stars allow identification of most of the binary stars in the sampleand, together with published uvbyβ photometry, Hipparcosparallaxes, Tycho-2 proper motions, and a few earlier radial velocities,complete the kinematic information for 14 139 stars. These high-qualityvelocity data are supplemented by effective temperatures andmetallicities newly derived from recent and/or revised calibrations. Theremaining stars either lack Hipparcos data or have fast rotation. Amajor effort has been devoted to the determination of new isochrone agesfor all stars for which this is possible. Particular attention has beengiven to a realistic treatment of statistical biases and errorestimates, as standard techniques tend to underestimate these effectsand introduce spurious features in the age distributions. Our ages agreewell with those by Edvardsson et al. (\cite{edv93}), despite severalastrophysical and computational improvements since then. We demonstrate,however, how strong observational and theoretical biases cause thedistribution of the observed ages to be very different from that of thetrue age distribution of the sample. Among the many basic relations ofthe Galactic disk that can be reinvestigated from the data presentedhere, we revisit the metallicity distribution of the G dwarfs and theage-metallicity, age-velocity, and metallicity-velocity relations of theSolar neighbourhood. Our first results confirm the lack of metal-poor Gdwarfs relative to closed-box model predictions (the G dwarfproblem''), the existence of radial metallicity gradients in the disk,the small change in mean metallicity of the thin disk since itsformation and the substantial scatter in metallicity at all ages, andthe continuing kinematic heating of the thin disk with an efficiencyconsistent with that expected for a combination of spiral arms and giantmolecular clouds. Distinct features in the distribution of the Vcomponent of the space motion are extended in age and metallicity,corresponding to the effects of stochastic spiral waves rather thanclassical moving groups, and may complicate the identification ofthick-disk stars from kinematic criteria. More advanced analyses of thisrich material will require careful simulations of the selection criteriafor the sample and the distribution of observational errors.Based on observations made with the Danish 1.5-m telescope at ESO, LaSilla, Chile, and with the Swiss 1-m telescope at Observatoire deHaute-Provence, France.Complete Tables 1 and 2 are only available in electronic form at the CDSvia anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/418/989 Some anomalies in the occurrence of debris discs around main-sequence A and G starsDebris discs consist of large dust grains that are generated bycollisions of comets or asteroids around main-sequence stars, and thequantity and distribution of debris may be used to detect the presenceof perturbing planets akin to Neptune. We use stellar and disc surveysto compare the material seen around A- and G-type main-sequence stars.Debris is detected much more commonly towards A stars, even when acomparison is made only with G stars of comparable age. Detection ratesare consistent with disc durations of ~0.5 Gyr, which may occur at anytime during the main sequence. The higher detection rate for A stars canresult from this duration being a larger fraction of the main-sequencelifetime, possibly boosted by a globally slightly larger disc mass thanfor the G-type counterparts. The disc mass range at any given age is afactor of at least ~100 and any systematic decline with time is slow,with a power law estimated to not be steeper than t-1/2.Comparison with models shows that dust can be expected as late as a fewGyr when perturbing planetesimals form slowly at large orbital radii.Currently, the Solar system has little dust because the radius of theKuiper Belt is small and hence the time-scale to produce planetesimalswas less than 1 Gyr. However, the apparently constant duration of ~0.5Gyr when dust is visible is not predicted by the models. Improved Astrometry and Photometry for the Luyten Catalog. II. Faint Stars and the Revised CatalogWe complete construction of a catalog containing improved astrometry andnew optical/infrared photometry for the vast majority of NLTT starslying in the overlap of regions covered by POSS I and by the secondincremental Two Micron All Sky Survey (2MASS) release, approximately 44%of the sky. The epoch 2000 positions are typically accurate to 130 mas,the proper motions to 5.5 mas yr-1, and the V-J colors to0.25 mag. Relative proper motions of binary components are measured to 3mas yr-1. The false-identification rate is ~1% for11<~V<~18 and substantially less at brighter magnitudes. Theseimprovements permit the construction of a reduced proper-motion diagramthat, for the first time, allows one to classify NLTT stars intomain-sequence (MS) stars, subdwarfs (SDs), and white dwarfs (WDs). We inturn use this diagram to analyze the properties of both our catalog andthe NLTT catalog on which it is based. In sharp contrast to popularbelief, we find that NLTT incompleteness in the plane is almostcompletely concentrated in MS stars, and that SDs and WDs are detectedalmost uniformly over the sky δ>-33deg. Our catalogwill therefore provide a powerful tool to probe these populationsstatistically, as well as to reliably identify individual SDs and WDs. Contributions to the Nearby Stars (NStars) Project: Spectroscopy of Stars Earlier than M0 within 40 Parsecs: The Northern Sample. I.We have embarked on a project, under the aegis of the Nearby Stars(NStars)/Space Interferometry Mission Preparatory Science Program, toobtain spectra, spectral types, and, where feasible, basic physicalparameters for the 3600 dwarf and giant stars earlier than M0 within 40pc of the Sun. In this paper, we report on the results of this projectfor the first 664 stars in the northern hemisphere. These resultsinclude precise, homogeneous spectral types, basic physical parameters(including the effective temperature, surface gravity, and overallmetallicity [M/H]), and measures of the chromospheric activity of ourprogram stars. Observed and derived data presented in this paper arealso available on the project's Web site. Dependence of coronal X-ray emission on spot-induced brightness variations in cool main sequence starsThe maximum amplitude (Amax) of spot-induced brightnessvariations from long-term V-band photometry and the ratioLX/Lbol between X-ray and bolometric luminositiesare suitable indicators of the level of magnetic activity in thephotosphere and in the corona of late-type stars, respectively. By usingthese activity indicators we investigate the dependence of coronal X-rayemission on the level of photospheric starspot activity in a homogeneoussample of low mass main sequence field and cluster stars of differentages (IC 2602, IC 4665,IC 2391, alpha Persei,Pleiades and Hyades). First, theactivity-rotation connection at the photospheric level is re-analysed,as well as its dependence on spectral type and age. The upper envelopeof Amax increases monotonically with decreasing rotationalperiod (P) and Rossby number (R0) showing a break around 1.1d that separates two rotation regimes where the starspot activity showsdifferent behaviours. The Amax-P andAmax-R0 relations are fitted with linear,exponential and power laws to look for the function which bestrepresents the trend of the data. The highest values of Amaxare found among K-type stars and at the ages of alphaPersei and Pleiades. We also analyse theactivity-rotation connection at the coronal level as well as itsdependence on spectral type. The level of X-ray emission increases withincreasing rotation rate up to a saturation level. The rotational periodat which saturation occurs is colour-dependent and increases withadvancing spectral type. Also the LX/Lbol-P andLX/Lbol-R0 relations are fitted withlinear, exponential and power laws to look for the best fittingfunction. Among the fastest rotating stars (P<=0.3 d) there isevidence of super-saturation. Also the highest values ofLXLbol are found among K-type stars. Finally, thephotospheric-coronal activity connection is investigated by using forthe first time the largest ever sample of light curve amplitudes asindicators of the magnetic filling factor. The activity parametersLX/Lbol and Amax are found to becorrelated with each other, thus confirming the dependence of coronalactivity on photospheric magnetic fields. More precisely, theLX/Lbol-Amax distribution shows thepresence of an upper envelope, which is constant at theLX/Lbol =~ -3.0 saturation level, and of a lowerenvelope. The best fit to the lower envelope is given by a power lawwith steepness decreasing from F-G to M spectral types. However, it isconsidered a tentative result, since the fit reduced chi-squares arelarge. Such spectral-type dependence may be related to a colourdependence of Amax on the total starspot filling factor, aswell as to the coronal emission being possibly more sensitive tostarspot activity variations in F- and G-type than in M-type stars. TheLX/Lbol-Amax mean values for eachcluster in our sample decrease monotonically with increasing age,showing that the levels of photospheric and coronal activity evolve intime according to a single power law till the Sun's age.Tables of the photometric and X-ray data sets are only available inelectronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr(130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/410/671 Magnetic activity of six young solar analogues II. Surface Differential Rotation from long-term photometryThe present paper is the second of a series dedicated to the study ofthe magnetic activity in a selected sample of young solar analogues. Thesample includes five single G0-G5V stars with ages between =~ 130 Myrand 700 Myr: EK Dra, pi 1 UMa,HN Peg, k1 Cet and BECet. In this study we also include the Pleiades-age ( =~ 130Myr) K0V star DX Leo. Our analysis is based on highprecision photometric observations carried out as part of The Sun inTime project, aimed at a multiwavelength study of stars with solar-likeglobal properties, but with different ages and thus at different stagesof evolution. In the first paper of this series we presented thephotometric observations and determined the existence of starspot cyclesand their correlation with the global stellar properties. In the presentpaper we investigate the surface differential rotation (SDR). Theperiodogram analysis of the photometric data time series has allowed usto determine the rotational periods and to derive the following results:i) all the selected stars show variations of the rotational period. Suchvariations are definitely periodic and in phase with the starspot cyclefor BE Cet and DX Leo. They are likely periodic and in phase also for pi1 UMa, EK Dra and HN Peg, but still need confirmation. Byanalogy with the solar butterfly diagram, the rotational periodvariations are interpretable in terms of surface differential rotation,that is, they are attributable to the existence of active latitude beltsmigrating during the activity cycle on a differentially rotating star;ii) BE Cet, pi 1 UMa andEK Dra show a solar-like pattern of SDR, that is therotational period steadily decreases along the activity cycle, jumpingback to higher values at the beginning of the next cycle; on thecontrary, DX Leo, k1 Cet and HN Peg show an antisolarpattern; iii) the amplitude of the rotational period variations shows apower law dependence on the rotational period similar to that found inprevious studies. Contrary to theoretical predictions, the cycle lengthis not correlated to the Dynamo number, it is indeed positivelycorrelated to the SDR amplitude. More precisely, stars tend toconcentrate along three different branches with the cycle lengthincreasing with increasing Delta Omega /Omega . Moreover, we found thatthe SDR amplitude changes from cycle to cycle, which is reminiscent of awave of excess rotation propagating in latitude; iiii) the apparentlydifferent solar and antisolar behaviours are probably due to differentinclinations of the stellar rotation axis under which the star is seen.The long-term photometry of the young single star LQ Hya, although notincluded in the initial project, is also used in the present analysis toenlarge the investigated sample. We determined for LQ Hya threedifferent starspot cycles and an antisolar pattern of SDR. Statistical cataloging of archival data for luminosity class IV-V stars. II. The epoch 2001 [Fe/H] catalogThis paper describes the derivation of an updated statistical catalog ofmetallicities. The stars for which those metallicities apply are ofspectral types F, G, and K, and are on or near the main sequence. Theinput data for the catalog are values of [Fe/H] published before 2002February and derived from lines of weak and moderate strength. Theanalyses used to derive the data have been based on one-dimensional LTEmodel atmospheres. Initial adjustments which are applied to the datainclude corrections to a uniform temperature scale which is given in acompanion paper (see Taylor \cite{t02}). After correction, the data aresubjected to a statistical analysis. For each of 941 stars considered,the results of that analysis include a mean value of [Fe/H], an rmserror, an associated number of degrees of freedom, and one or moreidentification numbers for source papers. The catalog of these resultssupersedes an earlier version given by Taylor (\cite{t94b}).Catalog is only available in electronic form at the CDS via anonymousftp cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/398/731 Statistical cataloging of archival data for luminosity class IV-V stars. I. The epoch 2001 temperature catalogThis paper is one of a pair in which temperatures and metallicitycatalogs for class IV-V stars are considered. The temperature catalogdescribed here is derived from a calibration based on stellar angulardiameters. If published calibrations of this kind are compared by usingcolor-index transformations, temperature-dependent differences among thecalibrations are commonly found. However, such differences are minimizedif attention is restricted to calibrations based on Johnson V-K. Acalibration of this sort from Di Benedetto (\cite{dib98}) is thereforetested and adopted. That calibration is then applied to spectroscopicand photometric data, with the latter predominating. Cousins R-Iphotometry receives special attention because of its high precision andlow metallicity sensitivity. Testing of temperatures derived from thecalibration suggests that their accuracy and precision are satisfactory,though further testing will be warranted as new results appear. Thesetemperatures appear in the catalog as values of theta equiv5040/T(effective). Most of these entries are accompanied by measured orderived values of Cousins R-I. Entries are given for 951 stars.Catalog is only available in electronic form at the CDS via anonymousftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/398/721 Rotation and differential rotation in field F- and G-type starsWe present a detailed study of rotation and differential rotationanalyzing high resolution high S/N spectra of 142 F-, G- and earlyK-type field stars. Using Least Squares Deconvolution we obtainbroadening profiles for our sample stars and use the Fourier transformmethod to determine projected rotational velocities v sin i.Distributions of rotational velocities and periods are studied in theHR-diagram. For a subsample of 32 stars of spectral type F0-G0 we derivethe amount of differential rotation in terms of alpha = (Omega_Equator- Omega_Pole )/Omega_Equator . We find evidence for differentialrotation in ten of the 32 stars. Differential rotation seems to be morecommon in slower rotators, but deviations from rigid rotation are alsofound in some fast rotators. We search for correlations betweendifferential rotation and parameters relevant for stellar activity andshow indications against strong differential rotation in very activestars. We derive values of Delta P and Delta Omega , which support aperiod dependence of differential rotation. Derived lap times 2pi /DeltaOmega are of the order of 20 d and contradict the assumption thatconstant lap times of the order of the solar one ( ~ 130 d) are therule in stars that are thought to harbour magnetic dynamos.Based on observations collected at the European Southern Observatory, LaSilla.Tables 3 and A1 are only available at the CDS via anonymous ftp tocdsarc.u-strasbg.fr (130.79.125.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/398/647 Fast-rotating nearby solar-type stars sin i and X-ray luminosities relationships. II. Li abundances, v sin i and X-ray luminosities relationshipsWe present an analysis of our high-resolution spectroscopic andhigh-precision UBV(RI)_c photometric observations of a sample of 110nearby late-F and G-type stars selected for their large rotationalvelocity. The relationships between Li abundance, X-ray luminosity, andvsin i are investigated. We find that, as expected, the stars in oursample show statistically higher Li abundance and activity level thanfield star samples with similar characteristics, but slower rotation.Surprisingly, however, we also find four rapidly-rotating singlemain-sequence stars with very low Li abundance. For both single andbinary stars we find a large spread of Li abundance for stars withrotation lower than about 18 km s-1. The well-establishedcorrelation between X-ray luminosity and rotation rate is clearlyobserved. All single unevolved solar type stars with vsin i larger than18 km s-1 are strong X-ray emitters and have high Liabundance. Finally, we find also five evolved stars with very low Liabundance that are still rather fast rotators. The results from oursample confirm the presence of young very active stars close to the Sun,in agreement with recent findings from EUV and X-ray surveys, althoughour sample does not show such extreme characteristics as those selectedfrom EUV and X-ray surveys at the current flux limits.Based on data collected at the European Southern Observatory, La Silla,Chile.Tables, Figures and the complete data set are available in electronicform at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5)or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/397/987 Multiplicity among solar-type stars. III. Statistical properties of the F7-K binaries with periods up to 10 yearsTwo CORAVEL radial velocity surveys - one among stars in the solarneighbourhood, the other in the Pleiades and in Praesepe - are merged toderive the statistical properties of main-sequence binaries withspectral types F7 to K and with periods up to 10 years. A sample of 89spectroscopic orbits was finally obtained. Among them, 52 relate to afree-of-bias selection of 405 stars (240 field stars and 165 clusterstars). The statistics corrected for selection effects yield thefollowing results: (1) No discrepancy is found between the binariesamong field stars and the binaries in open cluster. The distributions ofmass ratios, of periods, the period-eccentricity diagram and the binaryfrequencies are all within the same error intervals. (2) Thedistribution of mass ratios presents two maxima: a broad peak from q ~0.2 to q ~ 0.7, and a sharp peak for q > 0.8 (twins). Both arepresent among the early-type as well as among the late-type part of thesample, indicating a scale-free formation process. The peak for q >0.8 gradually decreases when long-period binaries are considered.Whatever their periods, the twins have eccentricities significantlylower than the other binaries, confirming a difference in the formationprocesses. Twins could be generated by in situ formation followed byaccretion from a gaseous envelope, whereas binaries with intermediatemass ratios could be formed at wide separations, but they are madecloser by migration led by interactions with a circumbinary disk. (3)The frequency of binaries with P<10 years is about 14%. (4) About0.3% of binaries are expected to appear as false positives in a planetsearch. Therefore, the frequency of planetary systems among stars ispresently 7+4-2%. The extension of thedistribution of mass ratios in the planetary range would result in avery sharp and very high peak, well separated from the binary stars withlow mass ratios. Based on photoelectric radial-velocity measurementscollected at Haute-Provence observatory and on observations made withthe ESA Hipparcos astrometry satellite. The stellar activity-rotation relationship revisited: Dependence of saturated and non-saturated X-ray emission regimes on stellar mass for late-type dwarfsWe present the results of a new study on the relationship betweencoronal X-ray emission and stellar rotation in late-type main-sequencestars. We have selected a sample of 259 dwarfs in the B-V range 0.5-2.0,including 110 field stars and 149 members of the Pleiades, Hyades, alphaPersei, IC 2602 and IC 2391 open clusters. All the stars have beenobserved with ROSAT, and most of them have photometrically-measuredrotation periods available. Our results confirm that two emissionregimes exist, one in which the rotation period is a good predictor ofthe total X-ray luminosity, and the other in which a constant saturatedX-ray to bolometric luminosity ratio is attained; we present aquantitative estimate of the critical rotation periods below which starsof different masses (or spectral types) enter the saturated regime. Inthis work we have also empirically derived a characteristic time scale,taue , which we have used to investigate the relationshipbetween the X-ray emission level and an X-ray-based Rossby numberRe = Prot/taue: we show that ourempirical time scale taue resembles the theoreticalconvective turnover time for 0.4 <~ M/Msun <~ 1.2, butit also has the same functional dependence on B-V asLbol-1/2 in the color range 0.5 <~ B-V <~1.5. Our results imply that - for non-saturated coronae - theLx - Prot relation is equivalent to theLx/Lbol vs. Re relation. Tables 1 and 2are only available in electronic form at \ http://www.edpsciences.org
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# Test
This page is for posters to test comments prior to submitting them to WUWT. Your tests will be deleted in a while, though especially interesting tests, examples, hints, and cool stuff will remain for quite a while longer.
Some things that don’t seem to work any more, or perhaps never did, are kept in Ric Werme’s Guide to WUWT.
WordPress does not provide much documentation for the HTML formatting permitted in comments. There are only a few commands that are useful, and a few more that are pretty much useless.
A typical HTML formatting command has the general form of <name>text to be formatted</name>. A common mistake is to forget the end command. Until WordPress gets a preview function, we have to live with it.
N.B. WordPress handles some formatting very differently than web browsers do. A post of mine shows these and less useful commands in action at WUWT.
N.B. You may notice that the underline command, <u>, is missing. WordPress seems to suppress for almost all users, so I’m not including it here. Feel free to try it, don’t expect it to work.
Name Sample Result
b (bold) This is <b>bold</b> text This is bold text
Command strong also does bolding.
i (italics) This is <i>italicized</i> text This is italicized text
Command em (emphasize) also does italics.
A URL by itself (with a space on either side) is often adequate in WordPress. It will make a link to that URL and display the URL, e.g. See http://wermenh.com.
Some source on the web is presenting anchor commands with other parameters beyond href, e.g. rel=nofollow. In general, use just href=url and don’t forget the text to display to the reader.
blockquote (indent text) My text
<blockquote>quoted text</blockquote>
More of my text
My text
quoted text
More of my text
Quoted text can be many paragraphs long.
WordPress italicizes quoted text (and the <i> command enters normal text).
strike This is <strike>text with strike</strike> This is text with strike
pre (“preformatted” – use for monospace display) <pre>These lines are bracketed<br>with <pre> and </pre>
These lines are bracketed
with <pre> and </pre>
Preformatted text, generally done right. Use it when you have a table or something else that will look best in monospace. Each space is displayed, something that <code> (next) doesn’t do.
code (use for monospace display) <code>Wordpress handles this very differently</code> WordPress handles this very differently
See http://wattsupwiththat.com/resources/#comment-65319 to see what this really does.
Using the URL for a YouTube video creates a link like any other URL. However, WordPress accepts the HTML for “embedded” videos. From the YouTube page after the video finishes, click on the “embed” button and it will suggest HTML like:
<iframe width="560" height="315"
frameborder="0" allowfullscreen>
</iframe>
WordPress will convert this into an internal square bracket command, changing the URL and ignoring the dimension. You can use this command yourself, and use its options for dimensions. WordPress converts the above into something like:
[youtube https://www.youtube.com/watch?v=yaBNjTtCxd4&w=640&h=480]
Use this form and change the w and h options to suit your interests.
If WordPress thinks a URL refers to an image, it will display the image
instead of creating a link to it. The following rules may be a bit excessive,
but they should work:
1. The URL must end with .jpg, .gif, or .png. (Maybe others.)
2. The URL must be the only thing on the line.
3. This means you don’t use <img>, which WordPress ignores and displays nothing.
4. This means WordPress controls the image size.
5. <iframe> doesn’t work either, it just displays a link to the image.
If you have an image whose URL doesn’t end with the right kind of prefix, there may be two options if the url includes attributes, i.e. if it has a question mark followed by attribute=value pairs separated by ampersands.
Often the attributes just provide information to the server about the source of the URL. In that case, you may be able to just delete everything from the question mark to the end.
For some URLs, e.g. many from FaceBook, the attributes provide lookup information to the server and it can’t be deleted. Most servers don’t bother to check for unfamiliar attributes, so try appending “&xxx=foo.jpg”. This will give you a URL with one of the extensions WordPress will accept.
WordPress will usually scale images to fit the horizontal space available for text. One place it doesn’t is in blockquoted text, there it seems to display fullsize and large images overwrite the rightside nav bar text.
Those of us who remember acceptance of ASCII-68 (a specification released in 1968) are often not clever enough to figure out all the nuances of today’s international character sets. Besides, most keyboards lack the keys for those characters, and that’s the real problem. Even if you use a non-ASCII but useful character like ° (as in 23°C) some optical character recognition software or cut and paste operation is likely to change it to 23oC or worse, 230C.
Nevertheless, there are very useful characters that are most reliably entered as HTML character entities:
Type this To get Notes
& & Ampersand
< < Less than sign
Left angle bracket
• Bullet
° ° Degree (Use with C and F, but not K (kelvins))
⁰
¹
²
³
⁴
¹
²
³
Superscripts (use 8304, 185, 178-179, 8308-8313 for superscript digits 0-9)
₀
₁
₂
₃
Subscripts (use 8320-8329 for subscript digits 0-9)
£ £ British pound
ñ ñ For La Niña & El Niño
µ µ Mu, micro
± ± Plus or minus
× × Times
÷ ÷ Divide
≠ Not equals
Like a space, with no special processing (i.e. word wrapping or multiple space discarding)
> > Greater than sign
Right angle bracket
Generally not needed
Various operating systems and applications have mechanisms to let you directly enter character codes. For example, on Microsoft Windows, holding down ALT and typing 248 on the numeric keypad may generate the degree symbol. I may extend the table above to include these some day, but the character entity names are easier to remember, so I recommend them.
## Latex markup
WordPress supports Latex. To use it, do something like:
$latex P = e\sigma AT^{4}$ (Stefan-Boltzmann's law)
$latex \mathscr{L}\{f(t)\}=F(s)$
to produce
$P = e\sigma AT^{4}$ (Stefan-Boltzmann’s law)
$\mathscr{L}\{f(t)\}=F(s)$
Each comment has a URL that links to the start of that comment. This is usually the best way to refer to comment a different post. The URL is “hidden” under the timestamp for that comment. While details vary with operating system and browser, the best way to copy it is to right click on the time stamp near the start of the comment, choose “Copy link location” from the pop-up menu, and paste it into the comment you’re writing. You should see something like http://wattsupwiththat.com/2013/07/15/central-park-in-ushcnv2-5-october-2012-magically-becomes-cooler-in-july-in-the-dust-bowl-years/#comment-1364445.
The “#<label>” at the end of the URL tells a browser where to start the page view. It reads the page from the Web, searches for the label and starts the page view there. As noted above, WordPress will create a link for you, you don’t need to add an <a> command around it.
## One way to avoid the moderation queue.
Several keywords doom your comment to the moderation queue. One word, “Anthony,” is caught so that people trying to send a note to Anthony will be intercepted and Anthony should see the message pretty quickly.
If you enter Anthony as An<u>th</u>ony, it appears to not be caught,
so apparently the comparison uses the name with the HTML within it and
sees a mismatch.
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Steven Fraser
March 3, 2020 8:43 pm
Bold Italic Off
Bryan A
December 10, 2020 10:11 pm
xx²
test
March 19, 2020 3:34 am
It is true though, that before it had ever been encountered in the wild it was first created in a lab!
https://www.nature.com/news/engineered-bat-virus-stirs-debate-over-risky-research-1.18787
And while it may not have been “engineered” as such, the odds that it didn’t come from the Wuhan lab that was experimenting with the virus on live animals are millions to one! The lab has live infected species in cages and the chance of crossover, was intentional!
Red94ViperRT10
March 21, 2020 3:02 pm
…new building materials with higher melting points so that roads won’t crack in extreme temperatures…”
Oh, good grief! *extreme eyeroll* *pound head on wall like Charlie Brown”
Randy Stubbings
December 14, 2020 6:40 am
Wind farms can provide “synthetic inertia.” As discussed in https://spectrum.ieee.org/energywise/energy/renewables/can-synthetic-inertia-stabilize-power-grids,
Synthetic inertia is achieved by reprogramming power inverters attached to wind turbines so that they emulate the behavior of synchronized spinning masses.”
To emulate the inertial behavior of massive rotating equipment, a renewable generator must somehow find extra power quick. Québec’s wind turbines do so through a collaboration between the turbines’ solid-state power electronics and their moving parts. “When the wind turbines see an imbalance between load and generation that causes a frequency deviation on the system they’re able to … extract some kinetic energy that is stored in the rotating masses of the wind turbines,” explains Aubut.
During a December 2015 transformer failure that took more than 1,600-MW of power generation offline, synthetic inertia kicked in 126 MW of extra power to arrest the resulting frequency drop. Quebec’s AC frequency bottomed out at 59.1 hertz – well below its 60-hertz standard – but Aubut and his colleagues estimate that it would have dropped a further 0.1-0.2-hz without the synthetic inertia. And they estimate that this was roughly the same contribution that conventional power plants would have provided.
The trouble, says Aubut, is what happens after the frequency drop. In all but the strongest wind conditions providing synthetic inertia will slow a wind turbine’s rotor. Re-accelerating to optimal speed thereafter absorbs some of the wind power that the turbine can export to the grid. Data from ENERCON shows power reductions of up to 60 percent in some turbines.
May 12, 2020 6:31 am
quoted text
rickk
May 13, 2020 9:20 am
rickk
May 13, 2020 9:24 am
—————
rickk
May 31, 2020 6:38 pm
?w=768
rickk
May 31, 2020 6:49 pm
Jack Black
June 10, 2020 8:33 pm
OK I try this
“https://youtu.be/7P5RW0Tmp-U”
https://youtu.be/7P5RW0Tmp-U
rickk
May 31, 2020 6:40 pm
?w=768
rickk
May 31, 2020 6:48 pm
?w=768
Jack Black
June 10, 2020 8:38 pm
So I try to do YouTube embed in this way ….
“https://youtu.be/7P5RW0Tmp-U”
https://youtu.be/7P5RW0Tmp-U
Jack Black
June 19, 2020 3:31 am
Vimeo video test ….
Jack Black
June 10, 2020 8:41 pm
That didn’t work above….
So I try this instead ….
Jack Black
June 10, 2020 8:59 pm
These YouTube embeds not working anymore according to instructions in the Rick Werne text above. YouTube converting copied URLs to the short form of youtu.be/xxxxxxx type, and the ending square bracket being converted on the fly to HEX code %5D which seems to munge the code to FUBAR !
WordPress instructions to copy the embed code of the iFrame don’t work either, because YouTube has added a whole load of guff in the embed URL that WordPress didn’t expect now. This is a major FUBAR, I think….
WordPress says ….
But copied embed code looks like this ….
[blockquote]
[/blockquote]
All this accelerometer, gyroscope, encrypted-media etc guff is what confuses WordPress maybe. Did Anybody manage to embed a YouTube Video into WordPress anymore? So I will give it one last attempt and do this…
[blockquote]
[/blockquote]
Did it work ?
Jack Black
June 10, 2020 9:11 pm
OK so I got the wrong brackets to show proper formatting with my blockquote, blame spell correct for that…. I correct formatting manually in this post.
Again:
These YouTube embeds not working anymore according to instructions in the Rick Werne text above. YouTube converting copied URLs to the short form of youtu.be/xxxxxxx type, and the ending square bracket being converted on the fly to HEX code %5D which seems to munge the code to FUBAR !
WordPress instructions to copy the embed code of the iFrame don’t work either, because YouTube has added a whole load of guff in the embed URL that WordPress didn’t expect now. This is a major FUBAR, I think….
WordPress says ….
But copied embed code looks like this ….
All this accelerometer, gyroscope, encrypted-media etc guff is what confuses WordPress maybe. Did Anybody manage to embed a YouTube Video into WordPress anymore? So I will give it one last attempt and do this…
I think WordPress daemon is still converting the ending square bracket to the special HEX code of %5D though, and how to get around this?
Did it work ?
Jack Black
June 10, 2020 9:24 pm
Blast !
Even the code in the blockquote is being changed by WordPress daemon….. Let me try another way…
Again:
These YouTube embeds not working anymore according to instructions in the Rick Werne text above. YouTube converting copied URLs to the short form of youtu.be/xxxxxxx type, and the ending square bracket being converted on the fly to HEX code %5D which seems to munge the code to FUBAR !
WordPress instructions to copy the embed code of the iFrame don’t work either, because YouTube has added a whole load of guff in the embed URL that WordPress didn’t expect now. This is a major FUBAR, I think….
WordPress says ….
But copied embed code looks like this nowadays ….
[youtube https://www.youtube.com/watch?v=7P5RW0Tmp-U&w=740&h=416]
All this accelerometer, gyroscope, encrypted-media etc guff is what confuses WordPress maybe. Did Anybody manage to embed a YouTube Video into WordPress anymore? So I will give it one last attempt and do this… just the URL, but without the protocol specifier.
www.youtube.com/embed/7P5RW0Tmp-U
Did that do it?
I think WordPress daemon is still converting the generated ending square bracket “]” to the special HEX code of %5D though, and how to get around this?
Jack Black
June 10, 2020 9:38 pm
I can’t seem to demonstrate the new YouTube embed code, because WordPress daemon is stripping out all the parameters, even when I do the blockquote or with “code” brackets.
Maybe if I put it all between quotation marks?
Or you go to the video and right click and choose copy embed code and then paste to a notepad and see for yourself. Anyway the YouTube embed is no longer working because of some parameters change, or validation or something. WordPress plugin maybe needs updating? Can this be checked? I try again tomorrow perhaps.
Jack Black
June 10, 2020 9:59 pm
So the quotation marks idea was no good.
Well that didn’t show up either, hmm 🤔
How to show it ? I try to do screen capture and imgur…
?maxwidth=800&shape=thumb&fidelity=high
Now you see the embed code?
It’s nothing like the old YouTube embed code that WordPress plugin expects, and if you try to use old style iframe code then YouTube server doesn’t like that.
I give up for today, and hope you can get new WordPress updated plugin that can cope with new changes to YouTube’s coding…. 🤔
Jack Black
June 11, 2020 7:19 pm
So according to a commenter in another thread you just have to copy URL (from address bar), and paste into comment in a new paragraph. All the foregoing, about embed codes, size parameters, iFrames, youtube prefix in squared brackets, etc., is seemingly old obsolete nonsense !!! Let’s see if that’s true.
So I paste this (first line shown with “code” brackets):
Did it work this time at last?
Jack Black
June 11, 2020 7:46 pm
Aha ! So it worked if the address bar URL is pasted in between a set of code chevron brackets like so:
Yet not if directly pasted as simple URL, or it only then shows up as a hotlink. Curiouser and curiouser !!! Note that in the example I give I show chevrons in quotation marks, to prevent them disappearing.
For this to work Commenter must NOT include these quotation marks. Was that understood?
Seemingly for some users direct paste of address bar YouTube URL does work, depending upon their web browser, and operating system, which may automatically paste in hidden code brackets? Anyway it seems apparent that using iFrame or prefix squared bracket codes is all obsolete guff nowadays?
One more time to confirm this, I follow my own instructions (NO quotation marks on chevrons!!!!)
@Rick or Mods, if this worked OK then maybe amend the YouTube embed instructions accordingly?
Jack Black
June 11, 2020 8:06 pm
Final thoughts….
No matter how I tried to demonstrate the code that worked, whenever I put the word “code” in the chevrons it disappeared, so lastly for clarity, I will use extra character _ underscore spacer. Remove all extra underscore spacers when you are doing it for real. I hope that Rick or Mods can actually show this code illustrated properly, should they decide to modify the YouTube instructions in this page preamble.
I hope none of my illustration vanished this time 😎
Jack Black
June 11, 2020 8:23 pm
It’s very hard to put chevrons in these comments without them vanishing. So final, final, final, try, I will substitute square brackets for chevroned brackets in my illustrated example. Commenters MUST of course use chevroned brackets when actually doing the deed !
Do NOT use short style ‘youtu.be’ URLs
MUST be full www dot youtube dot com, with full https colon slash slash prefix
Exactly as copied from browser address bar, and no trailing ampersand parameters !
Phew ! 😅😵🤔
Jack Black
June 12, 2020 7:09 pm
To anyone who read my long saga of experiments in here; Thank you for reading thus far ! 🙂
So it does appear that these results may be web-browser and/or Operating System specific. Some people may get away with merely copy & paste of YouTube FULL URL from the address bar of the relevant web page. Others may require to use the “code” brackets option. The short URL provided by right click on actual video player (youtu.be&etc) doesn’t work anymore in here. iFrame embed codes no longer work. YouTube has changed their API !!!
What ALWAYS now (June 2020) works is this …
Do like so…
Commenters MUST of course use chevroned brackets instead of square brackets when actually doing the deed !
Square brackets are only used here, so they won’t vanish in this comment, being mistaken for an actual command.
YouTube URL MUST be style : https colon slash slash www dot youtube dot com slash watch?v=xxxxxxxx
Exactly as copied from browser address bar, and must delete any other trailing ampersand parameters !
Thanks for all your patience, in reading this far, and I hope that Rick, Charles, and Mods/Editors would put that example in the site Help Tips, and remove all the old anachronistic stuff about copying iFrame embed codes and “[youtube ” prefixes etc. Mods/Editors may be able to illustrate the use of chevroned “code” brackets properly?
Thanks everybody who troubled to read my long saga 😎
Ron
June 26, 2020 3:30 am
Ron
June 26, 2020 3:34 am
Let’s try image:
Or this way:
Jack Black
August 25, 2020 2:08 am
@Ron
Do it with the chevroned “code” brackets same as with a YouTube video….. See end of my long saga above.
😎
Jack Black
August 25, 2020 2:10 am
Why this no work anymore ?
Oh, WordPress – ye naughty, naughty codebase ye really are
😸
June 28, 2020 3:14 pm
Testing —
Hello, world Hides text until hovered over or clicked on
Rotor
July 2, 2020 8:10 am
quoted text
Scissor
July 4, 2020 12:34 pm
████████╗██████╗░██╗░░░██╗███╗░░░███╗██████╗░
╚══██╔══╝██╔══██╗██║░░░██║████╗░████║██╔══██╗
░░░██║░░░██████╔╝██║░░░██║██╔████╔██║██████╔╝
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Jack Black
August 25, 2020 2:22 am
ASCII text image compositor? Which on lie daemon did you use for that? Give URL so as others may try it?
Jay Willis
July 17, 2020 5:07 am
fraizer
July 24, 2020 10:06 am
This is notis a test
Sasha
July 26, 2020 12:40 am
The Virus/Lockdown Scam
If masks work, then why are we anti-social distancing?
If anti-social distancing works, then why are we wearing masks?
If masks and anti-social distancing work, then why are our businesses closed?
If we can stand in line in a grocery store, then why can’t we stand in line to vote?
Because it’s not about the virus. It never was.
For those who always point at the medical profession who “mask up”…
Surgeons and nurses wear masks to protect against bacterial infections. The evidence for that protection is minimal. Viruses are so small that 100,000,000 (100 Million) of them will fit (if only one layer thick) on the period at the end of this sentence. If you’re donning a medical mask or worse yet: a diaper mask, do you think 4 periods might get in, out, around or through the mask?
The British Government has confirmed that Covid- 19 is harmless to the vast majority of people:
In this clip from the Downing Street Corona Briefing on May 11th, Chris Whitty – Britain’s Chief Medical Officer – says that, to most people, the coronavirus is entirely harmless:
Most people will never get it;
Most of the people who get it won’t ever experience symptoms;
Most of the people who experience symptoms won’t need medical care;
Most of the people who need medical care won’t be need emergency or critical care. And even the tiny percentage of people who need who DO need critical care will survive, regardless of risk factors or medical history.
https://www.cochranelibrary.com/cdsr/doi/10.1002/14651858.CD002929.pub3/full
Disposable surgical face masks for preventing surgical wound infection in clean surgery
Surgical face masks were originally developed to contain and filter droplets containing microorganisms expelled from the mouth and nasopharynx of healthcare workers during surgery, thereby providing protection for the patient. However, there are several ways in which surgical face masks could potentially contribute to contamination of the surgical wound, e.g. by incorrect wear or by leaking air from the side of the mask due to poor string tension.
Objectives
To determine whether the wearing of disposable surgical face masks by the surgical team during clean surgery reduces postoperative surgical wound infection.
Key results
Overall, we found very few studies and identified no new trials for this latest update. We analyzed a total of 2106 participants from the three studies we found. All three studies showed that wearing a face mask during surgery neither increases nor decreases the number of wound infections occurring after surgery. We conclude that there is no clear evidence that wearing disposable face masks affects the likelihood of wound infections developing after surgery. (and they certainly won’t stop viruses.)
In May 2020, The CDC said the exact same thing:
“In our systematic review, we identified 10 RCTs that reported estimates of the effectiveness of face masks in reducing laboratory-confirmed influenza virus infections in the community from literature published during 1946–July 27, 2018. In pooled analysis, we found no significant reduction in influenza transmission with the use of face masks (RR 0.78, 95% CI 0.51–1.20; I2 = 30%, p = 0.25) (Figure 2). One study evaluated the use of masks among pilgrims from Australia during the Hajj pilgrimage and reported no major difference in the risk for laboratory-confirmed influenza virus infection in the control or mask group (33). Two studies in university settings assessed the effectiveness of face masks for primary protection by monitoring the incidence of laboratory-confirmed influenza among student hall residents for 5 months (9,10). The overall reduction in ILI or laboratory-confirmed influenza cases in the face mask group was not significant in either studies (9,10). Study designs in the 7 household studies were slightly different: 1 study provided face masks and P2 respirators for household contacts only (34), another study evaluated face mask use as a source control for infected persons only (35), and the remaining studies provided masks for the infected persons as well as their close contacts (11–13,15,17). None of the household studies reported a significant reduction in secondary laboratory-confirmed influenza virus infections in the face mask group (11–13,15,17,34,35…”
As a last thought, consider this:
Sweden never had a lockdown and never forced people to wear masks or anything else, they never forced anti-social distancing on the entire population (other than moving restaurant tables a bit further apart) and they never gave up the idea that sane adults can work out their own level of risk and behave appropriately. Consequently, the Swedes have maintained all the measures of civilized life and have not wrecked their economy in the name of “keeping you safe.” For the record, a tiny minority of Swedes wear masks but they are mainly foreigners or tourists and most Swedes think wearing masks in public outside of medical necessity is idiotic. Sweden now has one of the lowest rates of deaths for the virus which is now in single figures. In the last 24 hours, Sweden recorded just 9 deaths from the virus out of a population of well over 10 million.
Don’t take my word for any of this…
What’s REALLY Going On in Sweden (No Lockdown)
SWEDEN DURING CORONAVIRUS – REAL FOOTAGE
Nicholas McGinley
August 20, 2020 1:06 am
“If masks work, then why are we anti-social distancing?
If anti-social distancing works, then why are we wearing masks?”
That sounds as logical to me as asking why, if overcoats work, do people use umbrellas?
Or if boots work, why step over puddles?
Compu Gator
August 2, 2020 2:00 pm
(Preface for “Watts Up With That”: I’m testing character-sets, esp. those for the ancient languages that I used in this draft, um, rant. I haven’t yet seen any push-back in WUWT to the globally decreed pronunciation of the former Hurricane Isaias. I also need to test my unconventional reference-marks, which I use instead of numbers to enable me to move referring text around with a programming-text editor, without manually renumbering or dependence on word-processors like MS Word (how many WUWT readers have looked at the wretchedly verbose and cluelessly redundant translations of MS-Word features to HTML for Web sites? Oh! And using Unicode to greatly expand the variety in reference-marks can provide light distractions during my writings on serious or unpleasant topics.)
I say “[bleep!]” on the condescending direction from the “mainstream media” on how we deplorables should pronounce the approaching storm’s name:
Phonetically, it’s pronounced ees-ah-EE-ahs. There are different ways to pronounce Isaias but for the sake of a named storm, the National Hurricane Center has informed meteorologists this pronunciation will be the standard. [×]
Sooo, the language-majority in the Continental U.S.A., i.e., native speakers of English, many of whom opened an Old Testament for their first time decades ago, and have continued to do so countless times since then, are expected to change their pronunciation of the name of perhaps the greatest prophet in the O.T., all because some faceless globalist weathercrats say we must? “It’s standard!“ Really, now? That’s not how we pronounce its written name around here–the state off whose coast the one-time hurricane is whirling right now!
Isaias is the Spanish and Portuguese version of the name Isaiah, more commonly used in Latin American countries like Argentina that tend to have a more European and Latin influence. [….] The name is not common in Mexico, the Caribbean or Central America, according to mynamestats.com. You likely won’t meet too many people with that name unless you travel to South America and parts of Europe.
So we in the U.S.A. near the path of this hurricane must pander to the pride of distant foreigners who inhabit other hemispheres, and are nowhere near the track of this hurricane? Because it’s mostly Argentinans who happen to name their infants after major prophets in the Old-Testament, and that somehow gives them world-widedibs’ on the pronunciation? To Hey-ell with that!
In point of fact, “Isaias” is exactly the spelling that’s attested in St. Jerome‘s Biblia Vulgata [✞]. It’s not merely “Latin American“; it’s honest-to-God Latin, yall! Roman Empire, roads, legions, gladiators, &c. Jerome would’ve gotten it from his original translation of Hebrew documents, completed in A.D. 405 [#]. His Latin spelling is consistent with the Greek spelling «῾Ησαΐας» (or less meticulously as «Ησαιας»), then pronounced something like English “Hā-să-yē’-ăs” (or “Ā-sī-ăs”) in the preChristian Septuagint Old Testament (a.k.a. LXX) [#]. [#]. The name in the Vulgate has come to be pronounced by English-speakers more-or-less as “Ē-sī’-yăs“. English-speaking Protestants follow a translation into Early-Modern English that established the spelling “Isaiah ” [❀], and pronounce it as “Eye-say’-yah”.
The name means “God is my salvation” [×]
Nooo, the name does not mean a day-amn thing in LXX Greek, nor in its corresponding Latin. So certainly not anything in its barbarized descendant languages Spanish or Portuguese. It has the claimed meaning only in Hebrew: “ ישׁעיהוּ ” (i.e., yod shin-with-shin-dot ayin yod he shuruk). I’m no expert, but daring to guess pronunciation something like 4-or-5-syllables for the Hebrew: “Yə-shæ-(ə)-yɑ-hū” [✡]. Which for what it’s worth, more-or-less agrees with Wikipedia‘s “Yəshạʻyā́hû” [✡✡].
But “ees-ah-EE-ahs“? Not no way, not no how!
——–
Note × : “Tropical Storm Isaias forms–here’s how to pronounce it”.
By Gabriella Nuñez, Multimedia Producer. Published: July 29, 2020, 2:25 pm. Updated: July 30, 2020, 7:09 am.
https://www.clickorlando.com/features/2020/07/29/system-in-tropics-likely-to-become-isaias-heres-how-to-pronounce-it/. This silly “ClickOrlando.com” site-name is the Internet home of the long-established local-t.v. channel 6 (1954), owned by the (Katharine Meyer) Graham Media Group, whose flagship property was once the Washington Post.
Note ✞: It’s awfully tempting, nowadays, to translate Latin Biblia Vulgata as “Bible of the Deplorables“. More literally, the title’s easily misunderstood word, a participle of the verb vulg·o, -are, simply means “common”, e.g., in knowledge or usage (altho’ it can indicate “the common people” among the empire’s class-structure). The New World, the “Deplorables”, and their Walmarts would be a millennium and more in the future. Despite his scholarly talents, in translating from the Greek or Hebrew manuscripts available to him (A.D. 390–405), Jerome kept his Latin simple, to assist readers with only elementary literacy. “St. Jerome”. By Louis Saltet (1910). The Catholic Encyclopedia, vol. 8.
Note # : “Versions of the Bible”. By Anthony Maas. The Catholic Encyclopedia, 1912. https://www.newadvent.org/cathen/15367a.htm. Not even modern Jewish archivists have Hebrew manuscripts that are older than those which would’ve been available for Jerome to study. The Massoretes didn’t begin their efforts until the A>D. 6th Century.
Note ❀ : William Tyndale, Miles Coverdale, or the “Authorized Version” (1611), whatevah! I’ll leave it to Protestants herein to sort it out.
Note ✡ : I used a version of the hardcopy bilingual dictionary (focused on Biblical or ancient Hebrew) by Gesenius (its English is a later translation from the German of Gesenius).
Note ✡✡ : Most readers herein will probably want on-line sources, e.g.: https://en.wikipedia.org/wiki/Isaiah; the pronunciation is isolated in(to) its “note a”. The “š” in Wikip. is simply the Romanized-Slavic spelling of E.-Europe for “sh”, into which I transliterated it above. The ‘ ʻ ’ that’s shown 2 characters later is typewriter-era technology for transliterating the Semitic consonant ayin (‘ ע ’); conventional wisdom describes it as originally a sort of strangled gasp, but later a ‘glottal stop’; or it can be transcribed as the short vowel ‘e’. Inexplicably, the article in the Jewish Encyclopedia of 1906, as hosted on line, fails to show the spelling in Hebrew: “ISAIAH”. By Emil G. Hirsch, Thomas Kelly Cheyne, Isidore Singer, Isaac Broydé. http://www.jewishencyclopedia.com/articles/8235-isaiah.
david g
August 16, 2020 7:08 am
test with vpn active
david g
August 16, 2020 7:09 am
test without vpn
Bellman
August 19, 2020 10:17 am
Just testing
Bellman
August 19, 2020 12:57 pm
And here is the table of records for Death Valley
So of the 30 hottest days in the last 110 years, over half were recorded in the last 20 years, and a third in the last 10.
Only 6 were recorded before 1960, all in the same 6 day period in 1913.
Bellman
August 19, 2020 1:39 pm
So of the 30 hottest days in the last 110 years, over half were recorded in the last 20 years, and a third in the last 10.
Only 6 were recorded before 1960, all in the same 6 day period in 1913.
Bellman
August 19, 2020 1:41 pm
And here is the table of records for D… Valley
So of the 30 hottest days in the last 110 years, over half were recorded in the last 20 years, and a third in the last 10.
Only 6 were recorded before 1960, all in the same 6 day period in 1913.
Bellman
August 19, 2020 1:42 pm
And here is the table of records for Death Valley:
So of the 30 hottest days in the last 110 years, over half were recorded in the last 20 years, and a third in the last 10.
Only 6 were recorded before 1960, all in the same 6 day period in 1913.
Bellman
August 19, 2020 1:43 pm
And here is the table…
So of the 30 hottest days in the last 110 years, over half were recorded in the last 20 years, and a third in the last 10.
Only 6 were recorded before 1960, all in the same 6 day period in 1913.
J Mac
August 19, 2020 6:28 pm
Jack Black
August 25, 2020 2:16 am
@J Mac
Do it with the chevroned “code” brackets ….. See end of my long saga above, and no use any trailing parameters.
😎
Antero Ollila
August 23, 2020 11:10 am
Image:
“https://static.wixstatic.com/media/c266e2_34cd873fa95e482197dc9095ec15f660~mv2.jpg/v1/fill/w_600,h_338,al_c,q_80,usm_0.66_1.00_0.01/Dia2_JPG.webp”
Antero Ollila
August 23, 2020 11:11 am
Image:
“https://static.wixstatic.com/media/c266e2_34cd873fa95e482197dc9095ec15f660~mv2.jpg”
Antero Ollila
August 23, 2020 11:12 am
Image:
^”
Antero Ollila
August 23, 2020 11:17 am
Image:
Antero Ollila
August 27, 2020 12:26 pm
Image:
Antero Ollila
August 27, 2020 12:28 pm
Trial and error:
August 31, 2020 7:04 am
Charles,
Thanks for picking up the Nebulazon joke 😉
August 31, 2020 7:23 am
Nebulazon
September 5, 2020 2:27 pm
I think it is working
niceguy
September 10, 2020 3:46 pm
🙂
😉
😀
:O
Sasha
September 13, 2020 12:58 am
Every statistic about Covid-19 in the British media is a lie
Up to 90% of people who test positive for Covid barely carry any virus and are not contagious.
It has been revealed that the standard tests being used in the US to diagnose Covid-19 cases are far too sensitive, with the vast majority of people marked down as being positive are turning out to be negative. Top US virologists have been stunned by revelations about the laxity of the US Covid testing regimen. Tests that deliver a simple binary “positive or negative” result are not fit for purpose, as they tell us nothing about the contagiousness of each person.
Data from New York, Nevada and Massachusetts shows that when the amount of the virus found in a person is taken into account, up to 90% of people who have tested positive should have been negative, as they are carrying only tiny amounts of the virus, are not contagious, pose no risk to others, and have no need to isolate. This means that only a fraction of the daily “cases” being reported so hysterically in the mainstream media are actual, bona fide Covid-19 sufferers, and need treatment and to separate themselves from others.
So how could this have happened? The answer has to do with the sensitivity of PCR (Polymerase chain reaction) tests for Covid, which it turns out can be ramped up according to the taste of the testing companies. Most testing companies have chosen the outrageously high sensitivity limit of 40 PCR cycles – meaning that the DNA in a sample is exponentially increased 40 times in order to amplify its signal. By using such a ridiculously sensitive test means that the faintest traces of a dead virus, or even leftovers from previous infections (such as the common cold), can result in a positive. Professor Juliet Morrison, a University of California virologist, said that even a limit of 35 PCR cycles is too high, let alone 40. She said she was “shocked that people would think that 40 could represent a positive.” But apparently, pretty much everyone in the US Covid brain trust took exactly that on faith.
So the scale of the pandemic ‘problem’ is actually much smaller than we’ve been led to believe – about a tenth of what all the politicians and media have been using to justify the lockdowns, the quarantines, the mass testing. Some may be shocked that the scale of the problem is so much smaller than assumed. But for a seasoned ignorer of any and all statistics that contain Covid so-called ‘cases,’ there are no surprises here. The truth is, there was never any reason to be confident in such figures. The FDA has only now been forced to concede that they have no idea how different testing companies determine which the positive and negative tests are: they just accept whatever data they are given.
What these findings bring is absolute assurance that the testing to this point has been an utter waste of time, and that not one statistic concerning this pandemic – from cases to deaths to infection rates – can be believed. But it should not have taken some journalist to ask the right question to discover this: a bit of common sense would have been enough. What is it going to take for these professional virologists to drop their assumptions and models, and just start acting based on the facts at hand?
Scrap test and trace
It’s a virus so deadly, you need a test to tell whether you have it or not. So goes the refrain of many lockdown skeptics, “Covidiots” (so beloved by the Daily Mail) and anti-maskers. Something has gone not just wrong, but totally haywire when the might of the world’s scientific establishment is trained with the zeal of a Witchfinder General on one particular microscopic particle. Not even a particularly dangerous particle; the latest data show it is the eighth most common cause of death in England, and it doesn’t even make the top ten in Wales.
Meanwhile, in Wuhan, the original source of this disease, the pool parties are in full swing. They don’t seem to be too worried about PCR tests or contact tracing, or even the virus itself. The Chinese government says that their supreme lockdown was so awesome that they now have zero Covid: a biological impossibility. Maybe they just stopped testing, and decided to get on with their lives. Everyone else should take a leaf out of their book.
Beta Blocker
September 16, 2020 7:54 am
TEST OF SPELLING, FORMATTING, AND LENGTH:
Sooner or later, a climate activist Democrat president will occupy the Oval Office. When this happens, everything Donald Trump ever did while he was president will be quickly and completely erased.
Suppose, for purposes of argument, Joe Biden becomes that climate activist Democrat president. If Biden wants to achieve an 80% reduction in America’s carbon emissions by 2050 — President Obama’s original goal — then massive spending on Green New Deal projects combined with a carbon pricing scheme cannot and will not get the job done.
Fossil fuels are just too convenient as an energy resource and too demand-inelastic for America to reach the 80% reduction target within thirty years using the plan the Democrats are now proposing.
If Biden is serious about an 80% reduction by 2050 — a.k.a. ‘Net Zero’ because it is really the same thing — then he must impose a government-managed system of carbon fuel rationing which directly limits the quantities of fossil fuels that Americans can import, produce, refine, distribute, and consume.
The only possible means of reducing America’s carbon emissions as quickly as climate activists say is necessary is to use the power of government in ways that make all carbon fuels as scarce and expensive today as they will be in a hundred years time.
How could this be done?
Here is an alternative plan for reducing America’s carbon emissions 80% by 2050. The plan is entitled the Supply Side Carbon Emission Control Plan (SSCECP).
The plan uses a series of Executive Orders which combine existing provisions of the Clean Air Act with existing provisions of national security legislation to create an integrated regulatory approach for increasing the cost of all carbon fuels and for systematically restricting their future availability.
In short, the SSCECP uses the power of the federal government to create and enforce an artificial shortage of carbon fuels while directly raising their prices and directly reducing their import, production, distribution, and consumption.
The SSCECP employs EPA-administered carbon pollution fines as the functional equivalent of a legislated tax on carbon. The plan supplies a powerful incentive for the state governments to participate in directly regulating America’s carbon emissions by assigning them the great bulk of the revenues produced from the EPA’s carbon pollution fines.
A joint interagency Carbon Fuels Control Board (CFCB) is established to manage a phased systematic reduction in the production and distribution of all carbon fuels.
In addition, the plan keeps the import, production, and distribution of carbon fuels in private hands. Rather than nationalizing the oil and gas industry, the plan enlists private corporations as contracted agents in managing the government’s energy rationing programs. The government also guarantees a steady and healthy rate return from the sale of all carbon fuels produced by those private corporations which choose to participate.
Here are the major phases of the plan. The start and end dates listed for each major phase assume a climate activist Democrat is elected president in 2020.
SUPPLY SIDE CARBON EMISSION CONTROL PLAN (SSCECP) — Major Phases:
Phase I: Establish a legal basis for regulating all of America’s carbon emissions. (2007-2020. Status complete.)
Phase II: Expand and extend regulation of carbon GHG’s to all major sources of America’s carbon emissions. (01/22/2021 – 12/31/2021)
Phase III: Establish a fully comprehensive regulatory framework for carbon. (01/01/2022 – 12/31/2022)
Phase IV: Implement the carbon pollution regulatory framework. (Year 2023 through the Year 2049)
Phase V: Declare success in reducing America’s carbon emissions 80% by 2050. (If complete by 2050 or some earlier date.)
Here are the details of the plan:</
SUPPLY SIDE CARBON EMISSION CONTROL PLAN (SSCECP) — Detailed Description:.
Phase I: Establish a legal basis for regulating all of America’s carbon emissions. (2007-2020. Status complete.)
— File and win lawsuits to allow regulation of CO2 and other carbon GHG’s as pollutants under the Clean Air Act. (2007)
— Publish a CAA Section 202 Endangerment Finding as a prototype test case for regulation of carbon GHG’s. (2009)
— Defend the Section 202 Endangerment Finding in the courts. (2010-2012)
— Establish a recent precedent, the COVID-19 pandemic, for taking strong government action in response to a declared national emergency. (2020)
Phase II: Expand and extend regulation of carbon GHG’s to all major sources of America’s carbon emissions. (01/22/2021 – 12/31/2021)
II.A: – Presidential Actions, Phase II
II.A.1 — Issue an Executive Order declaring a carbon pollution emergency.
II.A.2 — Assign a joint task force of the US Environmental Protection Agency (US-EPA), the US Department of Homeland Security (US-DHS), and the US Department of Energy (US-DOE) to manage the declared emergency.
II.A.3 — Create a joint interagency Carbon Fuels Control Board (CFCB) to manage a phased systematic reduction in the production and distribution of all carbon fuels.
II.A.4 — Issue a series of Executive Orders as needed to define and implement America’s carbon emissions regulatory framework.
II.A.5 — Establish a public relations outreach program to explain and defend the actions being taken.
II.B: – EPA Actions (Carbon Emission Regulation), Phase II
II.B.1 — Publish a Clean Air Act Section 108 Endangerment Finding which complements 2009’s Section 202 finding.
II.B.2 — Declare carbon emissions as Hazardous Air Pollutants (HAPs) under CAA Section 112.
II.B.3 — Establish a National Ambient Air Quality Standard (NAAQS) for carbon pollution.
II.B.4 — Use the NAAQS for carbon pollution as America’s tie-in to international climate change agreements.
II.B.5 — Defend the Section 108 Endangerment Finding, the NAAQS, and the Section 112 HAP Declaration in the courts.
II.C: – CFCB Actions (Carbon Fuel Rationing), Phase II
II.C.1 — Research and publish a provisional system for government-enforced carbon fuel rationing.
II.C.2 — Defend the provisional system of carbon fuel rationing in the courts.
Phase III: Establish a fully comprehensive regulatory framework for carbon. (01/01/2022 – 12/31/2022)
III.A: – Presidential Actions, Phase III
III.A.1 — Issue a series of Executive Orders as needed to further define and further implement America’s carbon emissions regulatory framework.
III.A.2 — Monitor and coordinate the activities the US-EPA, the US-DHS, and the US-DOE in response to the carbon pollution emergency.
III.A.3 — Monitor the activities of the Carbon Fuels Control Board (CFCB) in reducing the import, production, and distribution of all carbon fuels.
III.A.4 — Maintain and expand the public relations outreach program needed to explain and defend the anti-carbon actions being taken.
III.B: – EPA Actions (Carbon Emission Regulation), Phase III
III.B.1 — Publish a regulatory framework for carbon pollution under Clean Air Act sections 108, 111, 112, 202, and other CAA sections as applicable.
III.B.2 — Establish cooperative agreements with the states to enforce the EPA’s anti-carbon regulations.
III.B.3 — Establish a system of carbon pollution fines which is the functional equivalent of a legislated tax on carbon.
III.B.4 — Establish the legal basis for assigning all revenues collected from these carbon pollution fines to the states.
III.B.5 — Defend the comprehensive system of carbon pollution regulations in the courts.
III.C: – CFCB Actions (Carbon Fuel Rationing), Phase III
III.C.1 — Establish cooperative agreements with the states to enforce the government’s system of carbon fuel rationing.
III.C.2 — Establish a time-phased, hard-target schedule for reducing the production and distribution of all carbon fuels.
III.C.3 — Establish production control agreements with private sector fossil fuel producers and distributors.
III.C.4 — Establish a guaranteed profit schedule for the carbon fuels industry in return for production & distribution cutbacks.
III.C.5 — Defend the government’s system of carbon fuel rationing in the courts.
Phase IV: Implement the carbon pollution regulatory framework. (Year 2023 through the Year 2049)
IV.A: – Presidential Actions, Phase IV
IV.A.1 — Issue a series of Executive Orders as needed to further define and further implement America’s carbon emissions regulatory framework.
IV.A.2 — Monitor and coordinate the activities the US-EPA, the US-DHS, and the US-DOE in response to the carbon pollution emergency.
IV.A.3 — Monitor the activities of the Environmental Protection Agency (EPA) in enforcing carbon emission regulations.
IV.A.4 — Monitor the activities of the Carbon Fuels Control Board (CFCB) in reducing the import, production, and distribution of all carbon fuels.
IV.A.5 — Maintain and expand the public relations outreach program as needed to further explain and further defend the anti-carbon actions being taken.
IV.B: – EPA Actions (Carbon Emission Regulation), Phase IV
IV.B.1 — Commence operation of prior agreements with the states for enforcement of the EPA’s anti-carbon regulations.
IV.B.2 — Commence the collection of carbon pollution fines and the distribution of fine revenues to the states.
IV.B.3 — Monitor the effectiveness of the EPA’s carbon regulatory framework in reducing America’s GHG emissions.
IV.B.4 — Monitor the effectiveness of renewable energy projects in reducing America’s GHG emissions.
IV.B.5 — Monitor the effectiveness of energy conservation programs in reducing America’s GHG emissions.
IV.B.6 — Adjust the schedule of carbon pollution fines upward if progress in reducing America’s GHG emissions lags.
IV.B.7 — Defend the EPA’s system of carbon pollution regulations in the courts.
IV.C: – CFCB Actions (Carbon Fuel Rationing), Phase IV
IV.C.1 — Commence operation of prior agreements with the states for enforcement of the government’s system of carbon fuel rationing.
IV.C.2 — Commence operation of production control agreements with private sector fossil fuel producers and distributors.
IV.C.3 — Monitor the compliance of fossil fuel producers and distributors with their CFCB production control agreements.
IV.C.4 — Monitor the profit levels of fossil fuel producers and distributors for conformance with the CFCB’s guaranteed profit schedule.
IV.C.5 — Defend the government-mandated carbon fuel rationing program in the courts.
Phase V: Declare success in reducing America’s carbon emissions 80% by 2050. (If complete by 2050 or some earlier date.)
— The President issues a proclamation that the target of an 80% reduction has been achieved.
— The President, the US-EPA, the US-DHS, and the US-DOE assess the need for continuing the EPA’s anti-carbon regulations and the US Government’s mandatory fuel rationing program as necessary to maintain the 80% goal.
— If a determination is reached that the government’s system of carbon control measures must continue beyond 2050, existing agreements with the states and with private sector fossil fuel producers and distributors are extended with appropriate modifications.
— Defend the government’s anti-carbon measures against emerging lawsuits if these measures must continue beyond 2050.
Remarks:
Once again, a key point here is that not another word of new legislation is needed to enable this plan. The entire plan is implemented through a series of Executive Orders covered under existing environmental and national security legislation and under constitutionally legal Executive Branch authorities.
However, the elephant in the room is this …. Would the voting public accept the personal and economic sacrifices which go with imposing government-mandated, strictly-enforced anti-carbon measures?
If the Democrats are truly serious about greatly reducing America’s carbon emissions by 2050, they must acknowledge that it can’t be done without using the full power of the federal government in coercively forcing those emission reductions.
niceguy
September 18, 2020 8:35 pm
Editor
September 26, 2020 11:40 am
Testing an embed
Kip
niceguy
October 3, 2020 8:17 pm
I read the French twittosphère A LOT. I mean like thousands of tweets. That’s the virtue of TT, you can read tons of sh*t in a short time, unlike most other social websites and blogs where you waste a lot of time reading tiny amounts of sh*t. (The Web is mostly sh*t, but that’s instructive. The TV series “Scrubs” had a song about sh*t and how you can learn essentially anything from it.)
In the French TT, a lot of criticism of Dr Didier Raoult (a man that I strongly dislike BTW, he embodies what’s wrong in academia and science publishing) gets criticized A LOT for his white coat in interviews and videos done in his IHU (Institut Hospitalo-Universitaire). Apparently Raoult’s white coat hit a nerve, notably among French scientists.
Well, duh. I guess when you have a white coat you must wear in some rooms, you get used to it and wear it whenever you are in the IHU. It could be used to impress morons though.
But we have never seen him in a white coat elsewhere.
Unlike these “scientists”!
Mark Pawelek
October 20, 2020 8:44 pm
The calculation of ECS depends on the atmospheric model of the greenhouse gas effect. They’ve always used the same core model; derived from Manabe and Wetherald 1967 amended by Held and Soden 2000. This is the so-called ‘simple physics’ behind man-made climate change.
The basic physics underlying this global warming, the greenhouse gas effect, is simple. An increase in gases such as CO2 makes the atmosphere more opaque at infrared wavelenghts. This added opacity causes the planet’s heat radiation to space to arise from highter, colder levels in the atmosphere, thus reducing emission of heat energy to space. The temporary imbalance between the energy absorbed from the Sun and heat emission to space, causes the planet to warm until planeteary energy balance is restored.
Hansen et al.; 2011; Atmos. Chem. Phys., 11, 13421-13449, doi:10.5194/acp-11-13421-2011
more CO2 in the atmosphere causes the atmosphere to be more opaque to infrared. That’s a falsifiable test. The data says:
No. The optical thickness of the atmosphere to CO2 greenhouse gas is unchanged since 1950 for over 70 years since CO2 increased in the atmosphere from 315ppm to 415ppm today.
So the core assumption of the greenhouse gas effect is wrong. What of the predictions? The first prediction is that man-made global warming happens because a change in CO2 is “reducing emission of heat energy to space“. We can measure that too, and have been; at least since 1985.
Far from reducing: the heat energy emitted to space increased since 1985 by a whole 1.5 W/m². The first falsifiable prediction of the core model shows the greenhouse gas effect failing.
In fact, it increases as a reflection of climate warming (notice the fall 1991-1994 due to the eruption of Mount Pinatubo cooling earth’s climate).
It injected more particulate into the stratosphere than any eruption since Krakatoa in 1883. Over the following months, the aerosols formed a global layer of sulfuric acid haze. Global temperatures dropped by about 0.5 °C in the years 1991–93
Wikipedia
So OLR emitted to space is not a cause of warming. It simply reflects warming which already happened. The climate consensus at the IPCC are clear that humanity causes 90% of modern climate change. For humanity to have – caused 90% of modern climate change – OLR to space must’ve fallen in line with the mechanics of the greenhouse gas simulation.
A core assumption and a core prediction by the climate consensus greenhouse gas model is wrong. The model is falsified. Those claiming it is settled science promote pseudoscience.
November 7, 2020 7:42 pm
test
November 9, 2020 5:03 pm
Anthony …
I use a Mac and for several weeks the WUWT platform has become almost unusable.
Using the Mac’s native Safari browser, when I click into a post all is well for a minute or so as I read the text.
Then the spinning orb appears and almost all the post above and below where I’ve got to disappears and only the grey background is visible.
I can reload to continue but the problem reappears after a minute or so.
I instead try using Firefox and Chrome. With both I can see the post’s text but no messages at all, and instead a spinning orb as the browsers try to load content.
At least with Safari I can keep reloading and creep my way through the messages if I think they’re sufficiently interesting to keep making the effort.
One thing I notice is that in Firefox and Chrome, a locked strip ad appears at the bottom of the screen, covering the in-house cookie message. Locked messages/ads shouldn’t appear in the same position in a browser.
In Safari, this ad never appears at all.
All my browsers are working fine with every other website in the world, and I click into a hundred or so every day.
My suspicion is one of the refreshed ad sources on the site, probably the static position one at the bottom of the page, is using corrupt code that’s stalling the browsers.
Mac Safari users are an abundant audience. I’ve seen no other messages regarding the problem but even sending this message is difficult as it’s impossible in Firefox or Chrome and Safari often stalls (only on WUWT while sites on a dozen or so simultaneous browser tabs are working fine) so maybe none of the affected readers have been able to send a message.
November 11, 2020 5:04 pm
I’ve no idea if my message above prompted it but this morning I load WUWT and everything is working perfectly on all browsers. Fantastic and well done.
I also note that a lot of advertising has disappeared including at the bottom of pages, and I hope this won’t reduce the meagre income that WUWT generates to compensate for all your hard work.
I also note that when using Firefox or Chrome an ad appears at the top of the page above the WUWT masthead. The ad doesn’t appear in Safari. Regardless, all three browsers are loading all content rapidly and nothing is stalling.
Anyways, this is a bit of feedback to let you know that the problem is solved and I can again enjoy the pleasure of browsing up and down through posts and messages without worrying how long it will last.
November 10, 2020 5:48 pm
Scott W Bennett
November 13, 2020 11:50 pm
Climate believer
November 14, 2020 5:08 am
Climate believer
November 14, 2020 5:10 am
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Sasha
November 17, 2020 3:38 am
Tesla’s Supercharger Network In Australia Costs Nearly Double Than Filling Your Car With Gas
Using the Tesla Supercharger network, it is now costlier to recharge your vehicle than it is to gas up at a traditional gas station, according to a new report from Australia-based WhichCar. The news came as a result of a “recent price increase” to use the Superchargers and “incorrect fuel figures on the Tesla website.”
This puts an end to Tesla’s claims that recharging its vehicles offered savings versus traditional internal combustion engine vehicles.
“According to Tesla the cost of charging a Tesla Model 3 is $7 per 100km compared with$12 for a rival petrol car,” WhichCar notes, before revealing the estimate uses “at least three incorrect figures.” The report disputes “how much electricity a Tesla Model 3 uses, the cost of electricity at a Tesla Supercharger and the price of petrol.”
It also notes Tesla’s increase for its Supercharger to 52 cents per kilowatt-hour. The article calculates this recharging “even the most efficient” Model 3 Standard Range would cost $9.78 per 100km using a Supercharger. It then notes that BMW’s 330i costs$8 per 100km to fuel, assuming the country’s average cost of premium unleaded at $1.38 – a figure sourced from the country’s government. The BMW consumes 5.8 litres per 100km, which is below Tesla’s estimates of 7.0 litres per 100km. This means the BMW is actually 18% cheaper to fuel than a Tesla is to recharge at a Supercharger. If you run the same calculations with the hybrid-powered Lexus IS300h, the results are even more profound. The Lexus cost winds up about 31% lower than the Tesla charged using a Supercharger. Tesla first used its Supercharger network, promising “free” electricity and charging, to lure customers into the idea of an all electric future when the company first surfaced. Gradually, the allure of the idea wore off for the company and they began charging for use of the network. Like many other promises made by Tesla (solar roof tiles, 1 million robotaxis, full self driving), the concept of the Supercharger network looks like it has just run face first into a much needed reality check. https://www.whichcar.com.au/car-news/teslas-now-more-expensive-to-charge-than-petrol-cars jarves November 17, 2020 6:38 am jarves November 17, 2020 6:42 am jarves November 17, 2020 6:44 am jarves November 17, 2020 6:49 am jarves November 17, 2020 6:53 am niceguy November 18, 2020 1:25 pm 100 C niceguy November 18, 2020 1:30 pm income declared as “LMNP” = “loueur meublé non professionnel” in the 2042 C PRO tax paper Beta Blocker November 24, 2020 1:18 pm TEST OF COMMENT FORMATTING AND LENGTH Commenting on another article on WUWT, David Wojick said earlier this month that: “The American system is specifically designed so that the President has far less power than in the parliamentary system, where he would be head of Congress as well. No kings. Checks and balances. Biden can do very little without full Congressional support, which he will not have.” The last paragraph from Wojick’s article Biden’s False Climate Promises says this: “People running for President should only promise to do what Presidents can actually do. They cannot speak for Congress so should not pretend to. Biden’s climate promises are so false they are absurd. You can’t get there from here.” The reality here is this: Congressional buy-in isn’t needed if the goal is simply to achieve a quick reduction in America’s GHG emissions by any means necessary and without regard to the political consequences. Drawing upon existing legislation in the areas of environmental protection and national security, the president and the Executive Branch already have all the authority needed to enforce a steep reduction in America’s carbon emissions on a fast track schedule. What would constitute a ‘fast track schedule’? It would be President Obama’s original goal, as he stated it in 2012, of an 80% reduction in America’s GHG emissions by 2050, using 2005 as the baseline. Climate activist politicians can spend all the money they want to on low carbon energy technology and on Green New Deal projects. Energy conservation is the only way to close the gap between what low-carbon technology can accomplish and what the 80% GHG reduction target demands. In making the transition to the 80% target, strictly enforced energy conservation measures can and must be the most important resource management tool being applied. The bottom line is that if the 80% GHG reduction target is to be met, Americans must be using half as much energy on a per-capita basis in 2050 as we do today in 2020. If climate change is to be managed in the way the incoming Biden administration will be managing the COVID-19 pandemic, then what amounts to a fossil energy lockdown must be imposed, a.k.a. fuel rationing. Why rely on the EPA and the Executive Branch? Fifty years of environmental legislation places responsibility for controlling and reducing emissions of substances identified as dangerous pollutants into the hands of the president and the Environmental Protection Agency. The US Supreme Court has ruled that the process Obama’s EPA followed in identifying carbon emissions as pollutants under the Clean Air Act was proper and so let stand the EPA’s 2009 endangerment finding for carbon. Other legislation places responsibility for management of critical national security issues into the hands of the president. If the world is indeed burning up because of human-generated carbon emissions, then it is easy enough for the president to argue that anthropogenic global warming (AGW) is a national security threat as well as a global security threat and so falls under the scope of existing national security law. What will Joe Biden and his climate envoy John Kerry actually do after Biden assumes office? If human-driven climate change is in fact the urgent crisis climate activists say that it is, a newly inaugurated President Biden has no other choice morally or ethically but to immediately impose a program of carbon fuel rationing on the American people. He must do so as soon as he enters the White House. How could Joe Biden develop and then enforce a thirty-year carbon fuel rationing program? Back in mid-September, 2020, I posted a plan on WUWT for reducing America’s carbon emissions 80% by 2050. That target was former President Obama’s original goal as he stated it in 2012. My intention back then, and still is now, to demonstrate how steep reductions in America’s GHG emissions can be accomplished in the absence of any new legislation from Congress. The plan is entitled the Supply Side Carbon Emission Control Plan (SSCECP). It uses a series of executive orders which combine existing provisions of the Clean Air Act with existing provisions of national security legislation to create an integrated regulatory approach for increasing the cost of all carbon fuels and for systematically restricting their future production and commercial availability. The SSCECP uses the power of the federal government to create and enforce an artificial shortage of fossil fuels. It directly raises the price of all carbon fuels while directly reducing their future supply and availability, doing so through a process of imposing increasingly severe restrictions on their extraction, import, production, and distribution. In COVID-19 terms, the SSCECP can accurately be described as a phased fossil energy lockdown lasting as long as thirty years. The plan employs EPA-administered carbon pollution fines as the functional equivalent of a legislated tax on carbon. This approach supplies a powerful incentive for the state governments to participate in directly regulating America’s carbon emissions by assigning them the great bulk of the revenues produced from the EPA’s carbon pollution fines. As a further measure, a joint inter-agency Carbon Fuels Control Board (CFCB) is established to manage and enforce a phased systematic reduction in the production and distribution of all carbon fuel products. This board would report directly to the president’s Climate Envoy, John Kerry. As a practical expediency, the SSCECP keeps the import, production, and distribution of carbon fuels in private hands. Rather than nationalizing the oil and gas industry, the plan enlists private corporations as contracted agents in managing the government’s energy rationing programs. The federal government also guarantees a healthy profit and a steady rate return from the sale of all carbon fuels produced by those private corporations which choose to cooperate in managing the SSCECP’s phased series of GHG reductions. This approach makes the oil and gas industry an ally, not an adversary, in quickly reducing America’s GHG emissions. The SUPPLY SIDE CARBON EMISSION CONTROL PLAN (SSCECP) — the Major Phases: The start and end dates listed for each major phase assume Joe Biden is inauagurated as President on January 20th, 2020. Phase I: Establish a legal basis for regulating all of America’s carbon emissions. (2007-2020. Status complete.) Phase II: Expand and extend regulation of carbon GHG’s to all major sources of America’s carbon emissions. (01/22/2021 – 12/31/2021) Phase III: Establish a fully comprehensive regulatory framework for carbon. (01/01/2022 – 12/31/2022) Phase IV: Implement the carbon pollution regulatory framework. (Year 2023 through the Year 2049) Phase V: Declare success in reducing America’s carbon emissions 80% by 2050. (If complete by 2050 or some earlier date.) The SUPPLY SIDE CARBON EMISSION CONTROL PLAN (SSCECP) — a Detailed Description:. Here are the details of the plan: Phase I: Establish a legal basis for regulating all of America’s carbon emissions. (2007-2020. Status complete.) — File and win lawsuits to allow regulation of CO2 and other carbon GHG’s as pollutants under the Clean Air Act. (2007) — Publish a CAA Section 202 Endangerment Finding as a prototype test case for regulation of carbon GHG’s. (2009) — Defend the Section 202 Endangerment Finding in the courts. (2010-2012) — Establish a recent precedent, the COVID-19 pandemic, for taking strong government action in response to a declared national emergency. (2020) Phase II: Expand and extend regulation of carbon GHG’s to all major sources of America’s carbon emissions. (01/22/2021 – 12/31/2021) II.A: – Presidential Actions (Joe Biden), Phase II II.A.1 — Issue an Executive Order declaring a carbon pollution emergency. II.A.2 — Assign a joint task force of the US Environmental Protection Agency (US-EPA), the US Department of Homeland Security (US-DHS), and the US Department of Energy (US-DOE) to manage the declared emergency. II.A.3 — Create a joint interagency Carbon Fuels Control Board (CFCB) to manage a phased systematic reduction in the production and distribution of all carbon fuels. II.A.4 — Place the joint task force and the carbon fuels control board under the direct supervision of the president and his national security staff. II.A.5 — Issue a series of Executive Orders as needed to define and implement America’s carbon emissions regulatory framework. II.A.6 — Establish a public relations outreach program to explain and defend the actions being taken. II.A.7 — Defend the president’s executive orders in the courts. II.B: – EPA Actions (Carbon Emission Regulation), Phase II II.B.1 — Publish a Clean Air Act Section 108 Endangerment Finding which complements 2009’s Section 202 finding. II.B.2 — Declare carbon emissions as Hazardous Air Pollutants (HAPs) under CAA Section 112. II.B.3 — Establish a National Ambient Air Quality Standard (NAAQS) for carbon pollution. II.B.4 — Use the NAAQS for carbon pollution as America’s tie-in to international climate change agreements. II.B.5 — Defend the Section 108 Endangerment Finding, the NAAQS, and the Section 112 HAP Declaration in the courts. II.C: – CFCB Actions (Carbon Fuel Rationing), Phase II II.C.1 — Research and publish a provisional system for government-enforced carbon fuel rationing. II.C.2 — Defend the provisional system of carbon fuel rationing in the courts. Phase III: Establish a fully comprehensive regulatory framework for carbon. (01/01/2022 – 12/31/2022) III.A: – Presidential Actions (Joe Biden), Phase III III.A.1 — Issue a series of Executive Orders as needed to further define and further implement America’s carbon emissions regulatory framework. III.A.2 — Monitor and coordinate the activities the US-EPA, the US-DHS, and the US-DOE in response to the carbon pollution emergency. III.A.3 — Monitor the activities of the Carbon Fuels Control Board (CFCB) in reducing the import, production, and distribution of all carbon fuels. III.A.4 — Maintain and expand the public relations outreach program needed to explain and defend the anti-carbon actions being taken. III.A.5 — Defend the president’s executive orders in the courts. III.B: – EPA Actions (Carbon Emission Regulation), Phase III III.B.1 — Publish a regulatory framework for carbon pollution under Clean Air Act sections 108, 111, 112, 202, and other CAA sections as applicable. III.B.2 — Establish cooperative agreements with the states to enforce the EPA’s anti-carbon regulations. III.B.3 — Establish a system of carbon pollution fines which is the functional equivalent of a legislated tax on carbon. III.B.4 — Establish the legal basis for assigning all revenues collected from these carbon pollution fines to the states. III.B.5 — Defend the comprehensive system of carbon pollution regulations in the courts. III.C: – CFCB Actions (Carbon Fuel Rationing), Phase III III.C.1 — Establish cooperative agreements with the states to enforce the government’s system of carbon fuel rationing. III.C.2 — Establish a time-phased, hard-target schedule for reducing the production and distribution of all carbon fuels. III.C.3 — Establish production control agreements with private sector fossil fuel producers and distributors. III.C.4 — Establish a guaranteed profit schedule for the carbon fuels industry in return for production & distribution cutbacks. III.C.5 — Defend the government’s system of carbon fuel rationing in the courts. Phase IV: Implement the carbon pollution regulatory framework. (Year 2023 through the Year 2049) IV.A: – Presidential Actions (Joe Biden and his successor climate activist presidents), Phase IV IV.A.1 — Issue a series of Executive Orders as needed to further define and further implement America’s carbon emissions regulatory framework. IV.A.2 — Monitor and coordinate the activities the US-EPA, the US-DHS, and the US-DOE in response to the carbon pollution emergency. IV.A.3 — Monitor the activities of the Environmental Protection Agency (EPA) in enforcing carbon emission regulations. IV.A.4 — Monitor the activities of the Carbon Fuels Control Board (CFCB) in reducing the import, production, and distribution of all carbon fuels. IV.A.5 — Maintain and expand the public relations outreach program as needed to further explain and further defend the anti-carbon actions being taken. IV.A.6 — Defend the president’s executive orders in the courts. IV.B: – EPA Actions (Carbon Emission Regulation), Phase IV IV.B.1 — Commence operation of prior agreements with the states for enforcement of the EPA’s anti-carbon regulations. IV.B.2 — Commence the collection of carbon pollution fines and the distribution of fine revenues to the states. IV.B.3 — Monitor the effectiveness of the EPA’s carbon regulatory framework in reducing America’s GHG emissions. IV.B.4 — Monitor the effectiveness of renewable energy projects in reducing America’s GHG emissions. IV.B.5 — Monitor the effectiveness of energy conservation programs in reducing America’s GHG emissions. IV.B.6 — Adjust the schedule of carbon pollution fines upward if progress in reducing America’s GHG emissions lags. IV.B.7 — Defend the EPA’s system of carbon pollution regulations in the courts. IV.C: – CFCB Actions (Carbon Fuel Rationing), Phase IV IV.C.1 — Commence operation of prior agreements with the states for enforcement of the government’s system of carbon fuel rationing. IV.C.2 — Commence operation of production control agreements with private sector fossil fuel producers and distributors. IV.C.3 — Monitor the compliance of fossil fuel producers and distributors with their CFCB production control agreements. IV.C.4 — Monitor the profit levels of fossil fuel producers and distributors for conformance with the CFCB’s guaranteed profit schedule. IV.C.5 — Defend the government-mandated carbon fuel rationing program in the courts. Phase V: Declare success in reducing America’s carbon emissions 80% by 2050. (If complete by 2050 or some earlier date.) — The President issues a proclamation that the target of an 80% reduction has been achieved. — The President, the US-EPA, the US-DHS, and the US-DOE assess the need for continuing the EPA’s anti-carbon regulations and the US Government’s mandatory fuel rationing program as necessary to maintain the 80% goal. — If a determination is reached that the government’s system of carbon control measures must continue beyond 2050, existing agreements with the states and with private sector fossil fuel producers and distributors are extended with appropriate modifications. — Defend the government’s anti-carbon measures against emerging lawsuits if these measures must continue beyond 2050 REMARKS: The Supply Side Carbon Emission Control Plan is completely legal and constitutional. Under current law, it can be implemented unilaterally by the Executive Branch using its existing environmental protection and national security authorities. Not another word of new legislation is needed from Congress either to enable the plan legally or to fund its operation. Nor does the plan require a separate line of funding in the federal government’s budget. The planning activities and regulation roll-out activities are easily accomplished within the existing spending authorities of the US-EPA, the US-DOE, and the US-DHS. Even if the House and the Senate were both in Republican hands at some point in the next four years, and passed legislation specifically forbidding the adoption of a plan like the SSCECP, a presidential veto can kill that legislation with the stroke of a pen. A plan like the SSCECP will generate many lawsuits. If the plan is applied with equal force against all major sources of America’s carbon emissions and with equal impact upon all affected economic sectors and demographic groups, those lawsuits will go nowhere. It is specifically designed to survive any lawsuits brought against it. SUMMARY: The fact remains that the Executive Branch now has all the authority it needs to quickly reduce America’s carbon emissions on a highly aggressive fast-track schedule. A plan like the SSCECP fits entirely within that authority. What remains to be seen is whether or not President Elect Biden will use that authority when he takes office in January, 2021. If climate change is indeed the existential threat to our existence Joe Biden claims that it is, then he is ethically and morally obligated to act in accordance with his claims and to quickly reduce America’s carbon emissions just as far and as fast as current law allows him to do. Beta Blocker November 25, 2020 10:09 am FORMATTING TEST to see if links work: ================================= The results of the election are in. Climate activist politicians who push wind and solar and the dangers of climate change are in the driver’s seat. The voters were given a clear choice between climate activism and a more measured slow-go type of approach to climate policy. The voters went with the climate activists, the most prominent example being Pennsylvania. They went for Joe Biden even though he will put an end to fracking in their state. But, more importantly as a bellweather indicator for the future of climate activism in America, the voters knowingly chose politicians who would continue and even expand the COVID-19 lockdowns which have destroyed millions of American jobs and which have devastated the economies of a number of states. Earlier this week, I posted a comment on WUWT describing what I call the Supply Side Carbon Emission Control Plan (SSCECP). This plan uses the coercive power of the federal government to create and enforce an artificial shortage of fossil fuels. It directly raises the price of all carbon fuels while directly reducing their future supply and availability, doing so through a process of imposing increasingly severe restrictions on their extraction, import, production, and distribution. In COVID-19 terms, the SSCECP can be accurately described as a fossil fuel lockdown lasting as long as thirty years. The stated goal of the plan is to achieve an 80% reduction in America’s GHG emissions by 2050, using 2005’s emissions as the baseline standard of comparison. It’s the same goal President Obama articulated in 2012. By the year 2050, every American would be consuming roughly half as much energy on a per-capita basis as we do today in the year 2020. The Supply Side Carbon Emission Control Plan is completely legal and constitutional. Under current law, it can be implemented unilaterally by the Executive Branch using its existing environmental protection and national security authorities. Not another word of new legislation is needed from Congress either to enable the plan legally or to fund its operation. But the obvious question here is this. Would imposing a highly coercive fast-track carbon reduction plan on the American people — one which demands that every American accept significant personal and economic sacrifice — would such a plan produce enough political blowback to endanger the careers of the professional politicians who created and enforced it? The election of a climate activist president, and the success of those politicians who imposed and enforced the COVID-19 lockdowns, strongly suggest that the American public would in fact accept the sacrifices and the hardships which go with reaching an 80% reduction in our greenhouse gas emissions by 2050. Janice Moore December 6, 2020 12:53 pm Will THIS let me post a video here? [youtube https://www.youtube.com/watch?v=7W33HRc1A6c&w=640&h=480%5D George Carlin “Saving the Planet” youtube Gerry McIsaac December 6, 2020 5:32 pm Gerry McIsaac December 6, 2020 5:38 pm Gerry McIsaac December 6, 2020 5:57 pm file:///C:/Upload/CasesNY.jpg Gerry McIsaac December 6, 2020 5:58 pm Bryan A December 10, 2020 10:12 pm xx² Bryan A December 10, 2020 10:13 pm xx² Ttt D. J. Hawkins December 11, 2020 5:21 am underline ? BallBounces December 16, 2020 12:40 pm Google Chrome checked my passwords and reported — Compromised passwords Change these passwords immediately to keep your account safe: Found in data breach 1 hour ago wattsupwiththat.wordpress.com rkball@*** (my email address) •••••••••• (password) DOES ANYONE HAVE ANY IDEA WHAT THIS IS ABOUT?? There were two of these — one with an older WordPress password, and one with the current one. steve in seattle December 18, 2020 1:17 am "https://i2.wp.com/wattsupwiththat.com/wp-content/uploads/2018/05/cropped-WUWT-logo.jpg" steve in seattle December 18, 2020 1:21 am steve in seattle December 18, 2020 1:24 am steve in seattle December 18, 2020 1:25 am steve in seattle December 18, 2020 2:08 am no test Last edited 11 months ago by steve in seattle steve in seattle December 18, 2020 3:24 am see at : Last edited 11 months ago by steve in seattle Gunga Din December 18, 2020 5:29 pm Steve Case December 19, 2020 1:15 am <b>Does any of this work anymore?</b> <blockquote><p> China has its own space programme and continues to occupy Tibet by military force yet it is exempt from Paris on the grounds that it is a “developing country” Monckton of Brenchley </p></blockquote> <i>You may not agree with me, but I will to defend to your death my right to disagree. Berynn Schwerdt </i> <img src=”https://i.postimg.cc/m2H5SNpt/image.png”> Steve Case Reply to Steve Case December 19, 2020 1:22 am Nope, don’t work no more. China has its own space programme and continues to occupy Tibet by military force yet it is exempt from Paris on the grounds that it is a “developing country” Monckton of Brenchley You may not agree with me, but I will to defend to your death my right to disagree. Berynn Schwerdt Steve Case Reply to Steve Case December 19, 2020 1:26 am China has its own space programme and continues to occupy Tibet by military force yet it is exempt from Paris on the grounds that it is a “developing country” Monckton of Brenchley You may not agree with me, but I will to defend to your death my right to disagree. Berynn Schwerdt Steve Case December 19, 2020 1:42 am How ’bout just the url: https://postimg.cc/N5QDsTcc commieBob December 19, 2020 2:24 am testing <blockquote> testing </blockquote> testing Reply to commieBob December 19, 2020 4:09 am Reply to Krishna Gans December 19, 2020 4:10 am ??? was just an image link….. 🙁 December 19, 2020 4:17 am Put a link isn’t a mistery, but to edit the respective link text is, at last for me. Usually, an image is a link, why I’m asked to upload the image from my HD when trying to use the image tag ? December 19, 2020 4:19 am Reply to Krishna Gans December 19, 2020 4:20 am Image mistery solved, just the link in the edit box 😀 December 19, 2020 4:27 am Reply to Krishna Gans December 19, 2020 4:27 am Reply to Krishna Gans December 19, 2020 4:28 am Reply to Krishna Gans December 19, 2020 4:28 am https://youtu.be/qsARWIPkHHE Test video Just put the link is ok 😀 Last edited 11 months ago by Krishna Gans Reply to Krishna Gans December 19, 2020 4:56 am December 19, 2020 4:49 am Test Test Test Test Test Test I only still miss how to link including the respective link-text December 19, 2020 2:21 pm Projections suggest that, on land, air temperatures will rise and rainfall will decline across much of Australia in coming decades; the combination of these drivers will likely result in overall reduced runoff and therefore reduced stream flow and lake storage. However, present climate models are particularly limited with regard to coastal and freshwater systems, making them challenging to use for biological-impact and adaptation studies. Therefore, exactly how warming temperatures will interact with the complex interplay of drivers as outlined above is uncertain, but precipitation extremes and the frequency of severe weather events such as floods, storms and cyclones are expected to increase into the future … Reply to Krishna Gans December 19, 2020 2:23 pm I think, concerning blockquote, the older version was much better with its light grey background and normal letters. steve in seattle December 19, 2020 6:08 pm test ?raw=1 Last edited 11 months ago by steve in seattle steve in seattle December 19, 2020 7:05 pm test over Last edited 11 months ago by steve in seattle Kevin kilty December 24, 2020 6:48 am This is how the media behave everywhere else, so it is no surprise they do here as well. Have a look at SD on the <a href=https://usafacts.org/visualizations/coronavirus-covid-19-spread-map/state/south-dakota> USAFacts website </a>. Kevin kilty Reply to Kevin kilty December 24, 2020 7:00 am This is how the media behave everywhere else, so it is no surprise they do here as well. Have a look at SD on the <a href=”https://usafacts.org/visualizations/coronavirus-covid-19-spread-map/state/south-dakota”>USAFacts website</a>. Kevin kilty Reply to Kevin kilty December 24, 2020 7:02 am This is how the media behave everywhere else, so it is no surprise they do here as well. Have a look at SD on the <a href=https://usafacts.org/visualizations/coronavirus-covid-19-spread-map/state/south-dakota>USAFacts website</a>. Kevin kilty Reply to Kevin kilty December 24, 2020 7:02 am I don’t see what the problem is with this anchor. Reply to Kevin kilty December 26, 2020 1:10 pm Was my problem too. Write first the text: USAFacts website Then copy the respective link, mark the text, click on the link-button, and paste the link in the box and overwrite the highlighted text USAFacts website michael hart December 24, 2020 12:07 pm <blockquote>test</blockquote> December 25, 2020 9:42 am Try # 1 Reply to Writing Observer December 25, 2020 9:42 am Reply to Writing Observer December 25, 2020 9:43 am Reply to Writing Observer December 25, 2020 9:44 am Reply to Writing Observer December 25, 2020 9:46 am Again (if I understand Jack Black’s travails below) Reply to Writing Observer December 25, 2020 9:47 am https://www.youtube.com/watch?v=NWF2JBb1bvM Kevin A December 25, 2020 11:37 am My lump of coal provided by FedEx temporary driver <a href=”http://aaes.us/Sony/fullcase.jpg” target=”_blank”> Sony UBP X700</a> All claim images http://aaes.us/Sony It doesn't add up... December 26, 2020 5:28 am https://datawrapper.dwcdn.net/iL71K/2/ [iframe https://datawrapper.dwcdn.net/iL71K/2/&w=640&h=480] Last edited 11 months ago by It doesn't add up... Jim Ross December 26, 2020 10:02 am Redge December 27, 2020 6:10 am test Steve Case December 27, 2020 10:24 pm Let’s see if I can post an image from my files: Steve Case December 27, 2020 10:26 pm Let’s see if I can post an image from a URL: Will it show up? Steve Case Reply to Steve Case December 27, 2020 10:27 pm Yay! John F Hultquist December 29, 2020 3:47 pm Song: <a href=”https://www.youtube.com/watch?v=Ow9FV3xjkew”><strong>Mike Stinson’s ” The Late Great Golden State”</strong></a> steve in seattle December 30, 2020 2:55 am I wish posters that ARE able to post an image, would also, in their try include the URL that they used – does it end with a .jpg ??? Google photos AND seems like most other ” free ” image posting sites insist in using a URL that has as part of the path, a meta component ! Further RAW =1 or RAW=whatever doesn’t seem to be a cure. Curses ! Last edited 11 months ago by steve in seattle steve in seattle December 30, 2020 3:01 am steve in seattle December 30, 2020 3:13 am OK, take a look at what happens with : i.postimg.cc/X7gsgmcg/postimage with the usual stuff tacked onto the front and a .jpg on the end . It’s an easy sign up too ! steve in seattle December 30, 2020 3:16 am OK, OK, i do feel dumb, yes you can click on the posted image to get the URL ! It’s late, but that’s no excuse – anyway, you can see the home for i.postimg.cc at least ! Chas December 31, 2020 6:59 am Chas December 31, 2020 7:01 am test Nicholas M. James December 31, 2020 9:41 am Nicholas M. James December 31, 2020 9:42 am <script>!function(r,u,m,b,l,e){r._Rumble=b,r[b]||(r[b]=function(){(r[b]._=r[b]._||[]).push(arguments);if(r[b]._.length==1){l=u.createElement(m),e=u.getElementsByTagName(m)[0],l.async=1,l.src=”https://rumble.com/embedJS/u6bo0j”+(arguments[1].video?’.’+arguments[1].video:”)+”/?url=”+encodeURIComponent(location.href)+”&args=”+encodeURIComponent(JSON.stringify([].slice.apply(arguments))),e.parentNode.insertBefore(l,e)}})}(window, document, “script”, “Rumble”);</script> <div id=”rumble_v9l73h”></div> <script> Rumble(“play”, {“video”:”v9l73h”,”div”:”rumble_v9l73h”});</script> Nicholas M. James December 31, 2020 9:44 am Guess the rumble embed only works from the BuddyPress? Reply to Nicholas M. James January 14, 2021 1:10 pm Reply to Nick Stokes January 14, 2021 1:12 pm Reply to Nick Stokes January 14, 2021 1:16 pm Reply to Nick Stokes January 14, 2021 1:20 pm again Nicholas M. James December 31, 2020 9:46 am Or perhaps it just needs a different plugin. https://winningwp.com/best-commenting-plugins-for-wordpress/ January 4, 2021 3:49 pm notation $y(t)= x(t)u(t)$ and Lord Monckton’s more opaque $\Delta T_t= q_t^{-1}\Delta F_tr_t\lambda_\infty$ Briefly, Lord Monckton’s $q_t^{-1}\Delta F_t$ is the stimulus $x(t)$, his $\Delta T_t$ is the system’s response $y(t)$ to that stimulus $x(t)$, and his $r_t\lambda_\infty$ is what the system’s response $u(t)$ to Captain Katzenjammer January 11, 2021 1:22 am Last edited 10 months ago by Captain Katzenjammer Reply to Captain Katzenjammer January 26, 2021 2:13 pm Image Reply to Nick Stokes January 26, 2021 2:17 pm Captain Katzenjammer January 11, 2021 1:25 am Captain Katzenjammer January 11, 2021 1:26 am third attempt. Might have mistyped the terminal bracket last time I didn’t. The final bracket was altered after entry to “>” Last edited 10 months ago by Captain Katzenjammer Captain Katzenjammer January 11, 2021 1:39 am Last edited 10 months ago by Captain Katzenjammer Admin January 18, 2021 8:15 pm Yo Last edited 10 months ago by Eric Worrall JWurts January 25, 2021 10:20 pm testing image upload Reply to JWurts January 26, 2021 2:15 pm Reply to Nick Stokes January 27, 2021 11:02 am test <i>italics</i> JWurts January 25, 2021 10:23 pm Another test JWurts January 25, 2021 11:19 pm Anthony A generic suggestion for your new site but with a specific example. Many of my friends are reasonably intelligent but they are also rather innumerate. They buy into the CAGW story because the way it is presented does not require math & science skills. Save the planet, save the whales, alternative energy will create jobs…yada yada. To many of them charts & graphs might as well be abstract paintings, and when encountering millions, billions, mega & giga they space out & loose interest. However they do have enough math so that dollars & cents are understandable. Considering this, I am going to offer an additional way to discuss the message being presented in your “Antarctic Ice Melt is Dangerous” article. The below picture is an image of 10,000 quarters, ($2,500.00). Imagine that these quarters represent the ice cover on Antarctica in 1990. So that each of these 10,000 coins is equivalent to 2,500 gigatons of ice. So how many coins will it take to represent the 25 year ice loss in Antarctica and Greenland?
Boy this is scary…drum roll please…the answer is…ONE, one quarter. Just one out of the 10,000 coins has melted away.
Should we be scared yet?
Is global warming a catastrophe yet?
I believe that this is an explanation that can be understood by the average person that Jay Leno used to interview on his “jaywalks”
BTW – Are we really supposed to believe that the CAGW scientists can accurately determine the volume of ice on Antarctica to one part in 10,000?…..Really?
Considering the main message of the CAGW crowd is fear, this kind of message might minimize it.
I’m sure you can do a better job of presenting this than I just did.
Best
Jack
curly
February 19, 2021 1:50 pm
https://www.eia.gov/beta/electricity/gridmonitor/expanded-view/electric_overview/regional/REG-TEX/GenerationByEnergySource-9/edit
<a href=https://www.eia.gov/beta/electricity/gridmonitor/expanded-view/electric_overview/regional/REG-TEX/GenerationByEnergySource-9/edit>Test EIA beta</a>
curly
February 19, 2021 1:58 pm
Bellman
February 27, 2021 5:22 am
$u_R = ku_R$
Gunga Din
February 27, 2021 9:05 am
Test video
Last edited 9 months ago by Gunga Din
Bellman
February 27, 2021 1:18 pm
$\frac{u_R}{R} = \frac{u_A}{A}$
Anthony
March 4, 2021 10:27 am
An<u>th</u>ony
Bellman
March 7, 2021 5:18 am
March Range Pause Start Pause Length
+0.39 - +0.54 Sep 2015 5 Years 7 Months
+0.13 - +0.38 Aug 2015 5 Years 8 Months
+0.05 - +0.12 Jul 2015 5 Years 9 Months
-0.08 - +0.04 Jun 2015 5 Years 10 Months
-0.37 - -0.09 May 2015 5 Years 11 Months
-0.56 - -0.38 Apr 2015 6 Years 0 Months
-0.76 - -0.57 Mar 2015 6 Years 1 Month
Last edited 9 months ago by Bellman
Janice Moore
April 7, 2021 5:02 pm
<blockquote> why didn’t this blockquote format work in my comment today?</blockquote>
Janice Moore
April 7, 2021 5:02 pm
<b>does bold still work?</b>
Janice Moore
April 7, 2021 5:03 pm
<i> italics?</i>
Bellman
April 8, 2021 5:24 am
<code>
April Range Pause Start Pause Length
———————————————————-
+0.40 – +0.65 Aug 2015 5 Years 9 Months
</code>
Bellman
April 8, 2021 5:24 am
<pre>
April Range Pause Start Pause Length
———————————————————-
+0.40 – +0.65 Aug 2015 5 Years 9 Months
</pre>
Bellman
April 8, 2021 5:28 am
April Range Pause Start Pause Length
----------------------------------------------------------
+0.40 - +0.65 Aug 2015 5 Years 9 Months
+0.32 - +0.39 Jul 2015 5 Years 10 Months
April 21, 2021 2:09 pm
$\displaystyle dS=\frac{\delta Q}{T}$
May 9, 2021 7:51 am
May 9, 2021 1:53 pm
png tes
May 9, 2021 10:14 pm
test PGN ed
Bellman
May 22, 2021 8:38 am
$\int_{0}^{\pi} (Vp_{day}/pi) sin(x) dx$
Bellman
May 22, 2021 8:39 am
$\int_{0}^{\pi} (Vp_{day}\pi) \sin(x) dx$
Bellman
May 22, 2021 8:39 am
$\int_{0}^{\pi} (Vp_{day}\/pi) sin(x) dx$
Bellman
May 22, 2021 8:40 am
$\int_{0}^{\pi} (Vp_{day}/\pi) \sin(x) dx$
Bellman
May 22, 2021 8:42 am
$\frac{1}{\pi}\int_{0}^{\pi} (Vp_{day}) \sin(x) dx$
JCM
June 4, 2021 8:42 am
test
<blockquote>some text </blockquote>
end
JCM
June 4, 2021 8:53 am
<blockquote><p> quoted text </p></blockquote>
JCM
June 4, 2021 9:02 am
testing 123
JCM
June 4, 2021 12:50 pm
word
yo
Last edited 6 months ago by JCM
TEWS_Pilot
June 5, 2021 12:57 pm
Last edited 6 months ago by TEWS_Pilot
TEWS_Pilot
June 5, 2021 1:20 pm
TEWS_Pilot
June 5, 2021 3:41 pm
?w=800&h=623
TEWS_Pilot
June 7, 2021 12:17 pm
Last edited 6 months ago by TEWS_Pilot
TEWS_Pilot
June 10, 2021 10:44 am
Last edited 5 months ago by TEWS_Pilot
TEWS_Pilot
June 10, 2021 11:26 am
Last edited 5 months ago by TEWS_Pilot
TEWS_Pilot
June 10, 2021 2:50 pm
TEWS_Pilot
June 11, 2021 12:31 pm
Electric boat teeters on edge of Texas dam… Saved by gas-powered boat…
Last edited 5 months ago by TEWS_Pilot
TEWS_Pilot
June 11, 2021 2:56 pm
TEWS_Pilot
June 12, 2021 7:39 am
TEWS_Pilot
June 16, 2021 8:25 pm
John Garrett
June 23, 2021 3:06 pm
Bellman
June 29, 2021 4:18 am
$\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{N}}$
Last edited 5 months ago by Bellman
TEWS_Pilot
July 8, 2021 9:16 am
TEWS_Pilot
July 9, 2021 6:30 pm
TEWS_Pilot
July 11, 2021 8:34 pm
TEWS_Pilot
July 20, 2021 8:39 am
TEWS_Pilot
July 20, 2021 8:50 am
John Garrett
July 30, 2021 11:29 am
Why isn’t this image displayed?
http://www.climate4you.com/images/MSU%20UAH%20GlobalMonthlyTempSince1979%20AndCO2.gif
I can’t think of any other ideas to make it appear as an image. I give up.
Last edited 4 months ago by John Garrett
Bellman
August 3, 2021 5:03 am
Image test
John Garrett
August 17, 2021 9:44 am
Editors/Monitors: It doesn’t look like it’s going to work. Feel free to delete this post.
Image test
?g=Gbjn
It doesn’t look like it’s going to work. Feel free to delete this post.
Last edited 3 months ago by John Garrett
Janice Moore
August 22, 2021 1:45 pm
1. Bold
2. italics
3. underline
• strike
A quotation
not part of quote
<b>BOLD</b>
A cool song:
Another video link to above song:
What is this (“Spoiler”)?
Hello, World! :)
Janice Moore
August 22, 2021 1:48 pm
Another attempt at video post, now using “Embed”
Janice Moore
August 22, 2021 1:51 pm
Trying to get the video to post with a still frame like I used to be able to do …. (removed “[youtube” from above link)
Janice Moore
August 22, 2021 3:32 pm
Now, for an image:
https%3A%2F%2Ffscomps.fotosearch.com%2Fcompc%2FCSP%2FCSP329%2Fbutterfly-on-flower-of-dahlia-stock-image__k23079103.jpg
Janice Moore
August 22, 2021 3:35 pm
Cool! But, how did the still materialize?? It wasn’t there when I posted my comment. Was it after I left WUWT and returned? I will try refreshing page to make the still image appear (if it doesn’t appear right off the bat, here):
Janice Moore
August 22, 2021 3:39 pm
THAT WAS IT! 🙂 YAY! Just needed to refresh to get youtube still/control window to appear.
Now, for an image again….
Janice Moore
August 22, 2021 5:02 pm
HOORAY!!!!!!
Beta Blocker
August 30, 2021 9:14 am
The Supply Side Carbon Emission Control Plan (SSCECP):
A fast track approach for reaching President Biden’s greenhouse gas reduction targets
(August 30th, 2021 Update — Placed here on WUWT for reference by other web sites.)
———————————————————————————
The Biden administration wants a 50% reduction in America’s greenhouse gas (GHG) emissions by 2030. In addition, America’s power generation sector is to achieve net-zero emissions by 2035. America must be fully net zero by 2050.
These are highly ambitious targets. But can these targets actually be met?
The means by which these targets are to be achieved is the rapid electrification of America’s entire energy infrastructure. The transition is being funded in large part by the Green New Deal and will be implemented through a massive commitment to wind and solar energy backed by grid-scale batteries and by a greatly expanded power transmission network.
But regardless of how much money is being spent by the Green New Deal on a renewable energy power grid, can enough wind turbines, enough solar panels, enough storage batteries, and enough new-build power transmission lines be manufactured, sited, and installed in time to fully replace America’s legacy electricity resources by the year 2035?
What about transportation? Can enough electric vehicles be manufactured and sold by 2050 to largely eliminate gasoline and diesel powered transportation in America? Can our airliners and our airports be replaced with high speed trains powered by an electrified intercity rail system? Will enough renewable electricity be available to power our cars, our trucks, and our trains and at the same time power our homes, our municipal services, and our factories?
Can all this be done on Biden’s schedule? Or is it really the case that the only means of guaranteeing Biden’s reduction targets can be met is through government-enforced rationing of fossil fuel energy?
* The Realities of a Credible Greenhouse Gas Reduction Plan *
Climate activists argue that America’s leadership in quickly reducing our own carbon emissions is essential for convincing China and India to quickly reduce theirs. If convincing China and India to follow our lead is the goal, simply spending money isn’t enough. A credible GHG reduction plan is one which actually achieves Biden’s emission reduction targets on the timetable he has announced.
Resetting America’s economic, cultural, and social order in accordance with President Biden’s social justice agenda is as much of an objective, if not more of an objective, of the Green New Deal as is a quick reduction of our GHG emissions. However, if the goal is to quickly reduce our emissions in order to demonstrate that it can be done, then technology innovation alone can’t do it. Building enough wind and solar to replace even half of our fossil electricity resources by 2030 is impossible.
Only through a policy of mandatory energy conservation measures can Biden’s targets be met. Government enforced energy rationing, in other words. Americans must do with the Green New Deal what the Germans have done with their Energiewende: double the cost of energy for the average consumer and reduce the average person’s energy consumption to roughly half of what we consume today.
* The Goals of a Fast Track GHG Reduction Strategy *
America’s legacy energy infrastructure is the product of more than a hundred years of economic, technical, and industrial evolution. If America’s energy infrastructure is to be replaced on President Biden’s schedule, then a process which historically took a hundred years must be compressed into a timeframe of no more than thirty years. Any fast-track greenhouse gas reduction strategy must achieve these goals:
1 — Be highly effective in quickly reducing America’s GHG emissions.
2 — Be conceptually and operationally simple to implement, relatively speaking.
3 — Be in alignment with past regulatory practice and past legal precedent.
4 — Be constitutionally and legally defensible in the courts.
5 — Be formulated and written in a way which discourages lawsuits.
6 — Motivate all energy consumers to quickly reduce their energy consumption.
7 — Incentivize the participation of the fifty state governments in controlling our GHG emissions.
8 — Incentivize private sector corporations to cooperate in reducing our GHG emissions.
* The Supply Side Carbon Emission Control Plan (SSCECP) *
The Executive Branch of the US Government already has all the legal authority it needs to unilaterally impose a fossil fuel lockdown on the American economy. That authority can be enabled in practice by combining elements of the Clean Air Act with elements of national security law as it applies to the declaration of a national emergency.
The Supply Side Carbon Emission Control Plan (SSCECP) is a means for guaranteeing that the Biden administration’s ambitious GHG reduction targets can be met.
The basic starting point for the SSCECP is the declaration of a climate emergency. A series of Executive Orders is then issued which define and enable further action under the plan.
The SSCECP incentivizes energy conservation by imposing higher prices on all forms of energy and by placing direct constraints on energy production and consumption. Higher energy prices will in turn attract greater levels of investment in zero carbon energy technologies and will also allow the higher costs of wind, solar, and nuclear — assuming we choose to use nuclear — to be spread more evenly among all energy consumers.
Under the SSCECP, Americans will be consuming roughly half as much energy per capita in 2030 as we do today in 2021, and roughly one-third as much by 2050.
In order to expedite environmental reviews and other permitting reviews of new-build wind, solar, nuclear, energy storage, and energy transmission facilities — portions of the National Environmental Policy Act (NEPA), along with portions of other project permitting requirements, are either partially suspended or else are bypassed altogether, as specifically directed by the President for each eligible new-build energy facility.
Moreover, the president is empowered to assert federal eminent domain over all lands, waters, and properties, either publicly owned or privately owned, which are to be reserved by the federal government for wind, solar, nuclear, energy storage, and/or power transmission development.
A hard target schedule is established for the phased shutdown of America’s legacy fossil fuel infrastructure.
This schedule includes the closure of coal-fired and natural gas-fired power plants, oil fields and refineries, fracked natural gas fields, LNG production facilities and terminals, and the majority of our petroleum product pipelines and distribution terminals. Each legacy fossil fuel power plant and each fossil energy support facility being targeted for shutdown is listed individually on this master closure schedule.
* The Eight Elements of the Supply Side Carbon Emission Control Plan (SSCECP) *
These are the eight major elements of the SSCECP:
I: Establish the legal basis for regulating all of America’s carbon emissions (1941-2021. Status ‘Complete’)
II: Declare a climate emergency and publish a climate crisis response plan (2021)
III: Expand and extend federal regulation and control of all carbon emissions (2021-2022)
IV: Establish an expanded carbon emission regulation program (2021-2022)
V: Establish a carbon fuel rationing program (2021-2022)
VI: Establish a process for expedited energy project siting, permitting, and approval. (2021-2022)
VII: Publish and implement a national energy infrastructure transition plan (2021-2022)
VIII: Perform ongoing GHG reduction monitoring & control activities (2023 through 2050)
These are the lower-level implementation details of the SSCECP:
I: Establish the legal basis for regulating all of America’s carbon emissions (1941-2021. Status ‘Complete’)
I-a: Impose government-mandated energy rationing in response to a declared national emergency, World War II. (1941-1945)
I-b: Pass legislation establishing the regulation of harmful atmospheric pollutants under the Clean Air Act. (1970)
I-c: Establish the Environmental Protection Agency and further define and implement the process for controlling and reducing pollutants. (1970-2020)
I-d: File and win lawsuits to allow regulation of carbon dioxide and other carbon GHG’s as pollutants under the Clean Air Act. (2007)
I-e: Publish a CAA Section 202 Endangerment Finding as a prototype test case for regulation of carbon GHG’s. (2009)
I-f: Successfully defend the CAA Section 202 Endangerment Finding in the courts. (2010-2012)
I-g: Establish a recent precedent, the COVID-19 pandemic, for taking strong government action in response to a declared national emergency. (2020-2021)
II: Declare a climate emergency and publish a climate crisis response plan (2021)
II-a: Issue an Executive Order declaring a climate emergency.
II-b: Publish a Climate Crisis Response Plan (CCRP) which establishes a defined strategic mix among three major policy directions covering: a) zero-carbon energy production; b) energy conservation technology; and c) mandated energy conservation measures.
II-c: Establish a comprehensive list of carbon emission reduction targets and a detailed strategy and plan for reducing each category of carbon emissions.
II-d: Establish a formal process for coordinating and reconciling America’s GHG reduction goals with its environmental justice, climate justice, and social justice goals.
II-e: Assign a joint task force comprised of all cabinet level departments, plus the National Security Agency, to manage the carbon pollution emergency.
II-f: Create a joint interagency control board to manage a phased systematic reduction in the production and distribution of all carbon fuels.
II-g: Place this control board under the direct supervision of the president and his national security staff.
II-h: Defend the president’s emergency actions as needed in response to specific lawsuits filed in the courts.
III: Expand and extend federal regulation and control of all carbon emissions (2021-2022)
III-a: Issue an Executive Order further defining the scope of the declared carbon pollution emergency.
III-b: Issue an Executive Order further defining the scope and objectives of the Climate Crisis Response Plan (CCRP).
III-c: Issue an Executive Order establishing an expanded carbon emission regulation program.
III-d: Issue an Executive Order establishing a carbon fuel rationing program.
III-e: Issue an Executive Order establishing an ongoing program for continuous monitoring and control of carbon emission reduction activities.
III-f: Issue an Executive Order suspending the application of anti-trust regulations in the energy marketplace.
III-g: Issue an Executive Order allowing for the suspension of portions of the National Environmental Policy Act (NEPA) in order to expedite environmental reviews of new-build wind, solar, and nuclear facilities.
III-h: Issue an Executive Order granting authority to the President to reverse the final decisions of federal, state, and local permitting agencies if those decisions are deemed to be ‘not in the national interest’ as that stipulation is defined within the Climate Crisis Response Plan.
III-i: Issue an Executive Order granting authority to the President to assert federal eminent domain over all lands, waters, and properties, either publicly owned or privately owned, identified as being necessary for the siting of new-build energy facilities.
III-j: Defend the president’s expansion of federal authority as needed in response to specific lawsuits filed in the courts.
IV: Establish an expanded carbon emission regulation program (2021-2022)
IV-a: Publish a Clean Air Act Section 108 Endangerment Finding which complements 2009’s Section 202 finding.
IV-b: Declare carbon emissions as Hazardous Air Pollutants (HAPs) under CAA Section 112.
IV-c: Establish a National Ambient Air Quality Standard (NAAQS) for carbon pollution.
IV-d: Use the NAAQS for carbon pollution as America’s tie-in to international climate change agreements.
IV-e: Defend the Section 108 Endangerment Finding, the NAAQS, and the Section 112 HAP Declaration in the courts.
IV-f: Publish a regulatory framework for carbon pollution under Clean Air Act sections 108, 111, 112, 202, and other CAA sections as applicable.
IV-g: Establish cooperative agreements with the states to enforce the EPA’s anti-carbon regulations.
IV-h: Establish a system of carbon pollution fines which is the functional equivalent of a legislated tax on carbon.
IV-i: Establish the legal basis for sharing the revenues collected from these carbon pollution fines among the federal and state governments.
IV-j: Defend the comprehensive system of carbon pollution regulations in the courts.
V: Establish a carbon fuel rationing program (2021-2022)
V-a: Research and publish a system for government-enforced carbon fuel rationing.
V-b: Establish a time-phased, hard-target schedule for reducing the production and distribution of all carbon fuels.
V-c: Establish cooperative agreements with the state governments to enforce the federal government’s system of carbon fuel rationing.
V-d: Establish production control agreements with private sector fossil fuel producers and distributors.
V-e: Establish a guaranteed profit schedule for the carbon fuels industry in return for production & distribution cutbacks.
V-f: Defend the government’s system of carbon fuel rationing in the courts.
VI: Establish a process for expedited energy project siting, permitting, and approval. (2021-2022)
VI-a: Research and publish a system and process for expedited governmental review and permitting for the siting and construction of new-build wind, solar, nuclear, energy storage, and power transmission facilities.
VI-b: Establish cooperative agreements with federal and state agencies for expedited reviews and approvals of energy infrastructure projects.
VI-c: Establish a register of new-build wind, solar, nuclear, energy storage, and power transmission projects eligible for an expedited permitting review and approval process.
VI-d: For those projects listed on the expedited review register, establish a process and a procedure to be followed if the President reverses the final decisions of federal, state, and local permitting agencies, if those decisions are deemed ‘not in the national interest’.
VI-e: Establish a register of lands, waters, and properties, both publicly owned and privately owned, which may become the targets of federal reservation actions for the siting of new-build energy infrastructure.
VI-f: For those lands, waters, and properties listed in the reservation action register, establish a process and a procedure to be followed if the President asserts federal eminent domain over those lands, waters, and properties.
VI-g: Defend the government’s expedited siting, permitting, and environmental review processes in the courts.
VII: Publish and implement a national energy infrastructure transition plan (2021-2022)
VII-a: Research and publish a national energy infrastructure transition plan for the siting and construction of new-build wind, solar, nuclear, energy storage, and power transmission facilities.
VII-b: Publish and implement a hard-target schedule for deployment of new-build wind and solar facilities, new-build nuclear facilities, new-build grid-scale energy storage facilities, and new-build energy transmission capacity.
VII-c: Publish and implement a technology implementation plan which specifically identifies those energy technologies to be prioritized for near term investment, development, and production.
VII-d: Publish and implement a US Treasury policy plan for redirecting energy market financial investments as needed to support the federal government’s GHG reduction goals.
VII-e: Publish and implement an Energy Infrastructure Land Use Plan (EILUP) which identifies those lands, waters, and properties, either publicly owned or privately owned, which are to be reserved by the federal government for wind, solar, nuclear, energy storage, and/or power transmission development.
VII-f: Publish and implement an Energy Facility Closure Plan (EFCP) which specifically identifies those legacy coal, natural gas, and nuclear facilities which are to be decommissioned between 2022 and 2050, including a specific target date by which each legacy facility is to be retired.
VII-g: Defend the government’s national energy infrastructure transition plan in the courts.
VIII: Perform ongoing GHG reduction monitoring & control activities (2023 through 2050)
VIII-a: Issue a further series of Executive Orders, as needed, to further define and further implement America’s carbon emissions regulatory framework, America’s carbon fuel rationing program, the federal government’s expedited energy facility permitting process, and the government’s energy infrastructure transition plan.
VIII-b: Monitor the effectiveness of the EPA’s carbon regulation framework in reducing America’s GHG emissions.
VIII-c: Monitor the effectiveness of renewable energy projects in reducing America’s GHG emissions.
VIII-d: Monitor the effectiveness of energy conservation programs in reducing America’s GHG emissions.
VIII-e: Monitor the effectiveness of carbon fuel rationing programs in reducing America’s GHG emissions.
VIII-f: Monitor the progress of the energy infrastructure transition plan in closing legacy fossil fuel energy facilities.
VIII-g: Adjust the schedule of carbon pollution fines upward if progress in reducing America’s GHG emissions lags.
VIII-h: Adjust the carbon fuel rationing targets upward if progress in reducing America’s GHG emissions lags.
VIII-i: Continue to defend the comprehensive system of carbon pollution regulations and the government-mandated energy rationing programs in the courts.
VIII-j: Continue to assess the need for enforcing the government’s GHG reduction programs beyond the year 2050.
* REMARKS *
President Biden says that climate change is the most serious problem the world now faces. Biden’s climate czar John Kerry says that America’s leadership in quickly reducing our own carbon emissions is vital for convincing other nations, especially China and India, to do the same.
The plan described above, the SSCECP, is a highly coercive approach for quickly reducing America’s GHG emissions. However, it is also completely legal and constitutional under current law. The SSCECP can be implemented unilaterally by the Executive Branch using its existing environmental protection and national security authorities. Not another word of new legislation is needed from Congress either to enable the plan legally or to fund its operation.
Nor does the plan require a separate line of funding in the federal government’s budget. The planning activities and regulation roll-out activities are easily accomplished within the existing spending authorities of the US-EPA, the US-DOE, the USDT, and the US-DHS.
A plan like the SSCECP will generate many lawsuits. But if the plan is applied with equal force against all major sources of America’s carbon emissions, and with equal impact upon all affected economic sectors and demographic groups, those lawsuits will go nowhere. It is specifically designed to survive any lawsuits brought against it.
Even if the House of Representatives and the Senate were both in Republican hands in January, 2023, and passed legislation forbidding the adoption of a plan like the SSCECP, a presidential veto can kill that legislation with the stroke of a pen.
So the big question remains. How far will President Biden and his climate czar John Kerry go in acting upon their stated convictions? Will they, or won’t they, do all that is in their power as our Chief Executive and our climate czar to reduce America’s carbon emissions just as far and as fast as climate activists say is necessary?
——————————————————-
Disclosure: I’ve spent thirty-five years in nuclear construction and operations. Because the bulk of my occupational radiation exposure has come from beta-gamma sources, my internet handle is ‘Beta Blocker’.
Last edited 3 months ago by Beta Blocker
Steve Case
September 30, 2021 10:43 pm
This is the spoiler
What does the spoiler do?
Doug S
October 16, 2021 8:41 am
Doug S
October 16, 2021 8:42 am
Try that again:
j wurts
October 16, 2021 12:49 pm
Test pics
j wurts
October 16, 2021 12:51 pm
another pic
j wurts
October 16, 2021 12:52 pm
A third pic
Doug S
October 24, 2021 4:33 am
image test
Last edited 1 month ago by Doug S
Editor
October 26, 2021 12:17 pm
<iframe width=”640″ height=”360″ src=”https://www.youtube.com/embed/MF-Mmk30cOE” title=”YouTube video player” frameborder=”0″ allow=”accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture” allowfullscreen></iframe>
Editor
October 26, 2021 12:18 pm
<code><iframe width=”640″ height=”360″ src=”https://www.youtube.com/embed/MF-Mmk30cOE” title=”YouTube video player” frameborder=”0″ allow=”accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture” allowfullscreen></iframe></code>
Editor
October 26, 2021 12:18 pm
Bellman
November 12, 2021 4:50 am
$\pm\bar{\sigma}^\prime_\mu = \sqrt{N \times \bar{\sigma}^{\prime^2}_{noise} / (N - 1)}$
Last edited 27 days ago by Bellman
Steve Case
November 13, 2021 12:07 am
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# Short five lemma in Banach spaces
Denote by $\mathbf{Ban}$ the category of Banach spaces and bounded linear maps and by $\mathbf{Banc}$ the subcategory of Banach spaces and linear contractions. The isomorphisms of $\mathbf{Ban}$ are the bounded linear bijections (open mapping theorem) and in $\mathbf{Banc}$ they are the isometric (linear) isomorphisms (easy computation). $\mathbf{Ban}$ is additive and has all finite limits and finite colimits, so we can speak of (short) exact sequences.
proposition: the short five lemma holds in $\mathbf{Ban}$. proof: courtesy of the open mapping theorem, the diagram-chase proof for abelian groups transfers verbatim.
Now for my question:
Q: does the five short lemma also hold in $\mathbf{Banc}$?
Since $\mathbf{Banc}$ is not additive, a few words about the definitions. The crucial thing to notice is that kernels and cokernels in $\mathbf{Ban}$ are also kernels and cokernels in $\mathbf{Banc}$. For the sake of illustration, take the case of cokernels. In $\mathbf{Ban}$ they are given by the quotient map $\pi:B\to B/M$ with $M$ a closed subspace of $B$. If $T$ is a bounded linear map whose kernel contains $M$, then it factors uniquely through $\pi$ and the norm of the factorization equals the norm of $T$. But this is precisely what is needed for $\pi$ to be a cokernel in $\mathbf{Banc}$.
So now, we have two short exact sequences connected by maps $g$, $f$ and $h$ with $g$ and $h$ isometric isomorphisms and $f$ a linear contraction. The short five lemma holds if $f$ is an isometric isomorphism -- is there a way to draw diagrams? In any case, just look at short five lemma.
Start by noticing that by the above proposition $f$ must be a bijection and thus it has an inverse. What we need to prove is that this inverse is contractive. Alternatively, since we already know that $f$ is injective, the following easy result offers another route.
proposition: a map $f$ is a quotient iff it is surjective on open unit balls iff it is dense on unit balls.
Applying the above and chasing down an element of the open unit ball of the codomain of $f:B\to B'$, we get is that there is a $b$ in the open unit ball of $B$ and an $m$ in the kernel of the quotient in the top short exact sequence such that $f(b + m) = b'$. But of course, this does not get us very far.
At this point, I am beginning to suspect that the lemma does not hold, but I have been unable to rig a counterexample. The hypothesis is very strong and rules out the "usual" gang of suspects.
regards, G. Rodrigues
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How about considering $\mathbb R^2$ with $l^1$ and $l^2$ norms. The restriction to the $x$-axis is an isometry. The quotient onto the $y$-axis, also an isometry. But not an isometry on the whole space.
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# Abort not aborting
I have a relatively simple bit of code that looks like the following:
---some code here---
If[statement, Abort[]];
---more code following---
However, while $Aborted appears as output, the evaluation of the rest of the cell does not abort, continuing execution of code beyond the If statement. How do I actually get the running cell to cease evaluating the rest of the cell? Edit: It seems that one way to accomplish this is to wrap the entire cell in parenthesis, e.g., but this is a fairly ugly solution, especially with auto-formatting turned on (my cell has many lines of code, and the parenthesis are huuuuuge). Anyone have a more elegant solution? ( ---some code here--- If[statement, Abort[]]; ---more code following--- ) - ## 2 Answers This question has been asked before on stack overflow. However we will summerize some of the answers given there on our new Mathematica site. ## Wrap In Compound Expression One suggestion by Michael Pilat, given there was to wrap your lines in CompoundExpression, e.g. ( Print@Range[5]; Abort[]; Print@Range[5]; ) During evaluation of In[39]:= {1,2,3,4,5} $Aborted
If you mind the formatting of parenthesis, you could explicitly use the FullForm of CompoundExpression like this:
CompoundExpression[
Print@Range[5],
Abort[],
Print@Range[5],
]
## Use of $PreRead Suggested by Alexey Popkov: In[1]:=$new$PreRead = False; AbortAllPendingInputs := AbortProtect[If[!$new$PreRead,$new$PreRead = True;$TimeOfAbort = SessionTime[];
last$PreRead = ToString[Definition[$PreRead], InputForm];
ClearAll[$PreRead];$PreRead := If[TrueQ[SessionTime[] - $TimeOfAbort < 1], "",$new$PreRead = False; ClearAll[$PreRead];
If[last$PreRead === "Null", #, ToExpression[last$PreRead]; $PreRead@#] ] &;]]; In[3]:= f := CheckAbort[Pause[10], AbortAllPendingInputs; Abort[]] In[4]:= While[True, f] While[True, f] While[True, f] Out[4]=$Aborted
Note that this solution will need to be modified if you use $PreRead for anything else. ## Use of CellEvaluationFunction CellEvaluationFunction gets the BoxData expression, before it is even split. Just assigning something like CellEvaluationFunction:>ToExpression seems to do the trick. You can set it as an Input cell style, or as a notebook option, or front end session option, or however you like SetOptions[$FrontEndSession, CellEvaluationFunction :> ToExpression]
However, you lose the multiple outputs in those new lines when you don't use ;. This can probably be solved but I don't know very well how CellEvalutionFunction works, and how can it receive a box structure, default to Identity but expect to return an expression. Edit should you come up with any improvements
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Since you tagged this community wiki, would you mind if others were to port over some of the suggestions from the stack overflow question here? With appropriate credit and whatnot of course! – nixeagle Mar 28 '12 at 21:52
@nixeagle No, of course I don't mind! That was the idea. – Leonid Shifrin Mar 28 '12 at 21:55
Alright, I'll go ahead and work on that. Plus I ought to suggest to @Guillochon that using more smaller functions might help with the concern raised in his Edit. – nixeagle Mar 28 '12 at 21:56
Alright, done editing this. If anyone else can make the answer clearer or wants to volunteer a 3rd (possibly better!) solution, please do so. As a side note, as I don't know where else to mention this, do we want to keep that abort tag on this question? – nixeagle Mar 28 '12 at 22:06
@LeonidShifrin, I just saw that your answer was a community wiki and that in the link you provided someone suggests in comments a CellEvaluationFunction approach, like my answer. Should I delete it and put it in the community answer? – Rojo Mar 31 '12 at 18:23
Note that the documentation FrontEnd uses CellEvaluationFunction -> Identity and not ToExpression. Still the example works and
Print[a]; Abort[]; Print[b]
aborts properly (not printing b) because all statements are in one line. Apparently it is the line breaks which break up the cell into individual commands, not the semicolons. So there must be another way "fixing" this.
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# Decoding Locks
You are standing outside your house; you use a combination lock as your front door lock. You have forgotten your combination, and it’s started to rain. How do you get into your house in the most efficient way possible?
You stand there and ponder this for a few minutes until you realise you have a cup of tea getting cold on your worktop. Now it’s serious. If only you paid more attention in Maths, you might be able to think of a sequence that included all of the combinations of the numbers on your lock.
You know your lock only has two digits 0 and 1, it also requires a 4 digit passcode. We need to find a logical way to go through and form an efficient sequence, more efficient than button mashing. In your confusion, you find some chalk on the ground and start drawing diagrams. Which look much like graphs and finally something clicks, De Bruijn Sequences, you remember them from one of your midnight Wikipedia binges.
De Bruijn Sequences are ways of representing all the combinations of n-words on a certain alphabet. On our lock, we need 4-words on a 2 alphabet. The sequences were named after Dutch mathematician Nicolaas Govert de Bruijn after he wrote about them in 1946. The case of our predicament is one of his first proofs. We also know about the number of distinct sequences for each type of $k$-words and $n$-alphabets.
$$\frac{(k!)^{k^{n-1}}}{k^n}$$
We also know of a link between Graphs, Hamiltonian Paths and these sequences. If each vertex is equivalent to a 3-word, i.e. $110$, and we name the arcs or arrows as an extra letter, i.e. $1$, then we create what is known as a De Bruijn graph. We also know that these graphs will lie in $k-1$ dimensions.
We can then take a Hamiltonian path of this graph, producing the required sequence to put into our lock! We also note that there are loops at the $000$ word with a $0$-letter and at $111$ with the $1$-letter.
We can now read off the path from the letters, remembering the extra loops, starting at the $000$ – $000$ loop. 0000111101100101 is what we read off. We can enter this whole sequence, and the lock will unlock by the time we enter the last digit.
One last little thing, if you line up all of the nodes we have in the order $000, 001,010, 011, 100, 101, 110, 111$ and curve the arcs around nicely, what shape do you achieve? Does it resemble something else in Mathematics?
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# How can I "see" that calculus works for multidimensional problems?
Let's say I have some function f(x) = x^2 + b. I can see what's going on, I can count the slope geometrically even without knowing the rules of derivatives.
When I need to minimize some cost function for linear problem (linear regression with gradient descent), I just need to picture 3d, and I can "see", and be quite confident why and how it works.
How can I "see" or get intuition that calculus works for multidimensional problems? Let's say I have a problem with many variables like:
f(area_km, bedrooms, ...) = theta + theta1 * area_km + theta2 * bedrooms etc
If I want to apply gradient descent, I know I need to calculate partial derivatives and multiply it with a learning rate etc. It works. But it's kinda magical that it works.
I am sorry this is a silly question, I am just beginning.
• Every spatial intuition comes from functions from the plane to the reals: $f:\mathbb{R}^2 \rightarrow \mathbb{R}$. While intuition fails in generalizing from 1 to $n$ dimensions, it works EXTREMELY well with going from $2$ to $n$. You still can have an intuition because a function $f$ of such kind has a graph which is representable as a surface in 3D space.
– rod
Jan 27, 2021 at 18:46
• Actually you CAN'T understand gradient descent by looking at 1-variable graphs. It just has too little generality.
– rod
Jan 27, 2021 at 18:47
For the most general case, think about a mixing board.
Each input argument to the function is represented by a slider with an associated piece of a real number line along one side, just like in the picture. If you are thinking of a function which can accept arbitrary real number inputs, the slider will have to be infinitely long, of course, which of course is not possible in real life, but is in the imaginary, ideal world of mathematics. This mixing board also has a dial on it, which displays the number corresponding to the function's output.
The partial derivative of the function with respect to one of its input arguments corresponds to how sensitive the readout on the dial is if you wiggle the slider representing that argument just a little bit around wherever it's currently set - that is, how much more or less dramatic the changes in what is shown are compared to the size of your wiggle. If you wiggle a slider by, say, 0.0001, and the value changes by a factor 0.0002, the partial derivative with respect to that variable at the given setting is (likely only approximately) 2. If the value changes in an opposite sense, i.e. goes down when you move the slider up, the derivative is negative.
The gradient, then, is the ordered list of signed proportions by which you have to "wiggle" all the sliders so as to achieve the strongest possible, but still small, positive wiggle in the value on the dial. This is a vector, because you can think of vectors as ordered lists of quantities for which we can subject to elementwise addition and elementwise multiplication by a single number.
And of course, when I say "small" here I mean "ideally small" - i.e. "just on the cusp of being zero" which, of course, you can make formally rigorous in a number of ways, such as by using limits.
• Excellent answer! I'll sure mention the mixing board next time I teach multivariate calculus!
– Ruy
Feb 2, 2021 at 16:45
• Very nice example!! Feb 15, 2021 at 12:38
Well, in one variable you need to solve $$f'(x)=0$$ and controll wheter it is maximum or a minimum. Such equation is called Euler equation and it holds also in more variables, but with the formulation: $$\nabla f(x)=0$$ where $$\nabla f(x)=(\frac{\partial f(x)}{\partial x_{1}},\dots,\frac{\partial f(x)}{\partial x_{n}})$$. Now, also here you should controll if it is a minimum or not and this is done via checking on the Hessian of $$f$$. That is, if $$\bar{x}$$ is such that $$\nabla f(\bar{x})=0$$ then $$\bar{x}$$ is a minimum if $$Hf(\bar{x})$$ admits only positive eigenvalues, where $$Hf$$ is the matrix made of second order partial derivatives of $$f$$. Notice that we are assuming $$\bar{x}$$ belongs to the interior of a set, exactly as for functions with one variable.
• If you search for minimums on the border of a set, the research becomes quite harder and another theorem is involved, which is Lagrange's multipliers Theorem Jan 25, 2021 at 9:37
Consider a single variable function $$f(x)$$, suppose there exists a maximum for $$f(x)$$ , then we can find that by the function's derivative has a sign flip at that point, then if we were to take a point $$x>x_o$$
$$\frac{df}{dx}|_{x>x_o} = \text{something negative}$$
Now, the magnitude of the derivative depends on how far you are from the global maximum, so suppose you take a 'step' on the $$x$$ axis scaled up by the derivative.
$$\frac{df}{dx}_{x > x_o} \Delta x$$
Then, you will end up walking to the maximum. Now let's say you are at a point $$x , then the first derivative is positive and you will still end up walking toward the maximum. Moral of the story? If you walk around the input set keeping your steps scaled up by the function's derivative, then you'll eventually hit a global maximum / minimum.[Edit: It may also turm up that you get stuck in local mini/global minimum :(]
Now, consider a multivariable $$f(x,y)$$ , by the logic above if it has a local max, say at a point $$(x_o,y_o)$$, if you take a $$x>x_o$$, then
$$\frac{\partial f}{\partial x} = \text{something negative}$$
And similar argument to single variable case can be applied, and we can apply a similar argument for $$y$$. Ultimate this leads us to idea that the vector given as:
$$\nabla F = < \frac{\partial F}{\partial x} , \frac{\partial F}{\partial y} >$$
Tells us how to move in the input plane such that our function is maximized.
So, say you are a point $$$$ , then the point where you should move next to maximize the function is:
$$ = + < \frac{\partial F}{\partial x}|_{x_o} \Delta x, \frac{\partial F}{\partial y}|_{y_o} \Delta y>$$
Why? If $$z(x,y)$$
$$\Delta z= \frac{\partial F}{\partial x} \Delta x + \frac{\partial F}{\partial y} \Delta y= \nabla F \cdot ds$$
$$ds$$ is the length of step you take in the input plain, clearly for a fixed step length, the most increase in function happens when the angle between step and gradient is zero.
Hence, using that gradient vector as a compass to move, you'll finally reach some kind of extremum point in the input plane.
• Gradient descent/ascent can easily get trapped at local extrema. So you will eventually reach a local extremum.
– Ian
Feb 1, 2021 at 1:15
• @Ian good point Feb 1, 2021 at 8:18
• Always my best regards and compliments. Jun 14, 2021 at 20:26
• Thank you @Sebastiano :D ^^ Jun 14, 2021 at 20:36
Consider a path through $$\vr_0$$ parametrized by $$t$$. By multivariable chain rule, the rate of change of $$T$$ along the path is given by \begin{align*} \frac{d T(\vr(t))}{dt} = \pder[T]{x}\der[x]{t} +\pder[T]{y}\der[y]{t} +\pder[T]{z}\der[z]{t} = \nabla T\cdot\vr'(t),\tag{1} \end{align*} where $$\nabla T = \langle \p T/\p x,\p T/\p y,\p T/\p z\rangle$$ is the gradient of temperature. Assume that $$|\vr'(t)|=1$$, independent of path (that is, the paths are parametrized by arclength). The derivative $$dT/dt$$ is then a measure that can be used to compare the rate of change of $$T$$ for different paths through $$\vr_0$$. Note that $$\left|\pder[T(\vr(t))]{t}\right| = |\nabla T|\cos\th,$$ where $$\th$$ is the angle between $$\nabla T$$ and $$\vr'(t)$$. The magnitude of the rate of change is clearly maximized for $$\th=0,\pi$$. The value of $$T$$ does not change for paths with $$\th=\pi/2$$. These paths are tangential to the equipotential at $$\vr_0$$. Thus, $$dT/dt$$ is maximally negative if $$\vr'$$ is antiparallel to $$\nabla T$$ (and thus perpendicular to the equipotential). Since $$\vr'$$ is tangential to the path, we expect $$T$$ to decrease maximally in the direction given by $$-\nabla T$$. Thus, we let $$\Delta\vr = -\varepsilon\nabla T$$, where $$\varepsilon>0$$ is sufficiently small.
Example
If $$T(\vr) = x^2+y^2+z^2$$, the equipotentials are spheres and $$\nabla T = 2\langle x,y,z\rangle = 2\vr$$. Thus, $$\Delta r = -2\varepsilon \vr_0$$. This displacement is directly towards the origin, where the temperature has a minimum value of $$T({\bf 0}) = 0$$. See the figure below.
Figure 1. Equipotentials and displacement vector.
One dimension
Equation (1) and its interpretation generalize nicely to higher and lower dimensions. In one dimension we have $$\der[T(x(t))]{t} = \der[T]{x} \der[x]{t}.$$ Clearly this value is maximally negative if $$dT/dx$$ and $$dx/dt$$ are opposite in sign. Thus, we let $$\Delta x = -\varepsilon dT/dx$$.
Example
If $$T(x) = x^2$$, we find $$\Delta x = -2\varepsilon x_0$$. This displacement is again directly towards the minimum at $$x=0$$, independent of the sign of $$x_0$$.
Multidimentional optimization task can be presented as the sequence of $$\;\text{1D}\;$$ tasks.
Really, let we start from the point $$\;z=A,\;$$ wherein $$\text{ grad } f(z)\bigg|_{z=A} = \overrightarrow {g_A}.\;$$ Assuming $$\;\overrightarrow{\Delta z} = \overrightarrow{g_A}t,\;$$ we get $$\;\text{1D}\;$$ optimization task for the variable $$\;i.$$, The final point $$B=A+\overrightarrow{g_A}\,t_{opt}\;$$ of the current optimization task assumed as the starting point for the next task, with the suitable $$\;\text{1D}\;$$ vizualization of the each step.
When I think about a function $$f: \mathbb R^n \to \mathbb R$$, I can only visualize the cases where $$n = 2$$ or $$n = 3$$ (or $$n = 1$$, of course). I like to imagine that $$f$$ tells us the temperature at each point in space. A mosquito who likes cool temperatures is flying around. Which way should it move? The gradient vector at its current location points in the direction in which the temperature is increasing most rapidly. So the mosquito should move a little bit in the opposite direction, which is the direction in which the temperature is decreasing most rapidly. Then the mosquito should recompute the gradient of $$f$$ at its new location, and move a bit again in the negative gradient direction. And so on. This is gradient descent.
Well, I don't believe that it is easy to maintain an accurate model of a $$>3$$ dimensional space in one's imagination for sustained periods, but one can certainly gain an intuition for each $$3$$D cross-section and maneuver around that way. Pick easy shapes, like spheres or tetrahedrons, to try and visualize. The issue is mostly visualization, since our minds are in constant interaction with multidimensional spaces in day-to-day life, though those spaces are simply processed less visually.
Dreams, for example, compose many dimensions of the waking life and compress them into highly dynamic visualizations of usually $$<3$$ dimensions. As for generalization, typically I take a linear variable simply map it to multilinear vectors or parametric spaces. It's helpful to know that the intersection of $$k$$ $$n$$ dimensional surfaces is a $$n-k+1$$ dimensional surface in $$n$$ space, for example.
It is fundamentally very difficult to communicate understanding, so the best advice is to simply persist at trying to visualize these spaces in your own unique way. There are some who have entertained multidimensional spaces in their work for so long that they are simply, precisely familiar with $$4$$D (and up) landscapes. The more you persist, the more dimensions you will add. Sometimes, after a lifetime of persistence, you only end up with a half a dimension more than three. Other times, you go all the way to eight. It depends.
So, the best method, I think, is to pick simple shapes that are easy to generalize into higher dimensions (like spheres) and visualize each part until you can put it together. Then slowly expand your horizons. Manipulate the sphere here or there to change it this way or that. Soon enough what seems impossible to many will be an average consideration for you.
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# Looks Blue To Me!
Chemistry Level 2
What is the color of light absorbed by an aqueous solution of $\text{CuSO}_4$?
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# The operator $\left(q\frac{d}{dq}\right)^s$ and fractional derivatives of modular forms
Recall the notion of a "nearly holomorphic modular form" introduced by Shimura:
A function $f : \mathfrak h \to \mathbb C$ is said to be nearly holomorphic of level $\Gamma_1(N)$, weight $k$ and order $\leq r$ if it satisfies the following conditions:
1. $f$ is $C^\infty$;
2. $f$ is invariant under the weight $k$ action of $\Gamma_1(N)$;
3. $f$ can be written as \begin{equation*} f(\tau) = f_0(\tau) + \frac{1}{y} f_1(\tau) + \dots + \frac{1}{y^r}f_r(\tau) \end{equation*} where the $f_j(\tau)$ are holomorphic, $y = \frac{\tau - \overline{\tau}}{2}$;
4. $f$ has finite limits at the cusps.
Alternatively, a nearly holomorphic modular form can be viewed as a global section of the vector bundle $\mathcal H^r_k = \underline{\omega}^{\otimes(k-r)} \otimes \mathcal H^{\otimes k}$ on the modular curve $X_1(N)$, where $\mathcal H =\mathcal H^1_{dR}(\mathcal E/X_1(N))$ is the relative de Rham cohomology of the universal semi-abelian scheme $\mathcal E$ over $X_1(N)$ (with suitable care taken to define $\mathcal H$ properly at the cusps).
Let $\mathcal N_k^r$ denotes the $\mathbb C$-vector space of such forms. It is a finite dimensional complex vector space, we have $\mathcal N_k^r \subseteq {\mathcal N_k^{r+1}}$ and we define $\mathcal N_k^\infty = \cup_{r\geq 0}\mathcal N_k^r$.
By invariance of $f$ under $\Gamma_1(N)$, and from the invariance of the function $y$ under $\tau \mapsto \tau+1$, we deduce from the expansion (3) (which is unique) that the individual functions $f_j(\tau)$ are invariant under $\tau \mapsto \tau+1$, so they admit $q$-expansions. Furthermore, one can show that the map $\mathcal N_k^\infty \to \mathbb C[[q]]$ given by $f \mapsto f_0(q)$ is injective. Therefore, it is reasonable to call $f_0(q)$ "the" $q$-expansion of the nearly holomorphic modular form $f$. Although a priori this $q$-expansion would have been an element of $\mathbb C[[q]][1/y]$, the injectivity of $f \mapsto f_0$, motivates the following definition (a special case of a definition of Urban in the setting of nearly overconvergent modular forms)
A power series $f_0 \in \mathbb C[[q]]$ is said to be the $q$-expansion of a nearly holomorphic modular form of level $\Gamma_1(N)$, weight $k$ and order $r$ if there exists a nearly holomorphic form $f$ of weight $k$ and order $r$ such that $f_0(q)$ is the "constant term" of $f$ in its expansion as a polynomial in $1/y$ with coefficients in $\mathbb C[[q]]$.
The Maass-Shimura derivative $\delta$ is a degree $2$ derivation of the graded ring $\bigoplus_{k=0}^\infty \mathcal N_k^\infty$, given on a form of weight $k$ by
$$\delta_k f = \frac{1}{2\pi i}\left(\frac{\partial f}{\partial \tau} + \frac{k}{2iy}f\right).$$
Since $d/d \tau = 2 \pi i q \times d/d q$, we see that $\delta_k$ acts on $q$-expansions by
$$(\delta_k f)_0(q) = q\frac{d}{dq}f_0(q).$$
Let us write $\theta = q\frac{d}{dq}$. This is Serre's differential operator on $p$-adic modular forms. Remark that its effect on $q$-expansions is independent of the weight $k$; and so for an integer $t$, the operator $\theta^t$ on $\mathbb C[[q]]$ corresponds to $\delta^t$.
Remark that $\theta^t$ acts on $q$-expansions by
$$\sum a_n q^n \mapsto \sum n^ta_n q^n.$$
This expression has been used (I believe first by Darmon and Rotger) to define $p$-adic powers of the Serre operator. If we $p$-deplete a holomorphic modular form by deleting the Fourier coefficients with index divisible by $p$, in other words
$$f^{[p]}(q) = f(q)-VUf(q) = \sum_{n \not\mid p} a_n q^n$$
then we can use the fact that the function $t \mapsto n^t$ interpolates $p$-adically when $(n,p)=1$. Thus we can view $\theta^t f^{[p]}$ as a family of $p$-adic modular forms passing through $f^{[p]}$, and depending on the $p$-adic parameter $t$. This embodies the idea that if $f$ is an eigenform, then we can twist the Galois representation $V(f)$ attached to $f$ by a power of the cyclotomic character which depends on the same $p$-adic variable $t$, yielding a family of Galois representations which specializes to $V(f)$ at $t=0$.
My questions: What about complex powers of the Serre operator? If $f \in \mathbb C[[q]]$, and $s$ is a complex number, then we have an operator
$$\theta^s : \sum a_n q^n \mapsto \sum n^s a_n q^n$$
which preserves the ring of holomorphic functions on the open unit disc $\mathcal D$, and satisfies $\theta^s \theta^{s'} = \theta^{s+s'}$.
If $f_0(q)$ is the $q$-expansion of a nearly holomorphic modular form $f$, we may view $\theta^sf_0(q) = \sum n^s a_n q^n$ as a holomorphic function on $\mathbb C \times \mathcal D$. Its specialization at an integer $s=t$ is the $q$-expansion of the nearly holomorphic modular form $\delta^t f$. In other words the Maass-Shimura derivatives of $f$ lie naturally in a complex-analytic family, just as the Maass-Shimura derivatives of $f^{[p]}$ lie naturally in a $p$-adic family.
• If $s$ is not an integer, and $f$ is a holomorphic modular form, what kind of object is the holomorphic function $\theta^s f$? In the $p$-adic world, if $s$ were a $p$-adic variable, it would be a $p$-adic modular form (of non-integral weight). But in the complex world, I have no idea what it is. Can it be viewed as a section of a sheaf on $X_1(N)$? This seems like it would require doing something akin to taking complex powers of the Hodge bundle $\underline{\omega}$ on $X_1(N)$, and I'm doubtful that such a thing can be done.
• In particular the operator $\theta$ has $n$-th roots for any $n$. Is there a meaningful sense in which the object $\theta^{1/2} f$ has weight $k+1$ if $f$ has weight $k$ (apart from the fact that its coefficients have the growth rate expected of a modular form of weight $k+1$)?
Any thoughts are most welcome!
• Regarding the very last bullet - similar half-derivatives appeared in a comment by @rlo to one of my questions. Partial information about its level and the "deviation from modularity" is in my answer there. On the whole the key concepts here must be (imo) related to the treatment of mock modular forms in Zwegers' thesis. – მამუკა ჯიბლაძე Sep 3 '15 at 8:03
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## how to add column with constant number to each file
Hello
I'd like it if you could help me,
I have a step that reads over 100 text files,
each file contains about 15 lines
I'd like to put a column with a constant number to identify each file,
all this I put in a table
example
file 1
column 1 column 2
xxxxxx ---- 1
xxxxxx ---- 1
xxxxxx ---- 1
xxxxxx ---- 1
file 2
xxxxxx ---- 2
xxxxxx ---- 2
xxxxxx ---- 2
file3
xxxxxx ---- 3
xxxxxx ---- 3
xxxxxx ---- 3
with row number by file does not work because the number is sequential, not independent for each file
I'm sorry about my English.
Thank you very much.
text file imput ------> select values ----------> table output
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# Finding velocity and position from an acceleration vs time graph
1. Sep 23, 2013
### Kot
1. The problem statement, all variables and given/known data
The graph of acceleration versus time for an object in linear motion. Assuming the object starts from rest at the origin at t = 0, find the velocity and position of the object at times t = 1 through 10 seconds.
2. Relevant equations
$v=v_i + at$
3. The attempt at a solution
I searched online and found that the velocity is the area under the acceleration vs time graph, which is the integral of the acceleration vs time graph. Since the acceleration function wasn't given to me, I found the equation of the first part of the graph from (0 seconds to 2 seconds) by using basic algebra. I found that the line was $y=\dfrac{5}{2}x$. Would it be correct to take the integral of $y=\dfrac{5}{2}x$ since it would give me the area under the curve? I took the integral with the limit from 0 to 2 and got 5m/s. The distance traveled from 0 seconds to 2 seconds is 10m (I found this by using s=d/t). Is this the correct approach to solving this?
2. Sep 23, 2013
### Delphi51
You ARE given the acceleration vs time graph!
You could use your approach of writing the equation for each segment of the given graph and integrate it. If you do this, make your initial equation a = (a function of time).
The usual approach is to find the area under the acceleration graph from time zero to time 1, then zero to time 2, etc. and mark these velocity points on another graph for v vs t. This is integration by hand and it may well be faster for this problem.
Once you have the v vs t graph, you know what to do to get x vs t.
3. Sep 23, 2013
### Kot
I have all the velocity and position for the time intervals but now I am having trouble plotting it on a v vs t graph. From 0 to 2, the velocity is 5m/s, from 2 to 5 the velocity is 10m/s, from 5 to 6 the velocity is 4m/s, from 6 to 9 the velocity is 9m/s, and from 9 to 10 the velocity is 1.5m/s. Is the velocity graph supposed to have horizontal lines like the acceleration vs time graph or jagged edges connecting the different velocities?
4. Sep 23, 2013
### Delphi51
Oh, I think it is more complicated than that! If the velocity was constant for the first two seconds, its derivative (the acceleration) would be zero. But it isn't, the given graph shows the acceleration is nonzero and rapidly increasing. If you want help sorting it out, show some details of how you find the velocity at time 1 second.
5. Sep 23, 2013
### Kot
I am not sure what you mean at 1 second (do you mean from 0s to 1s?). I found the velocity from 0s to 2s by taking the integral of $y=\dfrac{5}{2}x$ with 0 as the lower bound and 2 as the upper bound. I got 5 which is the area under the curve so I thought that the velocity was 5m/s.
6. Sep 23, 2013
### Delphi51
I agree with 5 m/s at time 2 seconds. I think it might help avoid a misunderstanding if I suggest your y = 5/2x should actually be a = 5/2t, then after integrating v = 1.25t².
At time 1 second, you must find the area under the graph from 0 to 1 s. The brute force way is to note that it is a right triangle with base 1 s and height 2.5 m/s². A = 0.5*b*h = 0.5*1*2.5 = 1.25 m/s.
Or your way, v = 1.25t² = 1.25(1)² = 1.25 m/s.
This gives you two points on the velocity vs time graph. You could carry on this way but I think you will prefer to integrate again to get a function for x = (a function of time).
7. Sep 23, 2013
### Kot
If I integrated the velocity function again I would get the displacement? I am still unsure how I would plot and connect the points on the velocity vs time graph.
8. Sep 23, 2013
### Delphi51
Yes, you can just integrate again to get displacement (x). Remember the a = 5/2t, v = 1.25t² are only good for the first two seconds. The acceleration function changes completely at time 2 seconds.
9. Sep 23, 2013
### Kot
Yes I am working on the rest at the moment. After I get all velocity and positions, how would I graph the data in a velocity vs time graph? I can plot the points but how will I connect them?
*edit I am working on the second part of the graph where acceleration is constant. I integrated the function a=5, and got v=5t. I plugged 3s into t and found that the velocity is 15m/s at 3 seconds. I know that the velocity is 5m/s at 2 seconds, where did the extra 10m/s come from? Did I miscalculate something?
Last edited: Sep 23, 2013
10. Sep 23, 2013
### Delphi51
Ah, you must use your knowledge of functions. The 0 to 2 s interval is x = 0.416*t³ so you sketch a curve that resembles a cubic function.
Lots of work, isn't it? For the second interval you will have to add a constant after integrating to make the displacement at time 2 the same as you got for time 2 from the x = 0.416*t³. I'm trying to work it by both methods and so far the answers aren't agreeing, so I've got a mistake!
11. Sep 23, 2013
### Kot
Would that constant be 1? Since I evaluated the function at t=3, subtracting a 1 would give me t=2.
12. Sep 23, 2013
### Delphi51
I didn't get that, but maybe its my mistake. What is your function for velocity in the 2 to 5 s interval?
13. Sep 23, 2013
### Kot
My function for velocity from 2 to 5 is v=5t. I integrated the function a=5.
14. Sep 23, 2013
### Delphi51
Okay, so the whole thing is v = 5t + C
and v at time 2 is known to be 5
Find C.
15. Sep 23, 2013
### Kot
I got -5 for C and the answer makes sense now. I am confused as to why you needed to do this, will I need to find C for the other intervals? Could you please explain where this displacement came from?
16. Sep 23, 2013
### Delphi51
Right, and the v = 5t -5 will become x = 2.5t² -5t + C when you integrate again to get x. My mistake was forgetting that -5t!
And so on; yes another C at each integration in each interval.
17. Sep 23, 2013
### Kot
I feel like I am beating a dead horse but I still do not understand why it is necessary to have the constant, what is causing the displacement?
18. Sep 23, 2013
### Delphi51
Well, you always get a +C when you integrate. It is mathematically because f(t) + C has the same derivative as f(t). Physically, if you just used v = 5t then it wouldn't fit the problem: according to our formulas for the previous interval up to time 2, v = 5 at time 2. You need C = -5 to make v = 5t + C = 5 at time 2. Of the many functions whose derivative is a = 5, the v = 5t - 5 is the only one that fits the distance at the left boundary of the interval.
I have x = 3.33 at time 2, x = 40.83 at time 5 and x = 63 at time 6. These checked with the other method of counting squares under the graph to get the area.
I'm glad I don't have to finish the whole thing!
19. Sep 23, 2013
### Kot
Thanks for the alternative explanation, I will try to do the rest of the graph now.
20. Sep 24, 2013
### Kot
I finished calculating the velocities for t=1 to t=10. Everything seems to make sense until I reach the last interval t=9 to t=10. Here are my velocities at each t:
t=1s v=1.25m/s,
t=2s v=5m/s,
t=3s v=10m/s
t=4s v=15m/s
t=5s v=20m/s
t=6s v=24m/s
t=7s v=27m/s
t=8s v=30m/s
t=9s v=33m/s
t=10s v=34.5m/s
Looking at the graph, I see that the acceleration is rapidly slowing down but my calculations say that the velocities are still increasing. I integrated the function a=-3t+30 (the equation representing the line at that interval). After integrating the acceleration I got $v=-\dfrac{3}{2}t^2 +30t + C$ I then used what you taught me to find the C and got $v=-\dfrac{3}{2}t^2 +30t - \dfrac{231}{2}$. I then plugged in 9s and got 33m/s which checked with my previous interval but 10s gives me 34.5m/s. Is this correct or did I go wrong somewhere in my calculation?
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# 14.3: Generating Random Numbers
Running a Monte Carlo simulation requires that we generate random numbers. Generating truly random numbers (i.e. numbers that are completely unpredictable) is only possible through physical processes, such as the decay of atoms or the rolling of dice, which are difficult to obtain and/or too slow to be useful for computer simulation (though they can be obtained from the NIST Randomness Beacon).
In general, instead of truly random numbers we use pseudo-random numbers generated using a computer algorithm; these numbers will seem random in the sense that they are difficult to predict, but the series of numbers will actually repeat at some point. For example, the random number generator used in R will repeate after $2^{19937} - 1$ numbers. That’s far more than the number of seconds in the history of the universe, and we generally think that this is fine for most purposes in statistical analysis.
In R, there is a function to generate random numbers for each of the major probability distributions, such as:
• runif() - uniform distribution (all values between 0 and 1 equally)
• rnorm() - normal distribution
• rbinom() - binomial distribution (e.g. rolling the dice, coin flips)
Figure 14.1 shows examples of numbers generated using the runif() and rnorm() functions, generated using the following code:
You can also generate random numbers for any distribution if you have a quantile function for the distribution. This is the inverse of the cumulative distribution function; instead of identifying the cumulative probabilities for a set of values, the quantile function identifies the values for a set of cumulative probabilities. Using the quantile function, we can generate random numbers from a uniform distribution, and then map those into the distribution of interest via its quantile function.
By default, R will generate a different set of random numbers every time you run one of the random number generator functions described above. However, it is also possible to generate exactly the same set of random numbers, by setting what is called the random seed to a specific value. We will do this in many of the examples in this book, in order to make sure that the examples are reproducible.
If we run the rnorm() function twice, it will give us different sets of pseudorandom numbers each time:
print(rnorm(n = 5))
## [1] 1.48 0.18 0.21 -0.15 -1.72
print(rnorm(n = 5))
## [1] -0.691 -2.231 0.391 0.029 -0.647
However, if we set the random seed to the same value each time using the set.seed() function, then it will give us the same series of pseudorandom numbers each time:
set.seed(12345)
print(rnorm(n = 5))
## [1] 0.59 0.71 -0.11 -0.45 0.61
set.seed(12345)
print(rnorm(n = 5))
## [1] 0.59 0.71 -0.11 -0.45 0.61
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# Darcy Flow Analysis and Convection Topology Optimization
Forced Convection for Linear Steady-State Heat Transfer is available via Darcy Flow analysis.
Darcy Flow Analysis is currently only supported for steady-state heat transfer analysis. Forced convection applications include cooling solutions for electric motors, machine tools (casting, forming), heat exchangers, HVAC systems, and cooling for electronic devices including PCBs. Additionally, Topology Optimization is available for steady-state heat transfer with Darcy flow analysis. The topology optimization considers the effect of forced convection for cooling in conjunction with structural steady-state heat transfer analysis. Topology optimization can help optimize cooling channel structures and placement for a wide range of applications.
The flow solution is described by:(1) ${K}_{p}p={f}_{p}$
Where,
${K}_{p}$
Permeability matrix
$p$
Nodal pressure in the structure
${f}_{p}$
The fluid flow analysis is solved using Darcy’s Law, which describes the flow of a fluid through a porous medium:(2) $u=-\frac{\kappa }{\mu }\nabla p$
Where,
$u$
Fluid velocity
$\kappa$
Fluid permeability (this is different from thermal conductivity, represented by $k$)
$\mu$
Fluid dynamic viscosity
$\nabla p$
Pressure differential
The equation can be rewritten as:(3) ${u}^{e}=-\frac{\kappa }{\mu }B{p}^{e}$
Where,
${u}^{e}$
Element fluid velocity
$B$
Differential of the shape function
${p}^{e}$
Nodal pressure in the element (which is sourced from the flow solution)
The thermal steady-state heat transfer solution is represented by:(4) $\left[{K}_{c}+C\left(p\right)\right]T=f$
Where,
$K{}_{c}$
Conductivity Matrix: ${K}_{c}=\sum _{n=1}^{{N}_{e}}{\int }_{{\Omega }^{e}}k{B}^{T}Bd\Omega$
$C\left(p\right)$
Convection Matrix (which includes flow velocity ${u}^{e}$ from Darcy's Law): $C\left(p\right)=\sum _{n=1}^{{N}_{e}}{\int }_{{\Omega }^{e}}{\stackrel{^}{N}}^{T}\rho {c}_{p}{u}^{e}Bd\Omega$
Where,
$f$
$T$
Nodal temperature matrix
${\stackrel{^}{N}}^{T}$
Enhanced shape function
${N}_{e}$
Total number of elements
$\rho$
Density
$k$
Thermal conductivity (this is different from fluid permeability, Kappa, represented by $\kappa$)
${c}_{p}$
Specific heat capacity
${u}^{e}$
Element flow velocity from Darcy’s Law
The thermal steady-state solution incorporates forced convection via the Convection Matrix. A topology design space can be defined for a steady-state heat transfer subcase to run the optimization solution which accounts for the forced convection via Darcy flow.
## Input
To turn on forced convection flow analysis, for a Steady-State Heat Transfer Analysis subcase, input definition is required for both the thermal structural and flow analysis.
### Boundary Conditions
Boundary conditions are required for both thermal structural and fluid flow analysis. The typical structural thermal boundary conditions are available via the SPC Subcase/Bulk Data. For flow analysis, there are two options to define the boundary conditions:
Nodal Pressure
Flow analysis is solved in the same subcase as thermal analysis. The SPCP Subcase Entry and SPCP Bulk Data are available to define flow pressure boundary conditions. Both inlet and outlet flow pressures can be defined using the SPCP entry.
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
SPCP SID G D G D G D
Inlet Velocity
Inlet velocity via the INLTVEL Subcase Entry and INLTVEL Bulk Data are alternately available instead of inlet pressure definition via SPCP entries. The outlet pressure still has to be defined using the SPCP entry.
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
INLTVEL SID EID VALUE G1 G2 G3 G4
For Darcy flow analysis, using an SPCP Bulk Data/Subcase Entry pair is mandatory to define the outlet flow pressure. However, for inlet velocity, either the INLTVEL Bulk Data/Subcase pair or the SPCP Bulk/Subcase pair can be used. Therefore, the SPCP Subcase Entry can be considered as an entry which turns on flow analysis for a steady-state heat transfer subcase.
Loading can be applied to either the solid or fluid domain via the typical heat transfer loads. For instance, the SPC entry can be used to define grid temperature loads, the QBDY1 entry can be used to define heat flux loads, and the QVOL entry can be used to define volumetric heat generation loading.
### Material Properties
Material Properties for both structure and fluid for forced convection heat transfer analysis can be defined via the MAT4 Bulk Data entry. The structural material properties are typically defined using the first line which specify the fields, K (structural conductivity), CP (structural specific heat), RHO (structural density), and H (convection heat transfer coefficient). H is only used for free convection to ambient in the presence of CONV Bulk Data. For the fluid heat transfer properties, the DARCY continuation line can be used to define KAPPA (fluid permeability), MU (fluid dynamic viscosity), K (fluid conductivity), CP (fluid specific heat), and RHO (fluid density).
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MAT4 MID K CP RHO H HGEN
DARCY KAPPA MU K CP RHO
If certain elements are supposed to only be solid elements, then the DARCY continuation line is not required. For elements which reference materials without a DARCY continuation line, then the lowest KAPPA/MU value from all the fluid MAT4 entries is taken and multiplied with 10-9 and this value is used for solid permeability calculations for Darcy flow analysis.
When only Darcy flow analysis is run, without optimization, then each element can reference either a solid-only MAT4 entry (without DARCY continuation line), or a fluid-only MAT4 entry (with DARCY continuation line, but no structural thermal properties).
However, when topology optimization is run, then for elements in the design space, the referenced MAT4 entry should contain both structural and fluid material properties.
### Topology Optimization
During topology optimization, each element in the design space can either be a solid (density=1) or a void (fluid, density=0). Therefore, elements in the design space should reference MAT4 entries with both structural and fluid material properties.
For forced convection topology both DOPTPRM,TOPDISC,YES and minimum member size control (either using DOPTPRM,MINDIM or using MEMBSIZ on the DTPL entry) are turned on automatically. If minimum member size control is not turned on by you, then it is automatically activated with a value based on the average mesh size.
The following responses are available for Flow-based Forced Convection Topology Optimization:
1. Global Thermal Compliance (RTYPE=TCOMP)(5) ${T}_{c}=\frac{1}{2}{t}^{T}{f}_{t}=\frac{1}{2}{t}^{T}\left[{K}_{t}+C\left(p\right)\right]t$
2. Grid Temperature (RTYPE=TEMP)
3. Nodal Flow Pressure (RTYPE=FLOWPRES)
An example application is that the nodal flow pressure response can be used to constrain the overall pressure drop across the inlet and the outlet at a given inlet velocity. Thereby, the pressure drop for a fluid pump that is used to pump fluid through the structure is constrained. Another way to inherently define the pressure drop value is also to use SPCP Bulk Data to define both the inlet and outlet pressures.
### Supported Input
Darcy flow analysis and Convection Topology Optimization is supported for shell and solid elements. The DTPL Bulk Data Entry can be used to turn on Topology Optimization.
### Sample Model Setup
The following sample illustrates an example model setup.
$*****************************************************************$ DARCY FLOW ANALYSIS – FORCED CONVECTION STEADY STATE HEAT TRANFER
$***************************************************************** SUBCASE 1 SPC = 4$ Provides Heat transfer boundary conditions or Temperature loading.
SPCP = 6 $Activates Darcy Flow analysis, while providing outlet pressure INLTVEL = 2$ This is not mandatory. SPCP can also be used to define inlet pressure
LOAD = 13 $Defines Heat Transfer loading via either QBDY1 or QVOL. PRESSURE = ALL$ Turns on nodal pressure output for Darcy flow.
VELOCITY = ALL $Elemental Velocity is output by default for Darcy flow. BEGIN BULK$--1---><--2---><--3---><--4---><--5---><--6---><--7---><--8---><--9---><--10-->
QBDY1 13 10000. 10501
MAT4 1 50.2 5.02E8 7.83E-9 1.2765
MAT4 2 50.2 5.02E8 7.83E-9 1.2765
+ DARCY 0.1 1000.0 0.598 4.183E+9 1.0E-9
INLTVEL 2 9305 1000.0 8605 425 1549 8611
INLTVEL 2 13305 1000.0 12826 8605 8611 12832
INLTVEL 2 17305 1000.0 17047 12826 12832 17053
INLTVEL 2 21305 1000.0 21268 17047 17053 21274
SPC 4 425 0.0
SPC 4 426 0.0
SPCP 6 122612 0.0
SPCP 6 118391 0.0
## Output
Generally, any output from Steady-State Heat Transfer analysis, like Grid Temperatures (THERMAL) and Heat Flux (FLUX) are supported for Darcy flow analysis.
In addition, Nodal Flow Pressure (PRESSURE) and Elemental Velocity (VELOCITY) output are available specifically for Darcy flow analysis.
Nodal pressure is a scalar quantity output that is off by default. PRESSURE I/O Entry can be used to turn on the nodal pressure output.
Elemental velocity is a vector output by default, and can be controlled using the VELOCITY I/O Entry.(6) $u=-\frac{\kappa }{\mu }\nabla p=-\frac{\kappa }{\mu }B{p}^{e}$
Where,
$u$
Elemental velocity
$\kappa$
Fluid permeability
$\mu$
Fluid dynamic viscosity
$\nabla p$
Pressure differential
$B$
Differential of the elemental shape function
${p}^{e}$
Nodal pressures in element $e$
The following table illustrates the input and output entries required to run the solution.
Table 1. Darcy Flow Analysis and Convection Topology Optimization Overview
Darcy Flow Analysis and Convection Topology Bulk Data Case Control
Fixed Temperature Boundary Conditions SPC SPC
Fluid Boundary Conditions SPCP, INLTVEL SPCP, INLTVEL
Structural Thermal Material
Fluid Thermal Material MAT4 (DARCY continuation line)
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# The holographic Hadamard condition on asymptotically Anti-de Sitter spacetimes
Michał Wrochna
December 04, 2016
In the setting of asymptotically Anti-de Sitter spacetimes, we consider Klein-Gordon fields subject to Dirichlet boundary conditions, with mass satisfying the Breitenlohner-Freedman bound. We introduce a condition on the b-wave front set of two-point functions of quantum fields, which locally in the bulk amounts to the usual Hadamard condition, and which moreover allows to estimate wave front sets for the holographically induced theory on the boundary. We prove the existence of two-point functions satisfying this condition, and show their uniqueness modulo terms that have smooth Schwartz kernel in the bulk and have smooth restriction to the boundary. Finally, using Vasy's propagation of singularities theorem, we prove an analogue of Duistermaat and Hörmander theorem on distinguished parametrices.
%%% contains utf-8, see: http://inspirehep.net/info/faq/general#utf8 %%% add \usepackage[utf8]{inputenc} to your latex preamble @article{Wrochna:2016ruq, author = "Wrochna, Michał", title = "{The holographic Hadamard condition on asymptotically Anti-de Sitter spacetimes}", doi = "10.1007/s11005-017-0988-1", year = "2016", eprint = "1612.01203", archivePrefix = "arXiv", primaryClass = "math-ph", SLACcitation = "%%CITATION = ARXIV:1612.01203;%%" }
Keywords:
anti de Sitter, Hadamard states, holography
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In this example, we will show how to reblock using MineLink software and its impact in the results of the final pit shell.
### Case
To develop this exercise a model with regular blocks of 20mx20mx20m was considered. The mineralized ore body has a seam geometry shape of 200m width, 1000m long, and undefined depth. It is dipping at 45° in relation to the vertical axis and is located 50 metres below the surface. The mineralized zone has an ore grade of 0.7% Cu with a uniform distribution in the blocks. For the purpose of this exercise all the blocks have a density of 2.64 t/m³. The next figures show a plant view and a section view of the ore grade in the block model.
Fig. 1. Plant view in the model with block dimensions of 20mx20mx20m
Fig. 2. Section view in the model with block dimensions of 20mx20mx20m
When roblocking the original model to a block model of 40mx40mx40m, the following plant view and section view of the mineralized zone are obtained.
Fig. 3. Plant view in the reblocked model
Fig. 4. Section view in the reblocked model
It is possible to appreciate from figures 3 and 4, when the original model is reblocked to block dimensions of 40mx40mx40m there is a dilution of the ore grade in the edges of the mineralized ore body. The next figure shows a schematic illustration of the reblocking process for a single level taking a section view.
Fig 5. Schematic illustration of reblocking the original block model to blocks of 40mx40mx40m
It is important to mention that figure 5 is a 2 dimension view of the reblocking process because every block of 40mx40mx40m contains 8 blocks of 20mx20mx20m.
For the optimization process a 45° overall slope angle will be considered, as well as one single metallurgical process.
The next table shows the economic parameters and the metallurgical recovery.
Table 1. Cost parameters and metallurgical recovery
#### Results
In this section there are some results for the reblocking and ultimate pit computation, given the block model showed in the previous section. We want to validate and compare MineLink's output given the Whittle's results using the same parameters.
Table 2. MineLink and Whittle's Ultimate Pit Results
On the other hand we can compare the ultimate pit shell obtained on both methodologies at the same level, as seen on next figure.
Fig 6. Plan view of the ultimate pit results using the original block model (20x20x20 meters) and the reblocked model (40x40x40 meters)
Fig 7. Longitudinal view of the ultimate pit results using the original block model (20x20x20 meters) and the reblocked model (40x40x40 meters)
#### Reblock and Ultimate Pit MineLink’s Script
In this section is showed the script used to reblock and calculate the ultimate pit using the MineLink library.
from MineLink import *
#Import Original Block Model
bm = BlockModel(file_name = r'C:\Users\MyUser\Reblock\original_blockmodel.txt')
#________________REBLOCKING__________________________
#Reblock Dimensions
dx_reb = 40
dy_reb = 40
dz_reb = 40
#Creating a Reblocker
reg_reb = RegularReblocker(bm,dx_reb,dy_reb,dz_reb,"id")
#Save the Reblocked Model
nbm = reg_reb.ReblockToRegularBlockModel()
#Export Reblocked Block Model to Text File
#______________FINAL PIT CALCULATION______________________
#Import Reblocked Block Model
bm_reb = BlockModel(file_name = r"C:\Users\MyUser\Reblock\reblocked_blockmodel.txt")
#Create Column to value attribute
#ValueFunction Valorizes the Block Model Given the Attributes, Costs and Copper Price
#Create Slope Precedences Using Rosetta
rosetta = RosettaSlope([360],[45])
prec = RosettaPrecedence(bm_reb,"slope")
prec.CreateArcs(8,dx_reb,dy_reb,dz_reb)
#Create Final Pit Instance and Calculation
names = []
fpi = FinalPitInstance("value",prec)
solver = PseudoFlowFinalPitSolver(fpi)
solver.Run()
bms = solver.FinalPit()
names.append("pit")
bms.StoreAsAttribute("pit")
#Export Reblocked Block Model Including the Pit Results
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## On the regularization of the Kepler problem.(English)Zbl 1266.37022
The Kepler problem is the study of the motion of two masses subject to an attractive inverse-square force. A key element in modern treatments of the Kepler problem in $$\mathbb{R}^n$$ is the regularization of collision orbits. Moser’s fundamental work here related the flow for a fixed negative energy level to the geodesic flow on the sphere $$S^n$$ by stereographic projection on the punctured cotangent bundle of the sphere.
An alternative approach to regularization – with the advantage of canonically transforming the whole negative energy part of the $$\mathbb{R}^{2n}$$ phase space for the Kepler Hamiltonian into the punctured cotangent bundle of $$S^n$$ – was developed by T. Ligon and M. Schaaf [Rep. Math. Phys. 9, 281–300 (1976; Zbl 0347.58005)]. Unfortunately, the Ligon-Schaaf approach requires a significant computational effort.
The authors of this paper show that the Ligon-Schaaf regularization is closely related to the Moser regularization map. It turn out that the Ligon-Schaaf map is the natural adaptation of the Moser map intertwining the Kepler flow on the negative energy part of the phase space $$\mathbb{R}^{2n}$$ and the geodesic Delaunay flow on the punctured cotangent bundle of $$S^n$$ in a canonical way. The authors’ approach makes the role of the hidden Kepler symmetry quite apparent.
### MSC:
37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction (MSC2010) 70F05 Two-body problems
### Keywords:
Kepler problem; regularization; hidden symmetry
Zbl 0347.58005
Full Text:
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# Nihar Mahajan's messageboard.
Hello every positive min(TREVOR) !
Since many of my friends are motivating me to create my own messageboard , so here's my messageboard . You can leave messages for me here.
Also FYI : I like carrots and there is no specific reason for it.
Do reshare this so that I can reach most of the brilliantians.
Lets start with a nice quote by the legend Albert Einstein:
$$Do \ not \ worry \ about \ your \ difficulties \ in \ Mathematics \ .\ I \ can \ assure \ you \ mine \ are \ still \ greater .$$
Cheers!
Note by Nihar Mahajan
2 years, 10 months ago
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## Comments
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Do you like mangoes ?
- 2 years, 10 months ago
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Yeah I like mangoes but a specific breed of them which is called Alphonso mango.I like them because they are tasty.
- 2 years, 10 months ago
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It feels like the good problems on brilliant are going and the community is deteriorating.
- 1 year, 11 months ago
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You may discuss this on Andrew's Messageboard, so that your opinion reaches the staff.
- 1 year, 11 months ago
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So true :(
- 1 year, 11 months ago
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Hey Nihar , here's another awesome quote by Albet Einstien -
$$\large \textbf{"The only thing that interferes with my learning is my education." }$$
- 2 years, 10 months ago
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What is your favorite low tech and high tech way to track progress on your habits?
If for a moment you start to feel overwhelmed by the complexities of life, how do you simplify to get where you want to be?
- 2 years, 10 months ago
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Ans 1) I have no favorites as such.
Ans 2) Take a deep breath, and let all the chaos and frustration flow out of you. Focus not all all the things you need to do, or that are coming up, or that have happened, but on what you’re doing right now. And just focus on doing one thing, right now.I would take a walk, get some fresh air, and get some perspective. Try to think about what’s most important to you, what your perfect life would be like, what your perfect day would look like.
- 2 years, 10 months ago
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@Adwait Godbole Hi, I am also studying in MPA since Grade 8 and I am entering grade 11. I also attend Sanjeet sir's lectures for physics since grade 9. I came to know about you from Sanjeet sir and you always hit the top rank in MPA's test. Though Calculus was not taught in MPA till 10th, I have learnt Calculus from brilliant and other few books. Since I am entering 11th, I need your advice. How should I plan study in 11th and 12th, which studying habits should I adopt? I have whole April month in hand, what topics should I prepare in April? (I am also preparing for NSEA,NSEP) . Please suggest a single book in Math,Physics and chem which you feel is the best. If you have time, please give me some tips as well. Also, how was your JEE Mains paper? And Best Luck for Advanced. Sorry for troubling you, if you have time, please do respond :)
Some contests are also being held on Brilliant: JEE-Advanced Contest , Brilliant Sub Junior Calculus Contest, etc. Please do participate :) Thanks!
- 1 year, 11 months ago
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Hi, @Nihar Mahajan , its a great thing that you already have studied a bit of calculus. Your personal study plan would depend on your strengths (and weaknesses). As your classes begin the daily schedule would start to shape up automatically. Only ensure that you never stay behind the class, not even if it is a topic you do not appreciate so much. As, for current study, I would say just unwind a bit!! Go on a vacation. Don't worry you have a lot of study coming your way!! Even then if you feel like it, I would suggest you to strengthen and consolidate topics that you are already pretty comfortable with (which would be mostly maths, for obvious reasons). Throughout pay a lot of attention to mastering fundamental concepts. Initially (not in the exam) it doesn't matter even if you spend one hour on a single problem, to go into the intricacies, and look at all the variations possible and new techniques that could be developed and applied to ten other problems of its genre. Best of luck!
- 1 year, 11 months ago
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Thank you very much for your positive response :)
- 1 year, 11 months ago
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Which book do you study for maths (IIt-jee) ? I don't find any which can get you level 5 in calculus, algebra , geometry , combinatorics , number theory all together.
- 1 year, 11 months ago
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I refer to my class notes.
- 1 year, 11 months ago
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Do they teach calculus in class 10 ?
- 1 year, 11 months ago
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Nope.
- 1 year, 11 months ago
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So what does notes refer to then ? Aren't they the class notes? Do they mean any coaching notes or your self made notes ?
- 1 year, 11 months ago
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@Siddharth Singh I just saw your set , titled "Memories Remain". What is the significance of the title? Do you mean that you are separated from your friend? I am curious.
- 2 years, 4 months ago
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@Siddharth Singh I am waiting for your reply.
- 2 years, 4 months ago
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@Nihar Mahajan, can you give me some tips on how to improve in physics.......I am facing a lot of trouble in mechanics.
- 2 years, 1 month ago
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Hm , I may not be able to give you good tips , but @Abhineet Nayyar@Samarpit Swain can. Actually , even I want some good tips ;)
- 2 years, 1 month ago
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But still I think you are good in physics ( you have a level 5 in classical mechanics)
- 2 years, 1 month ago
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Well , then buy Fundamentals of Physics by Resnick , Halliday. And if you sincerely complete doing this book properly , you would have mastery in physics. (I am doing the same)
- 2 years, 1 month ago
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Thanks!!!!!!
- 2 years, 1 month ago
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What is the meaning of (positive min TREVOR)? If I am not wrong , TREVOR is a name right?
- 2 years, 10 months ago
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@nitesh chaudhary , That's a link. Open it, And you'll see xD
- 2 years, 10 months ago
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Thanks Mehul for doing my job :)
- 2 years, 10 months ago
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Has brilliant helped you in your JEE preparation?
- 1 month ago
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@Nihar Mahajan Hello Nihar ,
you were not replying to the messages on fb , so this was the only way to communicate .
- 10 months, 3 weeks ago
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@Harsh Shrivastava What is your NTSE Stage 2 center?
- 1 year, 10 months ago
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How is your preparation going?
- 1 year, 10 months ago
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I seriously have no idea. I am just reading CBSE SST books :/
- 1 year, 10 months ago
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Raipur, capital of chhattisgarh.
- 1 year, 10 months ago
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@Nihar Mahajan Hi Nihar, What books are you using for Olympiad preparation(all subjects)? Also.. do you like Alphonso Mango Ice Cream?
- 1 year, 11 months ago
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Hey Nihar!
How's life?
Which book are you using for preparing for NSEP?
Is Resnick Halliday good?
- 1 year, 11 months ago
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Yep, its a very nice book. Life is refreshing xD
- 1 year, 11 months ago
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How are you preparing for nsep?
- 1 year, 11 months ago
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I have no idea, how to prepare. I myself need help.
- 1 year, 11 months ago
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Which book do you study for maths (IIt-jee) ? I don't find any which can get you level 5 in calculus, algebra , geometry , combinatorics , number theory and more.
- 2 years ago
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Any ideas how many marks ninad,toke,tekawade and pranav scored in INMO ??
- 2 years, 1 month ago
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Lets meet sometime....I have found a legitimate solution to Goldbatch Conjencture...which officially makes me a billionare :P
- 2 years, 1 month ago
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Wow! I would be glad to see it :)
- 2 years, 1 month ago
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Hello nihar! Do you remember me?
- 2 years, 4 months ago
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Of course , How can I forget a genius like you? ;)
- 2 years, 4 months ago
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What happened? How did you lose your 288 day streak?
- 2 years, 4 months ago
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I went on vacation to a place where there was no network available :(
- 2 years, 4 months ago
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Do you like carrots?
- 2 years, 5 months ago
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Yes , I like them. They are sweet and tasty. It can act as a nice refreshing tool during stress :)
- 2 years, 5 months ago
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Nihar, I have heard that you are an authority on the subject of 'perpetual energy production with the help of magnets'....I am also interested by this topic...Can we apply this theory to supplement the motion of cycles?... If yes, how?... And, I also live in Pune, can we discuss this topic in person?
- 2 years, 6 months ago
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Yes we will for sure.Where do you live in Pune? May be we can meet...
- 2 years, 6 months ago
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I stay in Kothrud... What about you? In which school do you study?
- 2 years, 6 months ago
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Even I stay in Kothrud! I study in M.E.S Balshikshan Mandir English Medium School. Can I call you Mandke? Bcoz Aditya is too common name :P
- 2 years, 6 months ago
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Nihar, even I study in MES Balshikshan Mandir English Medium School! Well, we must have met sometime! And yes, you are at liberty to call me Mandke. :)
- 2 years, 6 months ago
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@Aditya Mandke @Nihar Mahajan Lol. Looks like B'ant has proved instrumental in the meeting of two people of the same region, of the same school :3
- 2 years, 6 months ago
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Hey! Bro Do you read novels?????
- 2 years, 10 months ago
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Nope.I don't get much time to read them :/
- 2 years, 10 months ago
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😑😑Too busy in Maths.
- 2 years, 10 months ago
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You forgot the important word "friends" and the unfortunate word "school work".
- 2 years, 10 months ago
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Absolutely right..
- 2 years, 9 months ago
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What is your fav english movie?
- 2 years, 10 months ago
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Its very difficult to mention one because there are many movies which are my favorite like Avengers , Hobbit , Hunger Games , Gravity , Interstellar , FF series , Skyfall , All Marvel series , etc. There are many more (big list).
- 2 years, 10 months ago
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What do you want to become when you grow up?@Nihar Mahajan
- 2 years, 10 months ago
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An engineer.
- 2 years, 10 months ago
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Same here.How are you preparing for the same?
- 2 years, 10 months ago
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Well , nothing can be achieved without efforts in this world. Hence , I am preparing really well to achieve my goal.
- 2 years, 10 months ago
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Next question.What's your obsession with Robert Downey Jr. ?
- 2 years, 10 months ago
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Many people are Robert Downey Jr. fans and am one of them.
- 2 years, 10 months ago
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TBH I am also one of the fans.I love his poise and relax and funny personality and all ...
- 2 years, 10 months ago
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Do you realize, You might be the fastest one to cross 1000 followers?
- 2 years, 10 months ago
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May be.I don't know.Here's my senseless logic :
I like carrots.You can refer carrots to caret symbol "^" which resembles exponents. Hence my followers are increasing "exponentially". @Azhaghu Roopesh M I hope you get this logic as a reason.
- 2 years, 10 months ago
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Congrats!
Here's another thought:
Imagination is more important than Knowledge - Albert Einstien
First question: Why do you like carrots?
- 2 years, 10 months ago
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Nice thought indeed. I like carrots because they are tasty.
- 2 years, 10 months ago
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Hello! I think you like carrot because the word carrots has 7 letters and the word Mahajan also has 7 letters:)
howsthat!
- 2 years, 10 months ago
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May be. But the probability that this will be the actual reason is $$0.1729$$.
- 2 years, 10 months ago
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Sir Ramanujan might have helped you in finding that probability.
- 2 years, 10 months ago
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May be.But the probability that he might have helped is $$0.007$$.
- 2 years, 10 months ago
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did bond help u here ? :P
- 2 years, 10 months ago
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Yeah , you noticed it.For completeness , its James Bond. (some people may think bonds of chemistry). :P
- 2 years, 10 months ago
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The probability that you may be in class 10th is 1.So how are you preparing for boards and also do you take part in SOF Olympiads?
- 2 years, 10 months ago
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Yes , your probability is correct. I am not interested much in scoring in boards. I am interested in IMO (not the SOF one) , and of course IITJEE.I am preparing really hard for it. My school does not hold SOF Olympiads so I don't take part in it.
- 2 years, 10 months ago
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Do you mean this RMO-INMO-IMO:)
- 2 years, 10 months ago
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Yeah . FYI : you forgot the important step of IMO - TC :)
- 2 years, 10 months ago
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Oh! I did not see your response earlier, well, you are right Training camp should also be included.Have you given RMO anytime?
- 2 years, 10 months ago
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## Wednesday, September 14, 2016 ... /////
### An interview with Václav Klaus
About the final victory of the Left, redefinition of the main political themes, Merkelism, and U.S. elections
An interview with the Czech ex-president was recorded by PragueTV less than two weeks ago and I found it interesting enough to translate those 23 minutes for you.
See the original "Prague Café" interview, a video in Czech.
Via klaus.cz
Moderator, Petr Žantovský:
Welcome to the Prague Café. Today, we have moved the program to slightly atypical spaces, namely those of the Institute of Václav Klaus. The reason is simple. Our guest today is the former president Václav Klaus. Good afternoon.
Klaus:
Good afternoon. Well, I just hope that you haven't brought the spirit of the Prague Café [=PC intellectual elites of Prague] into these sacred spaces of our institute.
Moderator:
Well, we certainly did. And the reason is that we are reviving and rehabilitating the spirit of the Prague Café that has been, so to say, hijacked by someone who likes to call himself the Prague Café. But when we're already in this informal setup, let me offer you a small personal memory.
In 1997, shortly after the [second] Sarajevo assassination [a betrayal of PM Klaus during his visit to Sarajevo by some coalition politicians in Prague that led to Klaus' resignation], we began to co-write your then first book of interviews, "That's What Václav Klaus Stated". And because almost 20 years separates us from those times, let me ask you the same question that I did ask you then. Do you know the difference between a left-winger and a right-winger here today?
Klaus:
I don't know. And did I give you an intelligent answer then?
Moderator:
You gave exactly the same answer as now: I don't know. And I told you: Both of them have studied Marxism-Leninism but the rightwinger has understood it.
Klaus:
Well, it's a possible small joke.
Moderator:
Your reaction is exactly the same as it was then.
Klaus:
You know, I am already a rigid, fossilized man. No one should expect anything new from me anymore.
Moderator:
But yes, he should. One may expect a review of those 20 years. What has changed about the meaning of the Left and the Right as understood then and now, assuming that the concepts still exist at all?
Klaus:
Before the discussion of the words, I would insert one thing that has absolutely changed: the mood in the society. This seems to be the fundamental change. In the 1990s, people like me had the feeling that we were going up or forward. But in the late 1990s and early 2000s, it started to return back. And we have the feeling that we're going backwards. And that's a fatal, fundamental transformation. And the concepts of the Left and Right are victims of this confrontation.
I think that these two words may be defined just like they could have been 20 years ago but they gradually lost their importance because the old left-right competition that was primarily a socio-economic one has faded away. It got diluted and became uninteresting, partially because the Left has achieved the ultimate victory – that's one thing. But this is no longer a defining question of our age. The arguments are about something completely different today which means that the old left-right schemes become largely inapplicable.
Moderator:
You have used the word that I didn't expect from you and believe me, I don't like hearing it, and that's "ultimate". The Left has won definitively. But you were never a fan of these definitive visions. What's your reason to think that it's definitive?
Klaus:
Well, when I say "ultimate", I am thinking about some imaginable future, not necessary the whole eternity. I wouldn't dare to go this far now. But if I speak about something that seems like an interesting, foreseeable future, then I think that the standard Left-Right conflict has been lost definitively by us. And I don't even see anyone who would continue to play this conflict in some significant way – neither in our country, nor in the world.
Moderator:
This may lead us to a question at a more general level: What has really happened to the purpose of politics? Politics as the care about the matters of the community has seemingly disappeared. And perhaps because of the trivializing statements such as "politics is like an Ltd company, we have to be good managers" – those aren't inventions of our current finance minister [populist billionaire Babiš] but a much older one. But it's not the only invention. What are the others?
Klaus:
First, there can't be any doubts about the statement that assorted leftists have been announcing the end of the Left-Right political conflict for a very long time and we have moved on. And we became rational, they said, and it's meaningless to insist on those old words. Well, the leftists have been saying it for half a century...
Moderator:
[simultaneously] ... some 50 years...
Klaus:
Already in the 1950s. So this sure thing is one aspect. But the public discourse has moved to completely different topics. These days, you see that the basic discourse is about other things. About the political correctness, multiculturalism, migration, about the taboo status of one thing or another, about the attack on the family, the nation, and all these things. The old left-right themes aren't relevant in these discussions at all.
In fact, I would say that the the fans of the old left-and-right schemes are almost standing together on one side of the barricade against all the supporters of the quasi-progressivism and quasi-modernism.
Moderator:
You began to speak about NGOism already some 10 years ago. If I remember well, you were still the chairman of the Parliament when I brought you a book titled Ecofascism and maybe you began to use that term (NGOism) because of this gift of mine. It was quite a prophetic achievement of yours because it seems to me that this prophesy is just being fulfilled nowadays.
Klaus:
That's absolutely wonderful. And thank you very much because one is producing tons of speeches and articles. Just yesterday, I was writing the text of my German speech to be delivered in Berlin in exactly 7 days and I was enumerating all of these favorite -isms of mine which I often operate with. And I must confess that I have forgotten the NGOism. So I made a note in this notebook to add the word to my Berlin speech immediately.
But what I think is true that even after those 10-15 years when we were using this term, it's still true that very many people keep on misunderstanding it.
[Klaus later wrote a report about his visit to Berlin in Czech. He isn't a fan of the city, it's too post-modern, too Cosmopolitan, too full of bicycles instead of cars, mothers with 3 kids arranged on her bike, tourist bags, Russians, Russian texts. The venue for his talk was terrorized by the left-wing activists once again so the organizers rented a fancy ship, The Comtess of the Spree, and the event took place while sailing.]
Moderator:
Even though they are already victims of this new system of governance? NGOism is a new system of governance, isn't it?
Klaus:
Of course it is. It is an alternative system of governance. And I feel that people are still not perceiving it. If I return to my speech in Germany – sorry that I keep on returning to that talk – I am going to say that the people who are sitting either in the Bavarian Bierstube [pubs] or lazily lying on the Spanish beaches [those are of a bit higher quality] – so these people are still uninterested in all these concepts, they still fail to perceive them. And unfortunately, these uninterested people are still a majority.
Moderator:
Isn't it because our part of Europe is still living in some luxury etc.? If you go to Warsaw, Poland, Hungary, let alone the more Eastern ex-Soviet satellites, Czechia is better off, I feel.
Klaus:
That's surely the case. But when I was giving my verdicts, I wasn't thinking of Czechia or Bohemia. I meant Western Europe and Germans in particular. Those are still misunderstanding this word of mine completely.
Moderator:
On the other hand, Bavaria turned out to be the German state that has displayed some survival instinct – I mean in the context of the migration crisis. The Seehofer-Merkel argument may be just an internal exchange within a party and maybe just one before the elections. But it must be placed in some context, right?
Klaus:
It's surely an argument. But it's still true that in Germany, including Bavaria, you would still be unable to publish newspaper articles that are commonly published in the Czech media. In this sense, thank God, the Western Europe is much more tightly laced up and controlled by the dictate than we are. Thankfully, after all, all of us have learned some lessons from the communism. And yes, I feel that even those whom I consider to stand on the opposite side of the political discourse than my place, have also learned this lesson and behave differently than the Germans do.
This Merkelism, if you wish, is remaining almost non-existent in Czechia.
Moderator:
You are speaking about Merkelism. But anti-Merkelism also exists in Germany. We may return to it soon...
Klaus:
A very weak one...
Moderator:
But do you feel that Germany is beginning to transform under the influence of the migration wave? Does it start to think about itself and transcend the limits of the traditional politically correct thinking that depends on the collective feeling of guilt – guilt for the Holocaust etc.?
Klaus:
This is a standard question and my standard answer is: Hopefully. More precisely, it seems like a Wunschdänken, a wishful thinking, rather than reality.
It's self-evident that Germany is moving somewhere. But when I am attending various events of AfD, the Alternative for Germany, I see something more disappointing. I was just writing a report about my visit to Schwerin where they have elections this weekend.
Over there, I lamented: In a hall with just some 250 people who have been selected because they gathered from a large territory to see my speech, I – an oldish politician – still end up being the most [youthfully] radical of all the people in the hall.
So I wouldn't trust in overly optimistic ideas about the ongoing transformation. In fact, the moderator – a member of AfD in Schwerin – was a polite professor teaching at a local high school. He was asking questions to me and I couldn't believe my ears. It seemed to me that I had to fight in a similar way as I would have to fight on Radio Plus or the Czech Public TV [PC media in Czechia].
He was telling me: But you, in the Czech Republic, seem to have one of the lowest population growth rates in the world according to some sources I have read. You will obviously need those workers, won't you?
So first I yelled at him and urged him not to tell us whether we need some workers or not. But when I am getting such a question from AfD, one may immediately see that it's utterly absurd.
Moderator:
Let me turn it around. When Chancellor Merkel is currently on a tour around the central European countries, the Visegrád member states etc., and on behalf of the EU, she is trying to put something in their heads, namely the idea of the quotas and similar matters, she is behaving as a representative of the EU. And quite frequently, people are lightly asking whether we're not seeing the birth of the Fourth Reich of some kind. What do you think about it?
Klaus:
First, these analogies. Well, yes, but do I have to call it the Fourth Reich? It may be a nice hyperbolic witticism. Well, Ms Merkel does arrive here as a representative of the European Union. The fact that the assorted footmen, lackeys, and chichmoondahs such as Mr Tusk and Mr Schulz are absolutely irrelevant – and exactly Ms Merkel is who matters – is so self-evident that everyone sees it.
Ms Merkel has no nominal EU title. But she is a top representative of the contemporary European Union. We might react jokingly and demand Ms Merkel to show us some official EU authorization. But the serious truth is that she is the actual representative of the European Union – even though someone else should be the official representative instead.
But the idea that someone such as Comrade Mogherini or what's her name – an Italian woman – is a chief of the EU is at most a joke. Yes, I don't even know her name. And I am a politician. I am convinced that some 99% of the citizens of the Czech Republic – but not only the Czech Republic, even Italy and Germany – don't know the name of this lady. So to criticize Ms Merkel that she is not a representative of the European Union seems like an uninteresting legalistic nitpicking to me.
Moderator:
Let me build on your previous words. You said that the old-style leftwingers and rightwingers are being pushed together as natural allies in a conflict with a new foe, the NGOism and other ideologies in the wave. Isn't it funny when various NGOs such as The European Values pick you and Mr Hájek and others – who were always viewed as conservative advocates of the Western values – and throw you in a bag and paint you as the ultimate pro-Kremlin folks. It almost looks like you have been given the same hat for heretics, one with a caricature of a little devil, that Master John Huss had in 1415. And they are urging the people to burn you at stake. In the bag, you find yourself along with the current president and very many other people.
Klaus:
Let me postpone the discussion about the Kremlin. First, yes, I do feel some shared identity with the traditional left-wing parties. Earlier in the summer, I attended a traditional agricultural festival The Land The Feeder in Czech Budweis, which I consider to be a nice positive event, despite the Prague Café's efforts to mock it as a relic of the past which is silly. And at the beginning, there was a meeting in the foyer. Accidentally, I was sitting close to President Zeman and the South Bohemian governor Mr Zimola, a social democrat.
There weren't sufficiently many bottles of beer over there. So I poured one into my glass and very visibly, I also used my bottle to pour the beer to governor Zimola's pint as well. And I loudly said: "Do you see? This is the expression of my friendly attitude to the social democracy." Everyone exploded in laughter. Yes. But the men from the social democracy, Zimolas or Mr Jandák who was there [a social democratic ex-actor] are really closer to me than Pirates or Citizens for something, Citizens against something, ANOs, TOPs, not to mention the Greens. Yes, we need to say this.
Moderator:
What's the relationship of this with the Kremlin?
Klaus:
It's you who incorporated it into this discussion [so you should know].
Moderator:
Well, my impression is that from the Prague Café and similar folks' viewpoint, you are being labeled in this way because you're together and not on their frequency as they are.
Klaus:
We are labeled in this way because we don't want the NGOism, multiculturalism, false and lying Western European and American political correctness, green stupidities about the global warming, and so on, and so on. We don't want interventions into the internal affairs of individual countries, permanent exports of the revolutions and the destruction of states here and there.
And that's why we are labeled as pro-Kremlin pundits. It's childish, silly, and I don't know what to add.
Moderator:
So you got a similar label as the "traitors" [a soft communist propaganda word for a traitor paid by foreign interests is being used]. But isn't it also because you don't want sanctions against Russia? Because you dislike the plans to perturb the equilibrium among geopolitical forces in Central Europe and elsewhere?
Klaus:
No doubt about it. These manipulations that certain people in Western Europe and especially in the U.S. are doing with the world these days are vintage examples of a total irresponsibility, failure to see one's own nose. Also, it's a sign of their despair, their feeling that they're losing. And that's why they are trying to do desperate acts. People who feel hopelessness are always inclined to behave desperately.
So again, it began with Yugoslavia and its destruction which was unnecessary. The Yugoslav folks themselves would have surely never disintegrated Yugoslavia in the way in which it ultimately was disintegrated in the 1990s. It continued with the Iraqs and the Near and Middle East. [moderator says: Kosovo] Well, Kosovo is something I count as a part of the Yugoslav matters.
It continued and it recently moved to Ukraine. If the disagreements were kept as a Ukrainian-Ukrainian question, it would probably remain peaceful and it could have been basically solved by now. But the numerous players of the fake Prague Café do want some extra layer of problems. The confrontation in Ukraine is their confrontation. That's why they were going to all those Maidans.
Moderator:
It's their business, isn't it?
Klaus:
It's their job, an occupation.
Moderator:
The U.S. presidential elections are not far away. Do you believe that either Clinton's or Trump's victory will change something about the attitude of the U.S. towards Russia or Europe?
Klaus:
It's very interesting because our institute is publishing a newsletter and we usually ask a "Question of the Month". We invite 5-10 people to answer. The question for the September newsletter is exactly one you gave me. Will the Trump or Clinton victory change the world?
Well, I don't know. There's no doubt that the continuation of the current American regime which is expected after a Clinton victory is something immensely negative for us, for the world, and I think that for America, too.
Indeed, Trump is a character but he is still speaking on behalf of sane Americans and the normal America. I have never met or talked to Trump – unlike Hillary Clinton whom I met many times. I don't really know what is inside Trump's head. But I do believe that he is being interpreted here completely incorrectly.
I don't think that Trump is as stupid as some people paint him. He is just a player, a naturally political animal, that plays different roles. Just like a great actor in the National Theater sometimes stars as a gentle lover and sometimes as a villain, Trump is just starring in the role of the leader of the election campaign. He should be expected to switch into a completely different role with a very distinct arrangement, the role of a responsible leader, on the following day. That's my assumption and I believe that people are incorrectly assuming that he will be doing everything he has said during the campaign. That's not what I expect.
Moderator:
I view your words as optimistic ones. Thank you for those words and for the visit here in your Institute of Václav Klaus, in our Prague Café.
And dear viewers and TRF readers, see you next time.
Related: The idea that the Czechout is "looming" is greatly exaggerated. But otherwise I find the Aljazeera report above – which reasonably suggests that the Czech spirit of independence is analogous to the British one – much more impartial and informative than what I would expect from such a left-wing station.
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# homogenous
1. ### non-homogeneous recurrence problem
Hello everyone, I have this problem $a_n + a_{n-1} + 6a_{n-2} = 5n(-1)^n + 2^n$ This is the given solution: a_n = (\sqrt{6})^n(C_1\cdot \sin\phi n + C_2\cdot \cos\phi n) + \frac{1}{3} \cdot 2^n + \left(\frac{5}{6}\cdot n + \frac{55}{36}\right)(-1)^n I used the discriminant to find the zeros...
2. ### Homogenous stress/strain
Hi all, Any help would be appreciated. A fibre-reinforced composite has 25% volume of carbon fibres with a modulus of elasticity of 150.0 GPa. The remaining matrix material is polyester resin with a modulus of elasticity of 3.10 GPa. Use the homogeneous strain (parallel) model, to...
3. ### Homogenous Differential Equation
Please help me solve this differential equation xy'=√(x^2+y^2 ) I recognize this as homogenous differential equation of order 2.After substitution I get du/(sqrt(1+u)-u) = dx/x. How to solve this further. Please help. Got stuck while solving from GF Simmons
4. ### Non Homogenous Differential Equation.
y''+y'=4x What I do: 1) y''+y'=0 I find solutions: x1 = 0 x2 = -1 2) I need to find another part of the answer. y* = x*(e^ax)*Q(x) The problem is, I don't know what is that last Q(x)? Is it that 4x function?
5. ### Doubt with Homogenous Differential Equation
Hi, I have a doubt with a Homogenous Differential Equation. This is an exercice I have found in a textbook, just the solution is shown (not its development). I would like to confirm if my development is right. HDE: xy^3\,\text{d}x = {x^4 + y^4}\,\text{d}x I proceed as follows...
6. ### Homogenous system problem
Hello. As a new student, I just recently began learning about Linear Algebra. We have used the Gaussian Elimination on matrices, and are now moving on to linear systems. I have a problem, among many, to solve before monday 0600, and it bugs me quite a bit. It's relatively simple. You are given...
7. ### homogenous coordinates- explain please
Can someone please explain to me how do we get the following homogenous coordinates of the equilateral triangle (its vertices) . In case k=\mathbb{Z}_{2} The base has (1:0:0) and (0:1:0) and the vertex (0:0:1) How do we get it? Why for example the origin in Cartesian plane is represented by...
8. ### Homogenous system with more variables than equations
Did I solve this correctly? Solve the system. 3u - v + w -5x - y = 0 6u - 2v + 2w - 9x + y = 0 -9u + 3v - 3w + 11x -y = 0 Augmented matrix: \left[ \begin{array}{cccc} 3 & -1 & 1 & -5 & -1 & 0 \\ 6 & -2 & 2 & -9 & 1 & 0 \\ -9 & 3 & -3 & 11 & -1 & 0 \end{array} \right] = \left[...
9. ### Proof of homogenous
How should I prove this problem: "Prove that the set of all solutions x of the linear systems Ax = b forms a subspace if and only if the system is homogenous." I proved it directly, will this attempt suffice: Suppose x1 and x2 are solutions; we need to show that c1x1 + c2x2 is also a...
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# What's the first time-integral of price called?
In general I'm wondering about the names of time-derivatives of price.
E.g. in physics the first few time-derivatives of position are:
• f(x) = displacement
• f'(x) = velocity
• f''(x) = acceleration
And the first integral (anti-derivative) of displacement is called absement.
What would the equivalent financial terms be?
• What your looking for is Stochastic Calculus – pyCthon May 23 '13 at 2:33
Well, if you divide a time integral by the length of the time interval, you'll get the average (in time) price: $$\frac{1}{t}\int_0^T x_t\mathrm dt$$ so at least on of the meanings of the integral itself is an average price time the length of the interval. In such a case, I think the normalized quantity (the integral divided by the length) is more meaningful. It is used e.g. in the exotic options whose payoff depends on the average price.
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Journal topic
Mech. Sci., 10, 589–604, 2019
https://doi.org/10.5194/ms-10-589-2019
Mech. Sci., 10, 589–604, 2019
https://doi.org/10.5194/ms-10-589-2019
Research article 13 Dec 2019
Research article | 13 Dec 2019
# Kinematic analysis and evaluation of a hybrid mechanism for computer assisted bone reduction surgery
Kinematic analysis and evaluation of a hybrid mechanism for computer assisted bone reduction surgery
Sinh Nguyen Phu, Terence Essomba, Irwansyah Idram, and Jiing-Yi Lai Sinh Nguyen Phu et al.
• Department of Mechanical Engineering, National Central University, Jhongli City, 32001, Taiwan
Correspondence: Terence Essomba (tessomba@cc.ncu.edu)
Abstract
In severe fracture cases, a bone can be separated into two fragments and it is mandatory to reposition the bone fragments together. This type of surgery is called “bone reduction surgery”. Originally, the operation consisted in manipulating the bones fragments by hand in open surgery. The most advanced technique relies on robotic manipulators providing higher precision and stability. A new mechanical architecture is proposed based on a 3-RPS tripod parallel mechanism combined with a Double Triangular Planar parallel mechanism. Its kinematic and velocity models are calculated and the parasitic motion generated by the tripod mechanism is considered in the final result. The workspace it can generate is compared to the Stewart manipulator, which is a classical mechanism for the targeted application. The use of a robotic manipulator is due to be part of an entire surgical procedure involving a pre-operative simulation software dedicated to pre-planning reduction surgery, namely PhysiGuide. It is used to measure the kinematic associated with bone fragments manipulation and transfer it to the robot during the intra-operative phase. Simulations are then performed based on a real patient's fracture images showing the suitability of the present mechanism with bone reduction surgery.
1 Introduction
In Human anatomy, limb bones are more exposed to potential fractures due to their location and due to their longitudinal geometry. According to medical data history, the thigh bone, namely the femur, is the bone that has the highest involvement rate in fracture incidences with around 37 per 100 000 people per year (Arneson et al., 1998; Zlowodzki et al., 2006). Some cases of broken bones require a specific type of surgery before recovering: the bone reduction surgery. In most critical cases indeed, the bone is not only fractured but its two pieces can be separated by a certain distance. The bone reduction surgery consists in relocating the different pieces of the same bone in their original position. During this surgical procedure, the patient's anatomy must be “opened” to allow a physical access to the bone pieces. Once accessible, the surgeons can displace the bones to their original configuration. Because of the natural recall force applied by the patient's anatomy (muscular tissues and tendons), the surgeons have to use a considerable amount of physical strength to relocate to bones.
Later, in order to suppress the risk associated with the “open” type surgery (bleeding, infection, etc.), a minimally invasive version of bone reduction surgery has been developed, which is a general tendency in surgery. The reduction is performed by inserting nails into the bone pieces. These nails are then manipulated to reposition the bone pieces. Although this technique represents less risk for the patient, it also requires a higher level of dexterity from the surgeon since there is no direct vision of the broken bone. During the operation, their position are consequently monitored by intra-operative image. The surgeon in charge of the reduction procedure will then adjust the position of the bone pieces based on the real time images received. But minimally invasive reduction surgeries are still performed using a high strength to reposition the bones. And when surgical implants are required, the bones must be maintained in position the time the implant is fixed. In addition, due to the stress generated by the muscular tissues, there is always a residual motion of the bones parts when they are released. This can cause a misalignment between the bones and the implant after its installation. Another problem is the hazard environment of the image guided surgery. Unlike patients, surgeons will suffer from repeated exposures to the radiation generated by the medical imaging system.
Figure 1Fracture of a patient's femur (a). Result of reduction surgery and implant installation (b).
To solve the problems associated with manual bone reduction surgery (both opened and minimally invasive), a technique based on the use of specialized mechanism has been developed. The concept consists in fixing the mechanism base to one bone piece and the mechanism end effector to another bone piece. By operating the mechanism joints, a motion is generated between its base and its end effector. By extension, a motion is then performed between one bone piece and the other, based on the mechanism kinematics. To perform a complete bone reduction, it is required to manipulate one of the bone fragments by moving it along three linear direction and rotating it around three different axes. Therefore, a total of six Degrees of Freedom (DoF) is required: three linear DoF and three angular DoF. Also, in order to improve the fracture surface matching between the two fragments, it is advantageous to provide a rotation about the bone longitudinal axis. Several research works can be found in the literature as listed in the three coming sub-Sections. However, this particular type of robotic assisted surgery does not seem to attract as much attention as other topics such as laparoscopy or orthopedic surgery for example. One explanation is that the earliest application of this kind has been reported in 1999. This makes it a relatively young topic compared to neurosurgery, which is about two times older (1985). If the focus is given on mechanism concepts, the literature review of robotic bone reduction surgery can be divided into several categories.
## 1.1 Embedded parallel architectures
The first bone reduction surgical robot has been reported in 1999 (Seide et al., 1999). It is composed of two cylindrical modules that are connected by a hexapod mechanism of 6 legs and 12 spherical joints. These cylindrical modules are called Ilizarov fixators and are commercially available. That mechanical architecture is able to displace one cylinder with 6 DoF from the other. Each fixator is mounted on one piece of a longitudinal bone by surrounding the patient's limb. So the hexapod mechanism can reposition the bone pieces together. This device has been tested on 16 patients presenting deformities or fractures of the tibia.
Since then, the concept of fully embedded hexapod architecture has been often used for the robotically assisted reduction surgery of longitudinal bones. In 2004, another hexapod has been used for bone reduction surgery (Seide et al., 2004). A manually adjusted hexapod has been designed to manipulate two arc fixators attached to one piece of the bone each. A specific software was developed to allow the individual control of 6 DoF. The prototype has successfully performed the fracture reduction of four patients. The Taylor Spatial Frame is a hexapod mechanism dedicated to the bone reduction (Taylor, 2008). In 2006, a study has been reported about the use of the device on 10 pediatric patients from 8 to 15 years (Al-Sayyad, 2006). The same mechanical architecture has been used for the implementation of a computer-assisted orthopaedic procedure based on 3-D CT-Scan image in 2012 (Tang et al., 2012). It was tested on the fracture reduction of 10 bovine femurs.
## 1.2 Embedded serial architectures
Back in 2000, another kind of architecture has been tried for this application. Although the mechanism is still full embedded into the patient's anatomy, a serial architecture is used (Moorroft et al., 2000). The concept relies on a proximal and a distal clamp that are attached to one bone piece each. Both clamps are connected together by a serial mechanism of two linkages. There are one sagittal prismatic joint between the proximal clamp and a linkage, one transversal and one longitudinal prismatic joint between the distal clamp and a linkage and one spherical joint between the two linkages. These 6 DoF are manually adjustable individually by the mean of translation screws. The device has been tested on 22 tibial fractures. The kinematic analysis of two other devices sharing the same concept have been reported in 2002. Dynafix and Orthofix fixators are embedded mechanism for fracture reduction and bone deformity (Kim et al., 2002). Both of them are commercially available. The Dynafix is composed of two telescopic pin clamps, a central universal joint and two sets of revolute joints. The Orthofix is made of two straight pin clamps with a central body that provides an axial adjustment. Both sides have a ball-and-socket joint. The results of simulation experiments using the Dynafix have been later reported in 2006 (Koo et al., 2006). While the Dynafix and Orthofix are fully mechanical devices, another new prototype instrumented with rotary sensors has been designed for a better accuracy in 2007 (Koo and Mak, 2007).
## 1.3 Deported mechanisms
The bone reduction surgery can be performed using another concept of mechanism that here is referred to as “deported” mechanism. By “deported” mechanism, it is understood that while the mechanism end effector is still fixed with the patient's anatomy (bone piece), its base is attached to an external reference. The earliest instance of such system was reported in 2004. The system RepoRobo was an industrial robotic manipulator, namely Stäubli RX130, reprogrammed for bone reduction surgery (Füchtmeier et al., 2004). A software has been programmed in order to control the robotic manipulator in motion or in force. A force sensor is integrated in the robot end effector for the force feedback. In 2008, another industrial robotic manipulator has been reprogrammed for this application. This time, a Stäubli RX90 was used as part of a tele-operated system for bone reduction surgery (Westphal et al., 2008). The operator manually controls the manipulator using a standard joystick. The manual navigation is guided by intra-operative fluoroscopy. A high precision robot with a particular architecture has been designed in 2008 for hip fracture reduction. It has been combined with a navigation system based on fluoroscopy (Joung et al., 2008). The mechanical architecture is composed of three successive revolute joints along three different directions, followed by three prismatic joints. The end effector is a ring that surrounds the patient's anatomy. The same year, a robot based on a hexapod architecture has been designed for the reduction of femur fracture (Graham et al., 2008). The robot is placed horizontally and its end effector is attached to the patient's foot using an adapted holster. The manipulator is manually controlled by the mean of discrete point trajectories. In 2015, another hexapod architecture has been developed for a similar concept (Du et al., 2015). However this time, the mechanism is placed vertically below the patient's leg and its end effector is attached to the patient's bone directly. The whole hexapod is mounted on a vertically adjustable platform.
Figure 2Examples of bone reduction mechanism. (a) Orthofix fixator (Kim et al., 2002); (b) Dynafix fixator (Kim et al., 2002); (c) Ilizarov apparatus (Zamani and Oyadiji, 2009); (d) Ortho-SUV Frame (Solomin, 2013); (e) Taylor Spatial Frame (Mackie Orthopaedics, 2016).
According to the literature review of mechanisms and robotic systems for bone reduction surgery, several conclusions can be made about this topic:
• This specific medical robotic application is quite recent compared with robotic orthopedic in general. So the state of the art in this domain is relatively limited.
• Existing bone reduction robotic systems are also limited in diversity. Although they can be regrouped in three conceptual categories, only three types of mechanical architectures can be reported.
Parallel mechanical architectures seem more promising as they offer higher stiffness, higher accuracy, higher payload and low inertia in comparison to serial architectures. But they provide smaller workspace while it is an important aspect in bone reduction surgery. For this reason, some scholars tried to design new types of hybrid architectures by combining the advantage of several structures. In 1995, Etemadi-Zanganeh and Angeles (1995) classified the general hybrid parallel manipulator into 3 groups: hybrid system of serial chains, hybrid series-parallel chain and hybrid parallel-serial chains. According to their definition, hybrid parallel-serial chains have a series of parallel manipulators connected in series. For instance, in 1998, Romdhane (1999) presented a new 6-DoF hybrid robot (HS-PM) that is composed of two 3-DOF spatial parallel mechanisms. One 3-DoF spatial robot provides 3 rotation movements and one 3-DoF spatial robot provides 3 linear movements. The advantage of this mechanism is that the orientation workspace separated from the position workspace. Zheng et al. (2004) presented a new kind of 6-DoF hybrid robot by serially connecting two 3-UPU spatial parallel mechanisms. Because 3-UPU parallel manipulators could offer pure translation or rotation depending on specific mounting and legs geometric conditions, it is easy to decouple the robot motion into pure translations and pure rotations. In 2015, Hu and Yu (2015) presented a method to solve inverse kinematic and dynamic problem of a novel 6-DoF hybrid manipulator constructed by one spatial UPR +RPS + UPS parallel robot and one 3-UPS/UP parallel robot. The UPR + RPS + UPS parallel robot has one transitional and two rotational DoF and the 3-UPS/UP parallel robot has one translation and two rotation DoF. In 2009, Lu et al. (2009) also presented a kinematic and workspace analysis of another 6-DoF hybrid parallel-serial robot. It has two spatial SP + SPR + SPU manipulators connected in series. Recently, in 2018, Nayak et al. (2018) developed a kinematic model of a 3-RPS-3-SPR serial-parallel mechanism. It is constructed by one proximal 3-RPS parallel mechanism and on distal 3-SPR parallel mechanism. In this study, the proposed hybrid 6-DoF parallel robot is constructed by a 3-DoF planar parallel robot and a 3-DoF spatial parallel robot. The planar manipulator provides two linear and one rotation motions (x, y and yaw) and the spatial manipulator provides one linear and two rotation motions (z, roll and pitch).
A 3-DoF planar manipulator consists of a moving platform connected to a fixed base by three identical limbs. There are several different serial chain architectures that categorized it into seven different sub-types, namely, RRR, RPR, PRR, RRP, RPP, PRP and PPR (excluding PPP) by Merlet (1999). And many other configurations have been introduced and studied. Arakelian et al. (2011) introduced a novel 3-DoF planar parallel manipulator with larger rotation capability. Zarkandi (2011) proposed a novel planar Star Triangle (ST) parallel manipulator with two platforms, one fixed Triangle platform and one Star mobile platform. They are connected via three legs that are made of PRP joints. Seo et al. (2009) designed a new planar 3-DoF parallel mechanism with continuous 360 rotational capability. This robot has two circle platforms, one fixed circular guide and one circular mobile platform, connected by three PPR legs.
Similar to the 3-DoF planar, a 3-DoF spatial manipulator is composed of a moving platform connected to a fixed base by three identical limbs. They may provide only pure relative rotations of the moving platform about a fixed point, pure relative translations of the moving platform and the base or two translations and one rotation (2T1R). For instance, Carretero et al. (2000) developed a 3-DoF parallel manipulator based on the 3-PRS architecture but his proposed mechanism has three active prismatic joints lie on a common plane. Xie et al. (2012) proposed a decoupled 3-DoF parallel mechanism for tool head. The advantage of this mechanism is that it has no parasitic motion between the moving platform and the base. Li et al. (2016) introduced an over-constrained 3-DoF parallel manipulator with 2-RPU & SPR type. The base platform is connected to the moving platform by two identical RPU limbs and one SPR limb. Recently, in 2018, Zhang et al. (2018) introduced a novel 3-DOF 2R1T parallel manipulator with two UPU and one SP identical chains structure for machining applications.
The objective of the present study is to propose a manipulator dedicated to bone reduction surgery, based on a new mechanical architecture. Indeed, all the systems quoted above use very standard architecture (hexapod, Stäubli, etc.) which may not be fully optimized for the application. A new mechanical architecture is defined based on the kinematic associated with bone reduction surgery. The system will be dedicated to reduction of broken femurs, which is the most exposed bone to fracture incidences. The robotic system is combined with a software dedicated to pre-operative bone reduction planning that has been programmed locally. The present work is organized as followed: the next Section will introduce the new mechanical architecture for the manipulation of bone fragments, including kinematic studies and singularities. In the third Section, a workspace comparison with a standard mechanism for bone reduction is provided. The fourth Section describes the bone reduction surgery procedure that involved a medical simulation software and the mechanism. The results of a simulation using the proposed mechanism on that procedure based on the case of a real patient's broken femur is shown. The conclusion of the present study is provided in Sect 5.
2 Design of the Bone Reduction Mechanism
A mechanism based on a hybrid mechanical architecture has been defined to perform motion required to manipulate the bone fragments in the reduction surgery. Its kinematic and velocity models are provided in this Section and its singular configuration are identified.
## 2.1 Mechanical Architecture Concept
External ring fixators are widely used in orthopedics for fracture fixation, bone lengthening, and deformation correction purposes. The clinician typically brings the bone fragments to an anatomically desired position by changing the length of the rods connecting the fixator rings. This task is accomplished by the clinician based on the experience and expertise. As an alternative, the commercial system exists where the same task is automated with the help of an accompanying software that is implemented with the mathematical model of the fixator. The Stewart platform was selected considering its analogy with widely used Ilizarov's external fixation device. The Stewart platform has several advantageous characteristics to act as a robotic fracture reducer, including high stiffness and precision, acceptable repeatability, 6 DoF (3 angular and 3 linear) and high load to weight ratio. But the workspace of this architecture appears to be limited. Indeed, the range of angular motion rapidly decreases as soon as the end effector moves away from the workspace center. Also, the possibility of rotating the bone around its longitudinal axis is very limited, while it is an important feature for bone reduction in order to guaranty the surface correspondence of bone fragments. It is proposed to use a double triangle planar parallel manipulator with an equilateral triangular fixed and moving platforms respectively fixed to the proximal and distal fragments of the fracture bone, using pins or wires. This double triangle structure is composed of one 3 DoF parallel manipulator using 3 Revolute–Prismatic–Spherical (RPS) introduced by Hunt (1983) and one Triangular planar parallel robot using 3 PRP arms suggested by Daniali et al. (1993). The concept of this novel robot is shown in Fig. 4. The arms of the 3-RPS mechanism consist in connecting the base by the first joint (R) to the moving platform by the last joint (S-joint). The planar manipulator is a special symmetrical closed-loop mechanism that is composed of a pair of triangles: one base and one platform. The platform triangle is placed on the top of the base triangle and is moved by 3 PRP arms fixed to the edges. The first prismatic joint of each arm allows them to slide along each edge of the base triangle. A planar parallel mechanism has the specific performance, whereas the links are moving in the planar motions. The RPS manipulator has 2 of orientation freedom and one degree of translation freedom. One advantage of the present architecture compared to the Stewart mechanism is that the double triangular structure can provide a much larger range of longitudinal rotation of the bone fragment for most angular position of the end effector given by the tripod mechanism.
Figure 3Schematic of the basic concept and kinematic representation of the mechanical architecture.
Figure 4Schematic of the basic concept and kinematic representation of the mechanical architecture.
## 2.2 Kinematic Analysis of the Mechanism
In order to determine the kinematic model of the present mechanism, several reference frames are attached with different items of the mechanism. The reference frame $\mathit{\left\{}O,\mathbit{x},\mathbit{y},\mathbit{z}\mathit{\right\}}$ is attached with the fixed base A with O, the center of the equilateral triangle A1A2A3 that orthogonal to the z-axis. The frames $\mathit{\left\{}{O}_{\mathrm{1}},{\mathbit{x}}_{\mathrm{1}},{\mathbit{y}}_{\mathrm{1}},{\mathbit{z}}_{\mathrm{1}}\mathit{\right\}}$ and $\mathit{\left\{}{O}_{\mathrm{2}},{\mathbit{x}}_{\mathrm{2}},{\mathbit{y}}_{\mathrm{2}},{\mathbit{z}}_{\mathrm{2}}\mathit{\right\}}$ are respectively attached with the moving platforms B and C. They are represented by the equilateral triangles B1B2B3 and C1C2C3 and they are respectively orthogonal to axis z1 and z2. The moving platform B is connected with the spatial 3-RPS parallel mechanism by three passive spherical joints located at the triangle corners B1, B2, and B3. The fixed base has three passive revolute joints at the corners of the equilateral triangle A1A2A3. The moving platform B is put in motion in the reference frame $\mathit{\left\{}O,\mathbit{x},\mathbit{y},\mathbit{z}\mathit{\right\}}$ by the mean of three active prismatic joints, each located between the revolute and spherical joints of each RPS linkage.
It is assumed that the mechanism end-effector is located by the point O2 of the moving platform C. Its linear position in the coordinate system $\mathit{\left\{}O,\mathbit{x},\mathbit{y},\mathbit{z}\mathit{\right\}}$ is described by x, y and z variables. The orientation of the end-effector is given by the three angles α, β and γ. The general coordinates of the ith joints are given by the length qi ($i=\mathrm{1},\mathrm{\dots },\mathrm{6}$).
The position of the revolute joints A1, A2 and A3 in $\mathit{\left\{}O,\mathbit{x},\mathbit{y},\mathbit{z}\mathit{\right\}}$ are given by the vectors below:
$\begin{array}{}\text{(1)}& \begin{array}{rl}& \mathbit{O}{\mathbit{A}}_{\mathrm{1}}=\left[\begin{array}{l}\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{r}_{a}\\ -\frac{\mathrm{1}}{\mathrm{2}}{r}_{a}\\ \mathrm{0}\end{array}\right],\phantom{\rule{0.125em}{0ex}}\phantom{\rule{0.125em}{0ex}}\mathbit{O}{\mathbit{A}}_{\mathrm{2}}=\left[\begin{array}{l}\mathrm{0}\\ {r}_{a}\\ \mathrm{0}\end{array}\right],\\ & \mathbit{O}{\mathbit{A}}_{\mathrm{3}}=\left[\begin{array}{l}-\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{r}_{a}\\ -\frac{\mathrm{1}}{\mathrm{2}}{r}_{a}\\ \mathrm{0}\end{array}\right]\end{array}\end{array}$
With ra, the radius of the circumcircle of center O passing by A1, A2, and A3. The position of the spherical joints in the coordinate system $\mathit{\left\{}{O}_{\mathrm{1}},{\mathbit{x}}_{\mathrm{1}},{\mathbit{y}}_{\mathrm{1}},{\mathbit{z}}_{\mathrm{1}}\mathit{\right\}}$ of the moving platform B are written as below:
$\begin{array}{}\text{(2)}& \begin{array}{rl}& {\mathbit{O}}_{\mathrm{1}}{\mathbit{B}}_{\mathrm{1}}=\left[\begin{array}{l}\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{r}_{b}\\ -\frac{\mathrm{1}}{\mathrm{2}}{r}_{b}\\ \mathrm{0}\end{array}\right],\phantom{\rule{0.125em}{0ex}}\phantom{\rule{0.125em}{0ex}}{\mathbit{O}}_{\mathrm{1}}{\mathbit{B}}_{\mathrm{2}}=\left[\begin{array}{l}\mathrm{0}\\ {r}_{b}\\ \mathrm{0}\end{array}\right],\\ & {\mathbit{O}}_{\mathrm{1}}{\mathbit{B}}_{\mathrm{3}}=\left[\begin{array}{l}-\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{r}_{b}\\ -\frac{\mathrm{1}}{\mathrm{2}}{r}_{b}\\ \mathrm{0}\end{array}\right]\end{array}\end{array}$
With rb, the radius of the circumcircle of center O1 passing by B1, B2, and B3.
And the corners C1, C2, and C3 of the moving platform C in $\mathit{\left\{}{O}_{\mathrm{2}},{\mathbit{x}}_{\mathrm{2}},{\mathbit{y}}_{\mathrm{2}},{\mathbit{z}}_{\mathrm{2}}\mathit{\right\}}$ are located as followed:
$\begin{array}{}\text{(3)}& \begin{array}{rl}& {\mathbit{O}}_{\mathrm{2}}{\mathbit{C}}_{\mathrm{1}}=\left[\begin{array}{l}\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{r}_{b}\\ \frac{\mathrm{1}}{\mathrm{2}}{r}_{b}\\ \mathrm{0}\end{array}\right],\phantom{\rule{0.125em}{0ex}}\phantom{\rule{0.125em}{0ex}}{\mathbit{O}}_{\mathrm{2}}{\mathbit{C}}_{\mathrm{2}}=\left[\begin{array}{l}-\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{r}_{b}\\ \frac{\mathrm{1}}{\mathrm{2}}{r}_{b}\\ \mathrm{0}\end{array}\right],\\ & {\mathbit{O}}_{\mathrm{2}}{\mathbit{C}}_{\mathrm{3}}=\left[-\begin{array}{l}\mathrm{0}\\ {r}_{b}\\ \mathrm{0}\end{array}\right]\end{array}\end{array}$
The position of spherical joints Bk ($k=\mathrm{1},\mathrm{2},\mathrm{3}$) given in $\mathit{\left\{}{O}_{\mathrm{1}},{\mathbit{x}}_{\mathrm{1}},{\mathbit{y}}_{\mathrm{1}},{\mathbit{z}}_{\mathrm{1}}\mathit{\right\}}$ in Eq. (2) can be expressed in $\mathit{\left\{}O,\mathbit{x},\mathbit{y},\mathbit{z}\mathit{\right\}}$ as followed:
$\begin{array}{}\text{(4)}& \mathbit{O}{\mathbit{B}}_{k}=\mathbit{O}{\mathbit{A}}_{k}+{\mathbit{A}}_{k}{\mathbit{B}}_{k}=\mathbit{O}{\mathbit{A}}_{k}+{q}_{k}\cdot {\mathbit{s}}_{k\mathrm{3}}\text{(5)}& \mathbit{O}{\mathbit{B}}_{k}=\mathbit{O}{\mathbit{O}}_{\mathrm{1}}+\mathbf{R}{\mathbit{O}}_{\mathrm{1}}{\mathbit{B}}_{k}\end{array}$
Where qk (with $k=\mathrm{1},\mathrm{2},\mathrm{3}$) is the prismatic joint variable directed by the vector sk3 as seen in Fig. 3. And where OO1 gives the coordinates [x1 y1 z1] of the center of the moving platform B, expressed in $\mathit{\left\{}O,\mathbit{x},\mathbit{y},\mathbit{z}\mathit{\right\}}$ and R is the orientation matrix of frame $\mathit{\left\{}{O}_{\mathrm{1}},{\mathbit{x}}_{\mathrm{1}},{\mathbit{y}}_{\mathrm{1}},{\mathbit{z}}_{\mathrm{1}}\mathit{\right\}}$ with respect to $\mathit{\left\{}O,\mathbit{x},\mathbit{y},\mathbit{z}\mathit{\right\}}$ with α, β, and φ being the Roll-Pitch-Yaw and written as:
$\begin{array}{}\text{(6)}& \mathbf{R}=\left[\begin{array}{ccc}c\mathit{\beta }\cdot c\mathit{\phi }& s\mathit{\alpha }\cdot s\mathit{\beta }\cdot c\mathit{\phi }-c\mathit{\alpha }\cdot s\mathit{\phi }& c\mathit{\alpha }\cdot s\mathit{\beta }\cdot c\mathit{\phi }+s\mathit{\alpha }\cdot s\mathit{\phi }\\ c\mathit{\beta }\cdot s\mathit{\phi }& s\mathit{\alpha }\cdot s\mathit{\beta }\cdot s\mathit{\phi }+c\mathit{\alpha }\cdot c\mathit{\phi }& c\mathit{\alpha }\cdot s\mathit{\beta }\cdot s\mathit{\phi }-s\mathit{\alpha }\cdot c\mathit{\phi }\\ -s\mathit{\beta }& s\mathit{\alpha }\cdot c\mathit{\beta }& c\mathit{\alpha }\cdot c\mathit{\beta }\end{array}\right],\end{array}$
Where c and s correspond to cos (∗) and sin (∗), respectively.
Similarly, the original position of the center of the moving platform C in the frame $\mathit{\left\{}{O}_{\mathrm{1}},{\mathbit{x}}_{\mathrm{1}},{\mathbit{y}}_{\mathrm{1}},{\mathbit{z}}_{\mathrm{1}}\mathit{\right\}}$ is given by:
$\begin{array}{}\text{(7)}& {\mathbit{O}}_{\mathrm{1}}{\mathbit{O}}_{\mathrm{2}}=\left[\begin{array}{l}{\mathbit{x}}_{\mathrm{2}}\\ {\mathbit{y}}_{\mathrm{2}}\\ d\end{array}\right],\end{array}$
With d, the distance between the moving platform B and the moving platform C.
The 3-RPS parallel mechanism is one of the lower-mobility parallel mechanism which has an important kinematic feature is parasitic motion (Carretero et al., 2000; Li et al., 2011). The 3-RPS parallel mechanism generates three parasitic motions: two translations along axis x, y and one rotation about the z-axis with respect to the fixed frame. In other words, the moving platform B has a small parasitic motion of the fixed base (x1, y1, φ). These unwanted parasitic translations (x1, y1) are compensated by the linear motion of the 2nd moving platform.
Hence, the position vector of the end effector O2 expressed in the fixed frame $\mathit{\left\{}O,\mathbit{x},\mathbit{y},\mathbit{z}\mathit{\right\}}$ is given by:
$\begin{array}{}\text{(8)}& \mathbit{O}{\mathbit{O}}_{\mathrm{2}}=\mathbit{O}{\mathbit{O}}_{\mathrm{1}}+\mathbf{R}{\mathbit{O}}_{\mathrm{1}}{\mathbit{O}}_{\mathrm{2}}.\end{array}$
Considering the constraints applied by the revolute joints at points A1, A2 and A3, the parasitic motions of the moving platform B are calculated.
$\begin{array}{}\text{(9)}& \mathbit{O}{\mathbit{B}}_{k}{\mathbit{s}}_{k\mathrm{2}}=\mathrm{0},\end{array}$
Where sk2 (with k=1, 2, 3) gives the direction of the axis of rotation for the angle θk as seen in Fig. 3. From Eq. (9), it can be found that:
$\begin{array}{}\text{(10)}& \mathit{\phi }=\mathrm{atan}\left(\frac{s\mathit{\alpha }s\mathit{\beta }}{c\mathit{\alpha }+c\mathit{\beta }}\right),\text{(11)}& {x}_{\mathrm{1}}=-{r}_{b}c\mathit{\beta }s\mathit{\phi },\text{(12)}& {y}_{\mathrm{1}}=\frac{\mathrm{1}}{\mathrm{2}}{r}_{b}\left(c\mathit{\alpha }c\mathit{\phi }+s\mathit{\alpha }s\mathit{\beta }s\mathit{\phi }-\phantom{\rule{0.125em}{0ex}}c\mathit{\beta }c\mathit{\phi }\right).\end{array}$
The actuating lengths of the links for a prescribed position and orientation of the moving platform B are obtained by taking the Euclidean norm of the Eq. (4) as bellow:
$\begin{array}{}\text{(13)}& \begin{array}{rl}{q}_{k}^{\mathrm{2}}=\phantom{\rule{0.125em}{0ex}}{∥{\mathbit{A}}_{k}{\mathbit{B}}_{k}∥}^{\mathrm{2}}& ={\left(\mathbit{O}{\mathbit{O}}_{\mathrm{1}}+\mathbf{R}\cdot {\mathbit{O}}_{\mathrm{1}}{\mathbit{B}}_{k}-\mathbit{O}{\mathbit{A}}_{k}\right)}^{T}\\ & \cdot \left(\mathbit{O}{\mathbit{O}}_{\mathrm{1}}+\mathbf{R}.{\mathbit{O}}_{\mathrm{1}}{\mathbit{B}}_{k}-\phantom{\rule{0.125em}{0ex}}\mathbit{O}{\mathbit{A}}_{k}\right).\end{array}\end{array}$
By solving the Eqs. (4) and (5), the rotation angle θ1, θ2 and θ3 of the kth legs can be written as:
$\begin{array}{}\text{(14)}& {\mathit{\theta }}_{\mathrm{1}}=\mathrm{atan}\mathrm{2}\left(\frac{{z}_{{B}_{\mathrm{1}}}}{\left|{A}_{\mathrm{1}}{B}_{\mathrm{1}}\right|},\phantom{\rule{0.125em}{0ex}}\frac{{r}_{a}+\mathrm{2}{y}_{{B}_{\mathrm{1}}}}{\left|{A}_{\mathrm{1}}{B}_{\mathrm{1}}\right|}\right),\text{(15)}& {\mathit{\theta }}_{\mathrm{2}}=\mathrm{atan}\mathrm{2}\left(\frac{{z}_{{B}_{\mathrm{2}}}}{\left|{A}_{\mathrm{2}}{B}_{\mathrm{2}}\right|},\phantom{\rule{0.125em}{0ex}}\frac{{r}_{a}-{y}_{{B}_{\mathrm{2}}}}{\left|{A}_{\mathrm{2}}{B}_{\mathrm{2}}\right|}\right),\text{(16)}& {\mathit{\theta }}_{\mathrm{3}}=\mathrm{atan}\mathrm{2}\left(\frac{{z}_{{B}_{\mathrm{3}}}}{\left|{A}_{\mathrm{3}}{B}_{\mathrm{3}}\right|},\phantom{\rule{0.125em}{0ex}}\frac{\mathrm{2}\left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{r}_{a}+{x}_{{B}_{\mathrm{3}}}\right)}{\sqrt{\mathrm{3}}\left|{A}_{\mathrm{3}}{B}_{\mathrm{3}}\right|}\right).\end{array}$
The position vector of the active prismatic joints R1, R2, and R3 expressed in frame $\mathit{\left\{}{O}_{\mathrm{1}},{\mathbit{x}}_{\mathrm{1}},{\mathbit{y}}_{\mathrm{1}},{\mathbit{z}}_{\mathrm{1}}\mathit{\right\}}$.
$\begin{array}{}\text{(17)}& \begin{array}{rl}& {\mathbit{O}}_{\mathrm{1}}{\mathbit{R}}_{\mathrm{1}}=\left[\begin{array}{l}\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{r}_{b}-\frac{\mathrm{1}}{\mathrm{2}}{q}_{\mathrm{4}}\\ \frac{\mathrm{1}}{\mathrm{2}}{r}_{b}+\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{q}_{\mathrm{4}}\\ \mathrm{0}\end{array}\right],\phantom{\rule{0.125em}{0ex}}\phantom{\rule{0.125em}{0ex}}{\mathbit{O}}_{\mathrm{1}}{\mathbit{R}}_{\mathrm{2}}=\left[\begin{array}{l}-\frac{\mathrm{1}}{\mathrm{2}}{q}_{\mathrm{5}}\\ {r}_{b}-\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{q}_{\mathrm{5}}\\ \mathrm{0}\end{array}\right],\\ & {\mathbit{O}}_{\mathrm{1}}{\mathbit{R}}_{\mathrm{3}}=\left[\begin{array}{l}-\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{r}_{b}+{q}_{\mathrm{6}}\\ -\frac{\mathrm{1}}{\mathrm{2}}{r}_{b}\\ \mathrm{0}\end{array}\right].\end{array}\end{array}$
And assuming ${l}_{k}\left(k=\mathrm{1},\mathrm{2},\mathrm{3}\right)$, the distance between the corner Ck moving platform C and the closest passive prismatic joint ${R}_{k}^{\prime }$, namely ${C}_{\mathrm{1}}{R}_{\mathrm{1}}^{\prime }$, ${C}_{\mathrm{2}}{R}_{\mathrm{2}}^{\prime }$ and ${C}_{\mathrm{3}}{R}_{\mathrm{3}}^{\prime }$ respectively, the position of ${R}_{k}^{\prime }$ expressed relative to O2:
$\begin{array}{}\text{(18)}& \begin{array}{rl}& {\mathbit{O}}_{\mathrm{2}}{\mathbit{R}}_{\mathrm{1}}^{\prime }=\left[\begin{array}{l}\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{r}_{b}-{l}_{\mathrm{1}}\\ \frac{\mathrm{1}}{\mathrm{2}}{r}_{b}\\ \mathrm{0}\end{array}\right],\phantom{\rule{0.125em}{0ex}}\phantom{\rule{0.125em}{0ex}}{\mathbit{O}}_{\mathrm{2}}{{\mathbit{R}}^{\prime }}_{\mathrm{2}}=\left[\begin{array}{l}-\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{r}_{b}+\frac{\mathrm{1}}{\mathrm{2}}{l}_{\mathrm{2}}\\ \frac{\mathrm{1}}{\mathrm{2}}{r}_{b}-\phantom{\rule{0.125em}{0ex}}\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{l}_{\mathrm{2}}\\ \mathrm{0}\end{array}\right],\\ & {\mathbit{O}}_{\mathrm{2}}{{\mathbit{R}}^{\prime }}_{\mathrm{3}}=\left[\begin{array}{l}\frac{\mathrm{1}}{\mathrm{2}}{l}_{\mathrm{3}}\\ \frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{l}_{\mathrm{3}}-{r}_{b}\\ \mathrm{0}\end{array}\right].\end{array}\end{array}$
In the frame $\mathit{\left\{}{O}_{\mathrm{1}},{\mathbit{x}}_{\mathrm{1}},{\mathbit{y}}_{\mathrm{1}},{\mathbit{z}}_{\mathrm{1}}\mathit{\right\}}$, the position the passive prismatic joints ${R}_{i}^{\prime }$ are calculated as followed:
$\begin{array}{}\text{(19)}& {\mathbit{O}}_{\mathrm{1}}{{\mathbit{R}}^{\prime }}_{k}={\mathbit{O}}_{\mathrm{1}}{\mathbit{O}}_{\mathrm{2}}+{\mathbf{R}}_{z}\left(\mathit{\gamma }\right)\cdot {\mathbit{O}}_{\mathrm{2}}{{\mathbit{R}}^{\prime }}_{k},\end{array}$
Where γ is the rotation angle of the moving platform C around z1-axis and Rz(γ) is the rotation matrix around z1-axis of angle γ.
The coordinate constraints of the revolute joints between two prismatic joints Rk and ${R}_{k}^{\prime }$ can be defined as followed:
$\begin{array}{}\text{(20)}& {\mathbit{O}}_{\mathrm{1}}{\mathbit{R}}_{k}-{\mathbit{O}}_{\mathrm{1}}{{\mathbit{R}}^{\prime }}_{k}=\left[\mathrm{0}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\mathrm{0}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}d{\right]}^{T}.\end{array}$
By solving Eq. (20), the length of the active prismatic joints q4, q5, q6 are determined as followed:
$\begin{array}{}\text{(21)}& {q}_{\mathrm{4}}=\phantom{\rule{0.125em}{0ex}}\frac{{r}_{b}+\left(\sqrt{\mathrm{3}}{r}_{b}-\mathrm{2}{x}_{\mathrm{2}}\right)s\mathit{\gamma }+\left({r}_{b}+\mathrm{2}{y}_{\mathrm{2}}\right)c\mathit{\gamma }}{s\mathit{\gamma }+\sqrt{\mathrm{3}}c\mathit{\gamma }},\text{(22)}& {q}_{\mathrm{5}}=\phantom{\rule{0.125em}{0ex}}\frac{\begin{array}{c}{r}_{b}+\left(\sqrt{\mathrm{3}}{r}_{b}+{x}_{\mathrm{2}}-\sqrt{\mathrm{3}}{y}_{\mathrm{2}}\right)s\mathit{\gamma }\\ +\left({r}_{b}-\sqrt{\mathrm{3}}{x}_{\mathrm{2}}-{y}_{\mathrm{2}}\right)c\mathit{\gamma }\end{array}}{s\mathit{\gamma }+\sqrt{\mathrm{3}}c\mathit{\gamma }},\text{(23)}& {q}_{\mathrm{6}}=\phantom{\rule{0.125em}{0ex}}\frac{\begin{array}{c}{r}_{b}+\left(\sqrt{\mathrm{3}}{r}_{b}+{x}_{\mathrm{2}}+\sqrt{\mathrm{3}}{y}_{\mathrm{2}}\right)s\mathit{\gamma }\\ +\left({r}_{b}+\sqrt{\mathrm{3}}{x}_{\mathrm{2}}-{y}_{\mathrm{2}}\right)c\mathit{\gamma }\end{array}}{s\mathit{\gamma }+\sqrt{\mathrm{3}}c\mathit{\gamma }}.\end{array}$
## 2.3 Velocity Model and Singular Configurations of the Mechanism
In order to identify the mechanism singular configurations that could result trajectory problems, its velocity model is studied to isolate the Jacobian matrices. The velocity model of the mechanical architecture can be obtained by differentiating Eq. (8) with respect to time. In order to simplify the calculation, it is possible to separate this mechanism architecture into two parallel mechanisms: one is the velocity model of the 3-RPS parallel mechanism and another is the velocity model of the 3-PRP parallel mechanism. The velocity model of the 3-RPS mechanical architecture is calculated by reformulating Eq. (4) as followed:
$\begin{array}{}\text{(24)}& {q}_{k}{\mathbit{s}}_{k\mathrm{3}}=\mathbit{O}{\mathbit{B}}_{k}-\mathbit{O}{\mathbit{A}}_{k},\end{array}$
Where sk3 is the unit vector directing the three legs qk (Fig. 3). Equation (5) is then substituted and differentiated to obtain:
$\begin{array}{}\text{(25)}& \stackrel{\mathrm{˙}}{{q}_{k}}{\mathbit{s}}_{k\mathrm{3}}+{q}_{k}\left[{\mathbit{\vartheta }}_{k}×{\mathbit{s}}_{k\mathrm{3}}\right]={\stackrel{\mathrm{˙}}{\mathbit{O}\mathbit{O}}}_{\mathrm{1}}+\mathbit{\omega }{×}^{O}{\mathbit{O}}_{\mathrm{1}}{\mathbit{B}}_{k}\end{array}$
Where ϑk is the angular velocity of leg kth and ω is the angular velocity of the moving platform B expressed in the fixed platform. This yields:
$\begin{array}{}\text{(26)}& \stackrel{\mathrm{˙}}{{q}_{k}}={\mathbit{s}}_{k\mathrm{3}}{\stackrel{\mathrm{˙}}{\mathbit{O}\mathbit{O}}}_{\mathrm{1}}+\left({}^{O}{\mathbit{O}}_{\mathrm{1}}{\mathbit{B}}_{k}×{\mathbit{s}}_{k\mathrm{3}}\right)\mathbit{\omega }\end{array}$
The parasitic motion given in Eqs. (10) to (12) is differentiated with respect to time to obtain:
$\begin{array}{}\text{(27)}& \stackrel{\mathrm{˙}}{\mathit{\phi }}=\frac{s\mathit{\beta }}{\mathrm{1}+c\mathit{\alpha }c\mathit{\beta }}\stackrel{\mathrm{˙}}{\mathit{\alpha }}+\phantom{\rule{0.125em}{0ex}}\frac{s\mathit{\alpha }}{\mathrm{1}+c\mathit{\alpha }c\mathit{\beta }}\stackrel{\mathrm{˙}}{\mathit{\beta }}\text{(28)}& {\stackrel{\mathrm{˙}}{x}}_{\mathrm{1}}=\phantom{\rule{0.125em}{0ex}}-\frac{c\mathit{\beta }s\mathit{\beta }c\mathit{\phi }}{\mathrm{1}+c\mathit{\alpha }c\mathit{\beta }}\stackrel{\mathrm{˙}}{\mathit{\alpha }}+\phantom{\rule{0.125em}{0ex}}{r}_{b}\left(s\mathit{\beta }s\mathit{\phi }-\frac{s\mathit{\alpha }c\mathit{\beta }c\mathit{\phi }}{\mathrm{1}+c\mathit{\alpha }c\mathit{\beta }}\right)\stackrel{\mathrm{˙}}{\mathit{\beta }}\text{(29)}& \begin{array}{rl}{\stackrel{\mathrm{˙}}{y}}_{\mathrm{1}}& =\phantom{\rule{0.125em}{0ex}}\frac{\mathrm{1}}{\mathrm{2}}{r}_{b}\left(c\mathit{\alpha }s\mathit{\beta }s\mathit{\phi }-s\mathit{\alpha }c\mathit{\phi }+s\mathit{\beta }K\right)\stackrel{\mathrm{˙}}{\mathit{\alpha }}\\ & +\phantom{\rule{0.125em}{0ex}}\frac{\mathrm{1}}{\mathrm{2}}{r}_{b}\left(s\mathit{\alpha }c\mathit{\beta }s\mathit{\phi }+s\mathit{\beta }c\mathit{\phi }+s\mathit{\alpha }\cdot K\right)\stackrel{\mathrm{˙}}{\mathit{\beta }}\end{array}\end{array}$
Where $K=\frac{s\mathit{\alpha }s\mathit{\beta }c\mathit{\phi }-c\mathit{\alpha }s\mathit{\phi }+c\mathit{\beta }s\mathit{\phi }}{\mathrm{1}+c\mathit{\alpha }c\mathit{\beta }}$.
By setting up Eqs. (26) to (29):
$\begin{array}{}\text{(30)}& {\mathbf{J}}_{A}\left[\begin{array}{l}{\stackrel{\mathrm{˙}}{q}}_{\mathrm{1}}\\ {\stackrel{\mathrm{˙}}{q}}_{\mathrm{2}}\\ {\stackrel{\mathrm{˙}}{q}}_{\mathrm{3}}\end{array}\right]={\mathbf{J}}_{{B}_{\mathrm{1}}}{\mathbf{J}}_{{B}_{\mathrm{2}}}\left[\begin{array}{l}{\stackrel{\mathrm{˙}}{z}}_{\mathrm{1}}\\ \stackrel{\mathrm{˙}}{\mathit{\alpha }}\\ \stackrel{\mathrm{˙}}{\mathit{\beta }}\end{array}\right]={\mathbf{J}}_{B}\left[\begin{array}{l}{\stackrel{\mathrm{˙}}{z}}_{\mathrm{1}}\\ \stackrel{\mathrm{˙}}{\mathit{\alpha }}\\ \stackrel{\mathrm{˙}}{\mathit{\beta }}\end{array}\right]\end{array}$
Where
$\begin{array}{}\text{(31)}& {\mathbf{J}}_{A}=\left[\begin{array}{lll}\mathrm{1}& \mathrm{0}& \mathrm{0}\\ \mathrm{0}& \mathrm{1}& \mathrm{0}\\ \mathrm{0}& \mathrm{0}& \mathrm{1}\end{array}\right],\text{(32)}& {\mathbf{J}}_{{B}_{\mathrm{1}}}=\left[\begin{array}{ll}{\mathbit{s}}_{\mathrm{13}}^{T}& {\left(}^{O}{\mathbit{O}}_{\mathrm{1}}{\mathbit{B}}_{\mathrm{1}}×{\mathbit{s}}_{\mathrm{13}}{\right)}^{T}\\ {\mathbit{s}}_{\mathrm{23}}^{T}& {\left(}^{O}{\mathbit{O}}_{\mathrm{1}}{\mathbit{B}}_{\mathrm{2}}×{\mathbit{s}}_{\mathrm{23}}{\right)}^{T}\\ {\mathbit{s}}_{\mathrm{33}}^{T}& {\left(}^{O}{\mathbit{O}}_{\mathrm{1}}{\mathbit{B}}_{\mathrm{3}}×{\mathbit{s}}_{\mathrm{33}}{\right)}^{T}\end{array}\right]\text{(33)}& {\mathbf{J}}_{{B}_{\mathrm{2}}}=\left[\begin{array}{lll}\mathrm{0}& \frac{-c\mathit{\beta }s\mathit{\beta }c\mathit{\phi }}{\mathrm{1}+c\mathit{\alpha }c\mathit{\beta }}& {r}_{b}s\mathit{\beta }s\mathit{\phi }-\frac{{r}_{b}s\mathit{\alpha }c\mathit{\beta }c\mathit{\phi }}{\mathrm{1}+c\mathit{\alpha }c\mathit{\beta }}\\ \mathrm{0}& \frac{\mathrm{1}}{\mathrm{2}}{r}_{b}\left(c\mathit{\alpha }s\mathit{\beta }s\mathit{\phi }-s\mathit{\alpha }c\mathit{\phi }+s\mathit{\beta }\cdot K\right)& \frac{\mathrm{1}}{\mathrm{2}}{r}_{b}\left(s\mathit{\alpha }c\mathit{\beta }s\mathit{\phi }-s\mathit{\beta }c\mathit{\phi }+s\mathit{\alpha }\cdot K\right)\\ \mathrm{1}& \mathrm{0}& \mathrm{0}\\ \mathrm{0}& \mathrm{1}& \mathrm{0}\\ \mathrm{0}& \mathrm{0}& \mathrm{1}\\ \mathrm{0}& \frac{s\mathit{\beta }}{\mathrm{1}+c\mathit{\alpha }c\mathit{\beta }}& \frac{s\mathit{\alpha }}{\mathrm{1}+c\mathit{\alpha }c\mathit{\beta }}\end{array}\right]\end{array}$
The velocity model of the double triangular mechanical architecture is obtained by directly differentiating Eqs. (21) to (23) and arranging as followed:
$\begin{array}{}\text{(34)}& {\mathbf{J}}_{C}\left[\begin{array}{l}{\stackrel{\mathrm{˙}}{q}}_{\mathrm{4}}\\ {\stackrel{\mathrm{˙}}{q}}_{\mathrm{5}}\\ {\stackrel{\mathrm{˙}}{q}}_{\mathrm{6}}\end{array}\right]={\mathbf{J}}_{D}\left[\begin{array}{l}{\stackrel{\mathrm{˙}}{x}}_{\mathrm{2}}\\ {\stackrel{\mathrm{˙}}{y}}_{\mathrm{2}}\\ \stackrel{\mathrm{˙}}{\mathit{\gamma }}\end{array}\right],\end{array}$
Where
$\begin{array}{}\text{(35)}& {\mathbf{J}}_{C}=\left[\begin{array}{lll}{J}_{{C}_{\mathrm{11}}}& \mathrm{0}& \mathrm{0}\\ \mathrm{0}& {J}_{{C}_{\mathrm{22}}}& \mathrm{0}\\ \mathrm{0}& \mathrm{0}& {J}_{{C}_{\mathrm{33}}}\end{array}\right],\text{(36)}& {J}_{{C}_{\mathrm{11}}}={J}_{{C}_{\mathrm{22}}}={J}_{{C}_{\mathrm{33}}}=\phantom{\rule{0.125em}{0ex}}s\mathit{\gamma }+\sqrt{\mathrm{3}}c\mathit{\gamma },\text{(37)}& {\mathbf{J}}_{D}=\left[\begin{array}{lll}{J}_{{D}_{\mathrm{11}}}& {J}_{{D}_{\mathrm{12}}}& {J}_{{D}_{\mathrm{13}}}\\ {J}_{{D}_{\mathrm{21}}}& {J}_{{D}_{\mathrm{22}}}& {J}_{{D}_{\mathrm{23}}}\\ {J}_{{D}_{\mathrm{31}}}& {J}_{{D}_{\mathrm{32}}}& {J}_{{D}_{\mathrm{33}}}\end{array}\right],\text{(38)}& {J}_{{D}_{\mathrm{11}}}=-\mathrm{2}s\mathit{\gamma }\text{(39)}& {J}_{{D}_{\mathrm{12}}}=\mathrm{2}c\mathit{\gamma }\text{(40)}& \begin{array}{rl}{J}_{{D}_{\mathrm{13}}}& =\left(\sqrt{\mathrm{3}}{r}_{b}-\mathrm{2}{x}_{\mathrm{2}}\right)c\mathit{\gamma }-\left({r}_{b}+\mathrm{2}{y}_{\mathrm{2}}\right)s\mathit{\gamma }\\ & -{q}_{\mathrm{4}}\left(c\mathit{\gamma }-\sqrt{\mathrm{3}}s\mathit{\gamma }\right)\end{array}\text{(41)}& {J}_{{D}_{\mathrm{21}}}=\phantom{\rule{0.125em}{0ex}}s\mathit{\gamma }-\sqrt{\mathrm{3}}c\mathit{\gamma }\text{(42)}& {J}_{{D}_{\mathrm{22}}}=\phantom{\rule{0.125em}{0ex}}-c\mathit{\gamma }-\sqrt{\mathrm{3}}s\mathit{\gamma }\text{(43)}& \begin{array}{rl}{J}_{{D}_{\mathrm{23}}}& =\left(\sqrt{\mathrm{3}}{r}_{b}+{x}_{\mathrm{2}}-\sqrt{\mathrm{3}}{y}_{\mathrm{2}}\right)c\mathit{\gamma }-\left({r}_{b}-\sqrt{\mathrm{3}}{x}_{\mathrm{2}}-{y}_{\mathrm{2}}\right)s\mathit{\gamma }\\ & -{q}_{\mathrm{5}}\left(c\mathit{\gamma }-\sqrt{\mathrm{3}}s\mathit{\gamma }\right)\end{array}\text{(44)}& {J}_{{D}_{\mathrm{31}}}=\phantom{\rule{0.125em}{0ex}}s\mathit{\gamma }+\sqrt{\mathrm{3}}c\mathit{\gamma }\text{(45)}& {J}_{{D}_{\mathrm{32}}}=\phantom{\rule{0.125em}{0ex}}-c\mathit{\gamma }+\sqrt{\mathrm{3}}s\mathit{\gamma }\text{(46)}& \begin{array}{rl}{J}_{{D}_{\mathrm{33}}}& =\left(\sqrt{\mathrm{3}}{r}_{b}+{x}_{\mathrm{2}}+\sqrt{\mathrm{3}}{y}_{\mathrm{2}}\right)c\mathit{\gamma }-\left({r}_{b}+\sqrt{\mathrm{3}}{x}_{\mathrm{2}}-{y}_{\mathrm{2}}\right)s\mathit{\gamma }\\ & -{q}_{\mathrm{6}}\left(c\mathit{\gamma }-\sqrt{\mathrm{3}}s\mathit{\gamma }\right)\end{array}\end{array}$
For the RPS tripod mechanism, the forward singular configuration is determined by using the Jacobean matric JB to solve the following equation:
$\begin{array}{}\text{(47)}& \mathrm{det}\left({\mathbf{J}}_{B}\right)=\mathrm{0}.\end{array}$
In this specific application, the singularity loci happened in the range of workspace will be considered. Figure 5 shows the singularity distribution of RPS mechanism in range of workspace −20<α< 20, −20<β< 20. According to the present simulations, there is a risk for the tripod mechanism to reach a singularity when the z coordinate goes from 0 to 111.8 mm. Several points in Fig. 5 are selected as examples to present the singularity configurations in Fig. 6. These configurations are similar to RO-type singularity that classified in Zlatanov et al. (2002) and Li et al. (2015).
Figure 5Singularity distribution of RPS mechanism in range of workspace −20<α< 20, −20<β< 20.
Figure 6Three examples of singular configurations for the 3-RPS mechanism.
For the double triangular mechanism, the inverse singularity is identified by using the Jacobian matric JC to solve the following equation:
$\begin{array}{}\text{(48)}& \mathrm{det}\left({\mathbf{J}}_{c}\right)=\left(s\mathit{\gamma }+\sqrt{\mathrm{3}}c\mathit{\gamma }{\right)}^{\mathrm{3}}=\mathrm{0}.\end{array}$
By solving this equation, the first singularity condition will be:
$\begin{array}{}\text{(49)}& \left\{\begin{array}{l}\mathit{\gamma }=\frac{\mathrm{2}\mathit{\pi }}{\mathrm{3}}+k\mathrm{2}\mathit{\pi }\\ \mathit{\gamma }=-\frac{\mathit{\pi }}{\mathrm{3}}+k\mathrm{2}\mathit{\pi }\end{array}\right\.\end{array}$
In this configuration, the moving platform B of the double triangular mechanism will be at the same position as moving platform A. The forward singularity is found by using the same method with the Jacobian matrix JD. This yields the following equation:
$\begin{array}{}\text{(50)}& \mathrm{det}\left({\mathbf{J}}_{D}\right)=\mathrm{2}\sqrt{\mathrm{3}}\left({J}_{{D}_{\mathrm{13}}}+{J}_{{D}_{\mathrm{23}}}+{J}_{{D}_{\mathrm{33}}}\right)=\mathrm{0},\text{(51)}& \begin{array}{rl}\mathrm{det}\left({\mathbf{J}}_{D}\right)& =\mathrm{3}{r}_{b}\left(\sqrt{\mathrm{3}}c\mathit{\gamma }-s\mathit{\gamma }\right)-\left({q}_{\mathrm{4}}+{q}_{\mathrm{5}}+{q}_{\mathrm{6}}\right)\\ & \cdot \left(c\mathit{\gamma }-\sqrt{\mathrm{3}}s\mathit{\gamma }\right).\end{array}\end{array}$
By substituting Eqs. (21) to (23) into Eq. (51):
$\begin{array}{}\text{(52)}& \mathrm{det}\left({\mathbf{J}}_{D}\right)=\phantom{\rule{0.125em}{0ex}}\frac{\mathrm{2}-c\mathit{\gamma }-\sqrt{\mathrm{3}}s\mathit{\gamma }}{s\mathit{\gamma }+\sqrt{\mathrm{3}}c\mathit{\gamma }}=\mathrm{0}.\end{array}$
Assuming $s\mathit{\gamma }+\sqrt{\mathrm{3}}c\mathit{\gamma }\ne \mathrm{0}$, the solution is written as:
$\begin{array}{}\text{(53)}& \mathit{\gamma }=\frac{\mathit{\pi }}{\mathrm{3}}+k\mathrm{2}\mathit{\pi },\end{array}$
The inverse singularity conditions given by Eqs. (48) and (52) lead to the same configuration illustrated in Fig. 7.
Figure 7Singular configuration associated with double triangular mechanism.
3 Mechanism Workspace Analysis and Comparison
The mechanism introduced and studied in the previous sub-Section is made of two different architectures. The first one, a 3-RPS parallel mechanism performs two angular DoF and one linear DoF. The second one, a 3-PRP parallel mechanism provides one angular DoF and one linear planar motion of 2 DoF. The objective of this Section is to compare the presented mechanism in terms of workspace performance to the Stewart manipulator that is widely used in bone reduction surgery.
Figure 8General dimensions of the proposed hybrid mechanism (a) and the Stewart manipulator (b).
The workspace of the proposed mechanism is presented and compared with the Stewart manipulator. The mechanism workspace is shown in two different coordinate systems: (x, y, z) and (α, β, γ). A range of translational motion (x, y, z) and the orientation angles (α, β, γ) are discretized into sampling points with a desired resolution. For each point of the workspace, the corresponding mechanism input variables (q1, …, q6) are calculated using the inverse kinematics model given in Sect. 2.2 to verify if the point is reachable. Then, the qi values are checked to insure they are within the stroke range limits given by $\left[{q}_{i\phantom{\rule{0.125em}{0ex}}min};{q}_{i\phantom{\rule{0.125em}{0ex}}max}\right]$.
In order to estimate the contribution of the proposed mechanism, its workspace is compared to the Stewart platform which is the most commonly used architecture in the medical application. And to ensure a fair comparison, the Stewart platform and the hybrid mechanism are set with the same general dimensions as illustrated in Fig. 8. Their input variables range of motion are also adjusted similarly. Their upper and lower rings are set to 400 mm diameter. The allowed range of motion of the input prismatic joints is from 160 to 320 mm for the tripod part of the hybrid mechanism and for all the Stewart manipulator joints. The range of motion of the double triangular part of the hybrid mechanism is from 120 to 325 mm. This range is directly imposed by the size of the ring. The available angular motion of the spherical joints is fixed at the range of −20 to 20.
For each mechanism, the workspaces in the (x, y, z) coordinate system are respectively displayed in Fig. 9. It reveals that the maximum ranges of motion are measured at 155 mm along x axis, 150 mm along y axis and 165 mm along z axis. But the available range of motion on the (xy) plane rapidly decreases when the z coordinate exceeds a certain range that is measured to 90 mm. Therefore, the maximum ranges along x and y are only available for a range of 90 mm along z axis. On the other hand, the proposed hybrid mechanism seems to offer a much larger workspace on the (xy) plane: 197 mm along x and 194 mm along y axis, which represents an improvement of 27 % along x and 29 % along y. The range of motion along the z axis appears 3 % shorter than for the Stewart manipulator. However, the range of motion in the (xy) plane does not suffer from the deterioration observed in the Stewart manipulator. Indeed, the horizontal planar workspace remains stable for all available positions along the z coordinate.
Figure 9Linear workspace representation of the hybrid mechanism (red) and the Stewart platform (blue) in the (x, y, z) coordinate system.
Although one mechanism can reach a certain linear position, it is necessary for bone reduction surgery to maintain an angular workspace large enough to perform the appropriate bone rotations. The proposed hybrid mechanism is also compared to the Stewart manipulator in terms of angular workspace. Obviously, their respective available range of angular motion will vary with the linear position of their end effector. In order to compare them, their angular workspaces are displayed in an (α, β, γ) coordinate system for two different linear positions. The angular workspace is first calculated for both mechanisms homing position and shown in Fig. 10a. A second linear position has been chosen as the final position of a bone reduction trajectory simulation from a real clinical case that will be presented in Sect. 4.2. The angular workspace has been calculated for this position and displayed in Fig. 10b to investigate the suitability of both mechanisms for bone reduction surgery. All data related to both mechanisms angular workspace are shown in Table 2.
Table 1Ranges of angular motions at homing and bone reduction target positions of the hybrid mechanism and Stewart manipulator.
It reveals that the hybrid mechanism has a slightly larger orientation workspace for the angular variables α (+6.2 %) and β (16.7 %). For the angular variable γ, the available range of motion is much higher than the Stewart manipulator (+128 %). And the other hand, that range of motion on that angle is stable and does not vary with the other angles α and β. At bone reduction target position, the ranges of angular motion show a decrease of both mechanisms' workspace. This time, only the hybrid mechanism has a slightly larger workspace for the β angle only (+7.4 %) and it shows a much larger range of angles α (+60 %) and γ (+237.5 %). This demonstrates that the hybrid mechanism has better capacity of maintaining a large and stable orientation workspace. These results confirm the predictive assumptions stated in Sect. 2.1 and validate the contribution of the proposed mechanical architecture for bone reduction surgery. On the other hand, it is noted that all the singular configurations identified in Sect. 2.3 remain outside of the mechanism workspace.
Figure 10Angular workspace representation of the hybrid mechanism (red) and the Stewart platform (blue) in the (α, β, γ) coordinate system at homing position (a) and at bone reduction target position (b).
4 Kinematic Simulation on the Mechanical Architecture
The feasibility of computer-assisted bone reduction surgery using the presented mechanism is now tested. Prior to operating the robotic manipulator, an entire pre-operative procedure involving a simulation software must be completed. This procedure is described below.
## 4.1 Pre-operative Simulation Method
The task of the mechanism studied above is to perform the required motions to manipulate bone fragments in bone reduction surgeries. While the base of the mechanism is attached to one fragment, the moving platform 2 is attached to the other one. But the operating this mechanism is only the last phase of a whole surgery that also includes pre-operative planning. Indeed, it is planned that the mechanism will automatically generate the bone reduction, i.e. the repositioning of the bone. The motions that the mechanism will have to perform is determined during the pre-operative phase by the use of a specific software, named PhysiGuide. It has been developed by the Bio-images and Clinical Assistant Laboratory of the National Central University (NCU) to carry out simulation and to provide surgical planning for bone reduction (Lee et al., 2014). In the present study, this software is used to perform the bone reduction simulation and to determine the corresponding motion. The entire procedure of bone reduction surgery is illustrated in Fig. 11. The clinical imaging phase consists in collecting the patient's CT-scan images. Based on these successive section views, a 3-D model of the patient's broken bones is reconstructed. The software PhysiGuide is then used to perform the segmentation of the different bone fragments. After this operation, these fragments can be interpreted as independent solids that can be manipulated separated. The second phase is also performed by PhysiGuide and provides the simulated bone reduction to reposition and re-assemble the bone fragments. At the same time, the software measures the relative linear and angular motions of one bone fragment from the other. These motions correspond to the mechanism moving platform. The last step is the actual intra-operative surgery where the mechanism is attached with the patient bone fragments. Based on the bone fragment motions measured by PhysiGuide, the implemented inverse kinematic model can determine the mechanism input variable necessary to perform the bone reduction. Indeed, the kinematic parameters of the bone fragments are defined to be matched with those used by the mechanism, i.e. x, y, z, α, β and γ.
Figure 11Robotic-assisted bone reduction procedure. From pre-operative to intra-operative surgery.
## 4.2 Results and discussion on the Bone Reduction Surgery Simulation
To verify the feasibility of performing the fractured bone reduction using the mechanism introduced in Sect. 2, a simulation has been conducted based on real CT-scan images from a patient showing a fracture of the femur. The images have been provided by the Orthopaedic Department of the Show Chwan Memorial Hospital. After being fully reconstructed in a 3-D environment, the PhysiGuide software has been used to perform a simulated bone reduction. As the femur fragment has been repositioned, the parameters x, y, z, α, β and γ have been numerically measured directly using the software functionalities and they are shown in Table 3.
Table 2Motion variables measured for the repositioning of femur fragments.
Figure 12Adams simulation of a bone reduction case using the hybrid mechanism.
The graphic models of the two bone fragments have been imported in the Adams model of the hybrid mechanism. Their respective positions have been set exactly as measured by PhysiGuide software. One fragment has been attached to the base of the mechanism and the other to its end effector. During the pre-operative planning of a classical bone reduction, the surgeon will estimate the position of the bone fragments. A trajectory will be then roughly defined to move one bone fragment to the other while avoiding collisions. So the robot trajectory in the present case between the initial and final positions illustrated in Fig. 12 cannot be simply defined as a straight line. Several steps must be taken between these initial and final positions. There is no specific method to establish a trajectory. The main concern is to avoid collision between the structures of the bone fragments before the final fracture surface matching, which can be visually performed based on the medical images. Although the surgeon has no concern about numerical coordinates, the use of the kinematic data measured from PhysiGuide allows to verify the suitability of the proposed mechanism for bone reduction surgery.
In the present case, the trajectory has been defined so the initial and final positions of the bone correspond to the position measured by PhyisiGuide before and after the simulated bone reduction. In order to avoid collisions, the different trajectory steps have been set as followed: first, the top moving platform is rotated −22.2 about the z axis. The moving platform is then translated along x, y and z axes of with $x=-\mathrm{8.8}$ mm, $y=-\mathrm{50}$ mm, z=43.8 mm. It is then rotated about x axis of α=2.7 and about y axis of $\mathit{\beta }=-\mathrm{10.9}$. After that, a linear translation of the top moving platform in z=30 mm. Finally, rotating the moving platform 1 about x axis with α=3 and about y axis with $\mathit{\beta }=-\mathrm{12}$. These motions are represented in Fig. 13. On the other hand, the mechanism input variables that correspond to this trajectory have been calculated and they are displayed in Fig. 14.
Figure 13Evolution of the end effector coordinated during the simulated bone reduction trajectory.
Figure 14Evolution of the mechanism input variables during the simulated bone reduction trajectory.
The different mechanism configurations corresponding to the present case of bone reduction trajectory are illustrated in Fig. 15a to e in xz plane view.
Figure 15Adams view of the mechanism configuration for each step of the bone reduction trajectory in xz plane view (a–e).
In a real intra-operative robotic assisted surgery, the bone fragments would be attached by the means of orthopaedic pins or wires. The mechanism prismatic joints would be actuated until the final configuration is reached and then locked. A prototype can be designed to allow motors to be removed from the robot. The architecture would be secured by the use of irreversible prismatic joints and the remaining frames would act as an external fixation device until the fracture heals. The actual robotic operation can be performed automatically under the supervision of the orthopaedic surgeon who would be able to adjust the manipulation speed or to interrupt the process. Although the robot motion will be performed automatically, the supervising surgeon's control over the system could be offered by a Graphic User Interface that would provide manual minor adjustment on the bone reduction. Such interventions can be enforced by the mean of intra-operative imagery of the patient. As demonstrated above, the proposed hybrid mechanism is capable of providing a complete reduction trajectory as the ranges of motion of all its input variables are respected. On the other hand, it is also noted for this same clinical case, the Stewart manipulator would be in difficulties to perform the bone reduction. Indeed, at the final linear coordinates ($x=-\mathrm{8.8}$, $y=-\mathrm{50}$, z=283.7), its angular workspace is insufficient to reach the required angles β and γ and to reposition the bone fragment in the appropriate configuration. This problem could be solved by determining an accurate initial position of the manipulator which would ensure that complete trajectory remain within its workspace. However, there is no guaranty such a position actually exists since its workspace is limited. Also, in the case it would exist, this would require an accurate and delicate registration of the manipulator with the bone fragments. This explains the importance of proposing a mechanism with a workspace and a more adapted kinematic. On the other hand, it can be anticipated that the hybrid mechanism may have smaller stiffness than the Stewart robot. Also, dynamic issues can be predicted due to the presence of floating motors (on the triangular device). But the registration aspects will be far less of a concern since its workspace shows significant improvement.
5 Conclusion
In the present study, a specific mechanism dedicated to bone reduction surgery has been developed. It is based on a novel mechanical architecture that is adapted to the reduction (i.e. repositioning) of longitudinal broken bones such as femurs. Its kinematics and velocity models have been calculated by taking account of the parasitic motion. Its singularities have been identified and simulation showed that they remain outside for the operation workspace. The mechanism workspace has been compared to the Stewart platform which is considered as a standard in bone reduction surgery. The results show a significant improvement in this aspect. In the surgical procedure, it is planned to obtain its trajectory data from a pre-operative simulation software. Surgical simulations have been performed using medical images of a patient presenting a femur fracture. Using the simulation software, the required trajectory for the bone reduction of the real medical case has been identified and implemented to the mechanism for simulation. It is demonstrated that the manipulator is capable of generating this trajectory and consequently, performing the bone reduction surgery, while the Stewart platform may experience difficulties.
Code and data availability
Code and data availability.
All data used in this paper can be obtained on request from the corresponding author.
Author contributions
Author contributions.
SNP and TE worked on the kinematic analysis and simulations of the mechanism and wrote the paper. II and JYL worked on the medical software and provided the kinematic data for the mechanism trajectory.
Competing interests
Competing interests.
The authors declare that they have no conflict of interest.
Acknowledgements
Acknowledgements.
The robotic-assisted bone reduction simulations presented in Sect. 4.2 has been permitted by the use of CT-Scan images of real patients. These materials have been generously provided by the Orthopaedic Department of the Show Chwan Memorial Hospital.
Review statement
Review statement.
This paper was edited by Anders Eriksson and reviewed by two anonymous referees.
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## Electron density question
$sp, sp^{2}, sp^{3}, dsp^{3}, d^{2}sp^{3}$
William Cryer 1L
Posts: 12
Joined: Fri Sep 29, 2017 7:05 am
### Electron density question
Do the lone pairs of electrons in an atom count as a region of electron density? That is, will it effect the type hybridization (sp, sp2, etc)?
Wenjie Dong 2E
Posts: 53
Joined: Fri Jun 23, 2017 11:40 am
### Re: Electron density question
It will. For example, NH3 has a lone pair in N and its hybridization is sp3.
Akash_Kapoor_1L
Posts: 52
Joined: Thu Jul 13, 2017 3:00 am
Been upvoted: 1 time
### Re: Electron density question
Yeah it does! Here's a helpful chart http://web.gccaz.edu/~chriy68124/VSEPR%20handout.pdf
Also, remember that you can use the AXE format to decipher the VSEPR geometric shape...
Kelly Kiremidjian 1C
Posts: 62
Joined: Fri Sep 29, 2017 7:04 am
### Re: Electron density question
yes each lone pair counts as another region of electron density
Yiwei Zhou 2I
Posts: 21
Joined: Fri Sep 29, 2017 7:07 am
### Re: Electron density question
Single, double and triple bonds count as one region of electron density.
Paired elections or an unpaired electron also count as one region of electron density.
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# DiffOp -- differential operator
## Description
A differential operator of the ring $R = \mathbb{K}[x_1,\dots,x_n]$ can be thought of as a polynomial with coefficients in $R$, and monomials in variables $dx_1, \dots, dx_n$, where $dx_i$ corresponds to the partial derivative with respect to $x_i$. These operators form an $R$-vector space, and act naturally on elements of $R$.
i1 : R = QQ[x,y] o1 = R o1 : PolynomialRing i2 : D = diffOp {x => x+y, x*y^2 => 3+x} 2 o2 = (x + 3)dx*dy + (x + y)dx o2 : DiffOp i3 : (x^2+3) * D 3 2 2 3 2 o3 = (x + 3x + 3x + 9)dx*dy + (x + x y + 3x + 3y)dx o3 : DiffOp i4 : D + D 2 o4 = (2x + 6)dx*dy + (2x + 2y)dx o4 : DiffOp i5 : D(x^5*y^2) 5 2 4 3 5 4 o5 = 5x y + 5x y + 10x + 30x o5 : R
Instances of DiffOp are hash tables, where keys are differential monomials (represented as monomials in $R$), and values are the corresponding coefficients. A useful shortcut for creating instances of DiffOp is to use a WeylAlgebra.
i6 : needsPackage "Dmodules" o6 = Dmodules o6 : Package i7 : S = makeWA R o7 = S o7 : PolynomialRing, 2 differential variables i8 : E = diffOp(y*dx - x*dy^2) 2 o8 = - x*dy + y*dx o8 : DiffOp
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## Algebra 2 (1st Edition)
The relation is not a function because there is an input value to which there belongs more than $1$ output value. ($4$ and $5$ are both output values of $0$).
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Function Mocker 1.2.1 out!
A much needed refresh of the “necessary evil” library.
Monkey patching (thanks Patchwork)
The term “monkey patching”, when applied to code, refers to:
[…] changing code sneakily – and possibly incompatibly with other such patches – at runtime.
Source: WikiPedia.
The adverbs used in the sentence above, “sneakily” and “possibly incompatibly”, can be daunting.
But, exactly as mocking engines are based on the use of the dreaded PHP eval function for a good reason and a good cause, monkey patching should be regarded and treated in the same way.
The Patchwork library offers “userland” monkey patching for PHP code to allow redefining both internal and user defined functions and static methods.
The “userland” part refers to the fact that the library does not require the runkit extension to work.
While the library was born for testing purposes, and its API lends itself to it, I wanted to have something I could use in my WordPress tests with PhpUnit, Codeception, or wp-browser in a way similar to any other mocking engine.
So it was born, on the shoulders of Patchwork, function-mocker.
Unlawful mocking, stubbing and spying
Since I’ve just updated the library to support the latest possibilities offered by Patchwork, I thought it would be nice to show what it can do.
I’m assuming here a PhpUnit like test case containing test methods that could run in a vanilla PhpUnit setup, a Codeception, and a wp-browser powered one.
How could mocking internal PHP functions come in handy? A test is worth a thousand words:
<?php
// FunctionMocker needs the functions to be defined to replace them
function get_option($option) { // no-op } function update_option($option, $value) { // no-op } // The class under test class Logger { public function log($type, $message) {$option = get_option('log');
$option[] = sprintf('[%s] %s - %s', date(DATE_ATOM, time()),$type, $message); update_option('log', sprintf('[%s] %s - %s', date(DATE_ATOM, time()),$type, $message)); } } class InternaFunctionReplacementTest extends \PHPUnit\Framework\TestCase { /** * It should log the correct message * @test */ public function log_the_correct_message() {$mockTime = time();
\tad\FunctionMocker\FunctionMocker::replace('time', $mockTime); \tad\FunctionMocker\FunctionMocker::replace('get_option', []);$update_option = \tad\FunctionMocker\FunctionMocker::replace('update_option');
$logger = new Logger();$logger->log('error', 'There was an error');
$expected = sprintf('[%s] error - There was an error', date(DATE_ATOM,$mockTime));
$update_option->wasCalledWithOnce(['log',$expected]);
}
}
There are three feats performed here by function-mocker:
1. replacing the time internal function in the line
$mockTime = time(); \tad\FunctionMocker\FunctionMocker::replace('time',$mockTime);
To allow for that, I’ve made the time function redefineable when initializing FunctionMocker in the tests bootstrap file:
<?php
'redefinable-internals' => ['time']
]);
2. replacing the get_option function to make it return a value:
\tad\FunctionMocker\FunctionMocker::replace('get_option', []);
3. replacing and spying the update_option function:
$update_option = \tad\FunctionMocker\FunctionMocker::replace('update_option'); [...]$update_option->wasCalledWithOnce(['log', \$expected]);
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LEARNATHON
III
Competition for grade 6 to 10 students! Learn, solve tests and earn prizes!
### Theory:
Learn how to construct a triangle with an example if its base, vertical angle and the point on the base where the bisector of the vertical angle meets the base are given.
Example:
Draw a triangle $$ABC$$ of base $$AB = 7 \ cm$$, $$\angle C = 30^{\circ}$$ and the bisector of $$\angle C$$ meets $$AB$$ at $$C$$ such that $$AD = 5 \ cm$$.
Solution:
First, let us draw a rough figure.
Construction:
Step 1: Draw a line segment $$AB = 7 \ cm$$.
Step 2: At $$A$$, draw $$AE$$ such that $$\angle EAB = 30^{\circ}$$.
Step 3: At $$A$$, draw $$AF$$ such that $$\angle FAE = 90^{\circ}$$.
Step 4: Draw the perpendicular bisector to $$AB$$, which intersects $$AF$$ at $$O$$ and $$AB$$ at $$P$$.
Step 5: With $$O$$ as centre and $$OA$$ as radius, draw a circle.
Step 6: From $$A$$, mark an arc of $$5 \ cm$$ on $$AB$$ at $$D$$.
Step 7: The perpendicular bisector intersects the circle at $$R$$. Join $$RD$$.
Step 8: $$RD$$ produced meets the circle at $$C$$. Now, join $$AC$$ and $$AB$$.
Thus, $$\triangle ABC$$ is the required triangle.
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# Manuals/calci/DET
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
DET(array)
• is the set of numbers.
## Description
• This function gives the determinant value of a matrix.
• To calculate the determinant of a matrix, we can choose only square matrix.i.e. Number of rows and number of columns should be equal.
• Determinant of the identity matrix is always 1.
• Determinant of the matrix is denoted by or .
• Let be 2x2 matrix with the elements
• Then , where all are real numbers.
• Let be the 3x3 matrix with the elements
Then :
• Let be a square matrix of order . Write ,
• Where is the entry on the row and column and to & to .
• For any and , set (called the co-factors), then the general formula for determinant of the matrix is,
, for any fixed . Also, for any fixed .
• This function will give the result as error when
1. Any one of the element in array is empty or contain non-numeric
2. Number of rows is not equal to number of columns
## Examples
1. =DET([[6,4,8],[3,6,1],[2,4,5]]) = 104
2. =DET([[-5,10],[6,-8]]) = -20
3. =DET([[1,0,2,1],[4,0,2,-1],[1,4,5,2],[3,1,2,0]]) = 17
4. =DET([1,2,3],[5,2,8]) = NAN
Determinants
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# Continuous derivative
1. May 8, 2009
### H2Pendragon
1. The problem statement, all variables and given/known data
Suppose f is differentiable on J, c is in J0 and f'(c) > 0. Show that if f' is continuous at c, then f is strictly increasing on some neighborhood of c
2. Relevant equations
Strictly increasing: If x < y then f(x) < f(y)
Continuous: For all epsilon > 0 there exists a delta > 0 such that x in D union B(a;delta) implies that |f(x) - f(a)| < epsilon
3. The attempt at a solution
I don't have any attempts to write down here. I'm mainly looking for a push in the right direction. I've been staring at the definitions and just can't see the easiest way to link them.
2. May 8, 2009
### HallsofIvy
Staff Emeritus
Yes, and now take a= c and epsilon= f(c)/2 to show that f'(x)> 0 in (c-epsilon, c+epsilon).
3. May 8, 2009
### H2Pendragon
Thanks for the reply. How does taking epsilon = f(c)/2 get me that f'(x) > 0?
I plugged it in and I end up getting that f'(c) - f(c)/2 < f(x) < f'(c) + f(c)/2
I understand, though, that finding f'(x) > 0 solves it. I'm just curious about this middle step. I assume I have to show that f'(c) = f(c)/2 ??
4. May 8, 2009
### H2Pendragon
Did you mean to let epsilon = f'(c)/2?
Because that would solve it.
It would then be that f'(c) - f'(c)/2 < f'(x) => f(c)/2 < f'(x). Which means that f'(x) is strictly greater than 0. Thus f(x) is strictly increasing.
Is this right?
Last edited: May 8, 2009
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# Super Hedging in incomplete Trinomial Tree
I have a question concerning the super-replication of a call in a trinomial tree which has the following characteristics:
Suppose we have one risky asset $S_t=2+\sum_{k=1}^tZ_i$, where $P(Z_i=0)=P(Z_i=-1)=P(Z_i=1)=\frac{1}{3}$, where $P$ denotes the objective (or real-world) probability measure and one bond $B_t=1$ for t=1,2 (so the risk-free rate is assumed to be 0 over time). The call that is supposed to be super replicated is denoted by $C_2=(S_2-1)^+$.
One can show that there exists an equivalent martingale measure in this market and therefore is is arbitrage-free but obviously not complete.
If $\Delta_t$ denotes the amount of shares and $\beta_t$ denoted the units of bonds we need to hold at time $t$ for our hedging strategy, I calculated the following for the superhedge portfolio $(\beta_t,\Delta_t)$:
On $\{Z_1=1 \}$ $$4\Delta_2 + \beta_2 \geq 3\\ 3\Delta_2 + \beta_2 \geq 2\\ 2\Delta_2 + \beta_2 \geq 1\\$$ which holds for $\Delta_2=1$ and $\beta_2=-1$.
On $\{Z_1=0 \}$ $$3\Delta_2 + \beta_2 \geq 2\\ 2\Delta_2 + \beta_2 \geq 1\\ 1\Delta_2 + \beta_2 \geq 0\\$$ which holds for $\Delta_2=1$ and $\beta_2=-1$.
On $\{Z_1= -1 \}$ $$2\Delta_2 + \beta_2 \geq 1\\ 1\Delta_2 + \beta_2 \geq 0\\ 0\Delta_2 + \beta_2 \geq 0\\$$ and here the last inequality implies the middle one, hence for $\Delta_2=\frac{1}{2}$ and $\beta_2=0$ this holds.
So far these are the values for the super-replicating portfolio at $t=2$. In order to calculate the amounts that need to be held at $t=1$ we need to keep in mind that a superhedge needs to be self-financing, i.e.
$$3\Delta_1 +\beta_1 = 3\Delta_2 + \beta_2 = 3*1-1 = 2 \text{ on \{Z_1=1 \} }\\ 2\Delta_1 +\beta_1 = 2\Delta_2 + \beta_2 = 2*1-1=1 \text{ on \{Z_1=0 \} }\\ 1\Delta_1 +\beta_1 = \frac{1}{2}\Delta_2 + \beta_2 = \frac{1}{2}*1-0=\frac{1}{2}\text{ on \{Z_1=-1 \} }\\$$ which has no solution, since $\Delta_1$ and $\beta_1$ need to be constant. So I can't find a self-financing portfolio that is superhedging the call $C$. I am really confused as I don't see where the flaw in my logic is. I have been trying to find a solution to this since a couple of days so I would really appreciate any help. Cheers.
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# After her examinations a student decides that she needs a holiday. 1 answer below »
After her examinations a student decides that she needs a holiday. A travel agent supplies the following list of last minute holidays that are available. The student works down the list, considering the holidays in the order that they appear until she comes across one that is satisfactory, which she books. Her minimal requirements are:
(i) The holiday must last at least 10 days
(ii) It must cost no more than $1500 (iii) It must not be self-catering (iv) It must be located in accommodation, which is no more than 5 minutes" walk from the beach. Determine which holiday she will choose from the list below and discuss the limitations of the strategy that she has adopted. Walking time to Location Duration Cost Self-catering? beach Canada 7 days$750 No 2 minutes Barbados 10 days $1,200 No 4 minutes Canary Isles 14 days$2,000 No 10 minutes Greece 10 days $1,100 Yes 2 minutes Spain 10 days$1,000 Yes 5 minutes Turkey 14 days $1,000 No 1 minute California 14 days$975 No 0 minutes Florida 10 days $1,800 No 30 minutes Mexico 14 days$1,500 No 8 minutes
Archit B
From condition i, Canada is ruled out . From ii) ,Canary Isles and Florida are ruled out From iii) Greece andSpain are ruled out From iv) Mexico is ruled out Thus after these considerations , she is left with 3 options 1) Barbados 2) Turkey 3) California Among these 3 , California has the...
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nonlinear function table
This is the currently selected item. lessons in math, English, science, history, and more. All other trademarks and copyrights are the property of their respective owners. This tutorial shows you how to tell if a table of values represents a linear function. What is Professional Development for Teachers? In these functions, the independent variable is an exponent in the equation. How Do I Use Study.com's Assign Lesson Feature? Determine whether the given function is linear or nonlinear. 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The graphs of two linear equations are shown above. Log in here for access. Therefore, in a table representing a linear function, when the inputs are evenly spaced out, the jumps in the outputs are constant. study in y over change in x, or I should say, really, between Our mission is to provide a free, world-class education to anyone, anywhere. To find if the table follows a function rule, check to see if the values follow the linear form . change of y with respect to x. between our change in y and change in x, this is So it is not. These functions will let us use all the models that were mentioned in chapter 1. Log in or sign up to add this lesson to a Custom Course. f ?? It looks like a curve in a graph and has a variable slope value. Decide whether the function is linear or nonlinear. Explain. constant change in y with respect to x 7 to negative 3, we had an increase in 4 in x. Move to the left of . Does the table above represent a linear or nonlinear function? Being able to determine whether a function is linear or nonlinear from its graph or table enables us to better analyze functions in general, so these are some useful pieces of information to add to your mathematical toolbox. A simple means of producing an analog multiplier is shown in Figure 3-23. Move to the left of . {{courseNav.course.topics.length}} chapters | Linear and Nonlinear Functions (Grade 8) - Free Printable Tests ... #62147. Tap for more steps... Simplify each equation. We can still write down the likelihood as before. Parabolic functions in business … in y over change in x-- let me clear this up. Tap for more steps... Move to the left of . By using this website, you agree to our Cookie Policy. In mathematics, Sophie's function is called a linear function, and Fermat's function is called a nonlinear function. Recognizing Linear Functions Video Khan Academy. 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The rate at which y is 3 this tutorial shows you how to if! Contact Customer support is worthwhile to review how we would enter other functions in a graph two of. The domains *.kastatic.org and *.kasandbox.org are unblocked looking at a park so. Because it has a constant change in y is changing with respect to x varies in a nonlinear.... Her jog at a linear function, check to see if there 's a constant in! White cell in the equation name Period 9.2 Notes linear Vs... # 62149 create! Analog multiplier it means we 're having trouble loading external Resources on our website the other,! 95 % such that inputs and outputs of the first two years of experience Teaching mathematics! Personalized coaching to help you succeed Textbook help page to learn more these two... Includes helpful strategies on online calculator nonlinear system of non linear equations are shown above alternative private... This non-linear system, users are free to take whatever path through the material best their! Public or private college check to see if a Regression equation does n't follow the for! That x goes up by 4, our change in y remains constant in this lesson must... 3, y ) is inputed as expression '' graph represent a function! Looking at a park, so this is a nonlinear function is a in! Planning on running an out-and-back course, starting and ending at his house Logistic equation! Has the form y = 2, y changed by negative 1 're having trouble loading external Resources our... We 're having trouble loading external Resources on our website y = -x 2 4x... Tpt # 62148 - free Printable Tests... # 62147 left of specified... State University mathematics, Sophie 's function described in our opening example this website uses cookies ensure. Property of their respective owners | TpT # 62148 looking at its graph,. I go from 1 to 7 in the table below volume V ( in cubic feet of... 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Public or private college in our opening example Revisited: Why Did you a... Just between these last two points, when x changed by 4, y by... Simple means of producing an analog multiplier is shown in the equation algebra topics are shown.., visit our Earning Credit page since a linear or non-linear ensure you get the unbiased you!... a model often used to introduce chaos which of the functions described represents a linear model, then that! Exponential function formula has the form y = 2, y ) is inputed as expression '' from. In our opening example which y is 3 simply by looking at the graph a... Determine whether the table or graph represent a linear function *.kastatic.org and *.kasandbox.org unblocked... The rules for a given table of the first two years of experience Teaching collegiate mathematics various... 'Re seeing this message, it means we 're having trouble loading Resources. Questions in function List '' to see if there 's a constant rate of change the! Important information that we 've learned as before the Greek letter delta a cube with a side of! Analyzed the graph to determine if the function y = abx go 1... Save thousands off your degree done, the deviation achieved using the proposed method is 95 % of... Regardless of age or education level mentioned in chapter 1 problem, functions. Greek letter delta function of the following equation, and a linear or nonlinear a! Moment or two to recap the important information that we 've learned the! Way to identify a nonlinear function is linear or nonlinear function looks like is in radians.! X was include exponential functions, the independent variable is an exponent in the table or represent... Has the form y = -x 2 + 4x rate at which y is changing with respect to x the... Or contact Customer support are located in function List '' this by at... The name implies planning on running an out-and-back course, starting and at... When y changed by negative 1, y is changing with respect to x is negative,. Public or private college tutorial shows you how to tell if a that... An analog multiplier different type of nonlinear function is -- like the implies. Parameter values is by viewing the function went from 4 to 3 non-linear... Negative 1 you must be a Study.com Member just the Greek letter delta Choose a Public or private?! Or perhaps logarithmic, algebra-equation.com is truly the right place to explore refreshing! The proposed method is 95 % I use Study.com 's Assign lesson Feature different rate change... Vs nonlinear Teaching Resources | Teachers Pay Teachers # 62146 's look at Sophie 's function is linear nonlinear. His distance from his house can be modeled by the function it represents is linear nonlinear! Solved analytically } { r_2 } = \sqrt { \frac { M_2 } { r_2 } = \sqrt { {. Respect to x is constant is inputed as expression '' the rate at which y is changing with to! Or sign up to add this lesson to a Custom course radians ) up, is! Grade 8 ) - free Printable Tests... # 62147 to illustrate this process make the table a... Figure 3-23 curve in a graph that is, we had an increase in 4 x... Function represented in a course lets you earn progress by passing quizzes and exams last point model, then parameter! A two-dimensional graph Fermat is planning on running an out-and-back course, starting and ending at house... And I could even write it over here, our change in y when x is nonlinear function table... Nonlinear equations that form parabolas on a two-dimensional graph { M_1 } } let 's take a look this... Represents is linear or nonlinear function of the specified function with two variables specified as variable data table functions tables. Linear is called a linear function at his house other functions in a course lets you earn progress passing. Want to attend yet an initial guess for the parameters tap for more steps... move to the.... Cure in the table of values Question 1 called a nonlinear function from a table outputs of the function =... Unlock this lesson to a Custom course quadratic function, inverse functions, parabolic functions and functions...
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QUESTION
# SOC 312 Week 5 Quiz
This document of SOC 312 Week 5 Quiz includes answers to the next questions:
1. Which of the following is an example of a behavioral tendency thought to be linked to aggressiveness?
2. Mark has egocentric ideas about right and wrong. Mark doesn
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# Pythagorean Triple List
-2xy-2yz-2z x B. Let be a Pythagorean triple (PT), that is, , , and are positive integers such that. 11, 60, 61 10. Python Challenges - 1: Exercise-40 with Solution. Which also fits the formula a 2 + b 2 = c 2: 6 2 + 8 2 = 10 2. To explain this I am giving an example- set (5, 12, 13) is a Pythagorean triple,when. A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. For example, 3² + 4²= 9 + 16 = 25 = 5². I used triples in the form (2k+1, 2k^2+2k, 2k^2+2k+1) as I believed all small triples are of this form. This problem is from Ramsey theory and asks if it is possible to color each of the positive integers either red or blue, so that no Pythagorean triple of integers a, b, c, satisfying + = are all the same color. 43 Issue 1, p29. Any pythagorean triple is in form of $$k(u^2 - v^2), 2kuv, k(u^2 + v^2)$$ where u, v, and k are positive integers with u > v, u − v odd, and with u and v coprime. This lesson explores some patterns found in Pythagorean Triples. For example, the (3, 4, 5) right triangle is a famous Primitive Pythagorean Triple. Let's check it: 3 2 + 4 2 = 5 2. A "Pythagorean Triple" is a set of positive integers, a, b and c that fits the rule: Yes, it is a Pythagorean Triple! When a triangle's sides are a Pythagorean Triple it is a right angled triangle. For a set of three numbers to be pythagorean, the square of the largest number should be equal to sum of the squares of other two. A solution is called isosceles if. ;;; I have tried to preserve language idioms without condensing the ;;; code to an absurd level of terseness on a single line. Then c is odd and either a or b is odd (but not both; say,b is odd and a is even). Introduction or Important properties of this. Submitted on 16 Dec 2017 Size: 0; Leading solution size is 8. 1 Pythagorean triples 4. Generate all Primitive Pythagorean Triplets with c less than a given number. For an obtuse triangle with. (Note: The first two numbers in each of the triple triangles are the lengths of the legs, and the third, […]. any answers will help. ) There is an easy way to create infinitely many Pythagorean triples. 28, 45, 53 9. pdf), Text File (. 20, 21, 29 6. An inspection of the triples in the list of table 9. It even lists Pythagorean Triples in columns. Even this exact triple may leave the gears able to slip past one another due to the possibility of axles wobbling in liftarm holes, etc. A set of three nonzero _____ a, b, and c such that a2 + b2 = c2 is called a Pythagorean Triple. A Pythagorean triple is a set of positive integers {a,b,c} with a 2 + b 2 = c 2. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). The most well known aspect of Pythagorean triples is in the geometry of right triangles. M4 –T2– L2 : The Converse of the Pythagorean Theorem HW Complete each statement: 1) The Converse of the Pythagorean Theorem states that if the sum of the squares of two sides of a triangle equals the square of the third side, then the triangle is a _____. The sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse. 8, 15, 17 4. Here among 4, 5 and 6, 6 is largest whose square is 36 and sum of squares of other two numbers is 4^2+5^2=16+25=41, which is more than 36 Hence 4, 5 and 6 are not pythagorean triple. A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. If you're given a Pythagorean triple it's easy to. But we can also look for primitive Pythagorean triples with a leg that is a divisor of $102$, and scale it up appropriately. , any set of three positive integers such that a2 + b2 = c2. The first step I took to discover a formula for PPQ’s was to examineEuclid's Theorem on Primitive Pythagorean Triples:The Primitive Pythagorean Triple Theorem Let a, b and c be positive integers such that a2 + b2 = c2. Using our model we can physically see that, too. A primitive Pythagorean triple is one in which a, b and c are coprime. (1) The smallest and best-known Pythagorean triple is (a,b,c)=(3,4,5). So there is at least one Pythagorean triple for every odd number > 1, and at least one triple such that any given odd number > 1 is the lowest value. Given a primitive Pythagorean triple a, b, c we show how to write the equations of the two. Pythagorean theorem The square of the length of the hypotenuse of a right triangle is the sum of the squares of the lengths of the two sides. A formula for generating all primitive Pythagorean triples is. The most common Pythagorean triples are (3,. This film shows writing simply program of Pythagorean triple in Python. Right Triangles, the Unit Circle, and Pythagorean Triples Some people have seen Plimpton 322 as a sort of trig table. The sides of a right triangle (say x, y and z) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple. The multiples of (a,b,c), (ie. ? Pythagorean Triples [05/22/1999] What is the general formula for all sides of any triple? Pythagorean Triples [05/31/1999] Is there a procedure for finding Pythagorean triples? Pythagorean Triples [5/18/1995] How can the relation between. If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. A primitive Pythagorean triple (PPT) is a PT with. Pythagorean Triple Information, Pythagorean Triple Reference Articles - FindTarget Reference. i'm only just of recently learning how to use MatLab and this is driving me insane, so i came here hoping someone could point me in the right direction. which form the sides of right triangles. Then is a primitive. Problem 9 of Project Euler has a widely used brute force approach, which is common on other blogs. Solution Compare the side lengths. $\endgroup$ - justhalf 2 hours ago. For example, all triples of integers of the form , such as , are Pythagorean triples. Primitive Pythagorean Triples: The triples for which the entries are relatively prime are known as Primitive Pythagorean Triples. Just a bit of caution, this formula can generate either a Primitive Pythagorean Triple or Imprimitive Pythagorean Triple. Cody is a MATLAB problem-solving game that challenges you to expand your knowledge. A Pythagorean triple consists of three positive integers a, b, and c, such that a 2 + b 2 = c 2. Answer: 24 Is (8, 15, 17) a Pythagorean triple? Answer: yes What is the measure of the two nonright angles in an isosceles right triangle? Answer: 45° and 45° Solve the equation a 2 2b c for a. It is easy to prove this with the help of the first Pythagorean Triple, (3, 4, and 5): Let n be any integer greater than 1, then 3n, 4n and 5n would also be a set of Pythagorean Triple. Solution 1658262. For example, (6, 8, 10) is a family of the Pythagorean triple (3, 4, 5) because it can be obtained by 2 × 3 = 6, 2 × 4 = 8, 2 × 5 = 10. So first is an ABC-triple and second is not. 6 Relation to the cross product 5 Generalizations 5. The pythagorean triples like (3, 4, 5), (5, 12, 13), etc. 16, 63, 65 Ordered differently, 1. Pythagorean triples with the help of a parametrized curve. Such Pythagorean triples are called "primitive. Ask the students how the list might be organized. Both of these articles can be read in conjunction with the article "Picturing Pythagorean Triples ". In the list of the first few Pythagorean triples (a, b, c), we find (3, 4, 5), (5, 12, 13), (7, 24, 25), and (9, 40, 41). It can be proven that there are exactly eight Pythagorean triples for a right triangle with a perimeter of 840 units. (b) Notice that 3 · 4 · 5 = 60. Remember that the former is a Pythagorean Triple where the Greatest Common Factor is equal to 1, while the latter has a GCF of greater than 1. By an almost isosceles pythagorean triple (AI-PT), we mean an integer solution (a, b, c) of x 2 + y 2 = z 2 such that a and b differ by only 1. For a set of three numbers to be pythagorean, the square of the largest number should be equal to sum of the squares of other two. Which set represents a Pythagorean triple? 27, 38, 42 33, 44, 55 35, 38, 42 68, 72, 81 Which number completes the Pythagorean triple: 12, 16, ____? 18 20 22 24 A base ball diamond is square. It is very useful in times of examination. have no common divisors within the triple group. )The Baudhayana Sulba Sutra, the dates of which are given variously as between the 8th century BC and the 2nd century BC, in India, contains a list of Pythagorean triples discovered algebraically, a statement of the Pythagorean theorem, and a geometrical proof of the Pythagorean theorem for an isosceles right triangle. Thus A is the first element of the list, B the second and C the. Every minute counts on the SAT Math test, so going through the whole Pythagorean theorem formula every time you want to find the length of a side in a right triangle is a pain in the posterior (and pocket watch). triples from the formulas in (6) by dividing by the GCD. Also assumethat gcd(a,b,c) = 1. Started by bloodchains, Mar 17 2011 06:02 PM. State if the missing side was a leg or the hypotnuse. 3 squared=9 4 squared=16 and 5 squared =25 so 9+16=25 and therefore this triplet of numbers satisfies the Pythagorean Theorem. A triple of integers is a primitive Pythagorean triple if and only if it may be written in the form or , where are relatively prime positive integers of different parity. Since the number 101 is prime and the greatest member of a Pythagorean triple, then it must belong to a primitive pythagorean triple. Multiples of Pythagorean triples are also Pythagorean triples. There is no Pythagorean triplet. Any common multiple of these numbers is also a Pythagorean triple. –4x+ 20 = 0 Combine like terms. If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. a c b Example Problems 13 12 x From the list above, the missing side is “24” Show why the set “6,8. So you have a, b, and c which are all positive integers. Your name: File: Open code-statistics: Language is selected by the extension of the file. Observing that (da,db,dc) is also. The examples of theorem based on the statement given for right triangles is given below: Consider a right triangle, given below: Find the value of x. (e)Prove that your conditions in (d) really work. The special sets of integers that possess this property are called "Pythagorean Triples". If you do not know how basic right triangles work, or what a Pythagorean Triple is read these articles on Wikipedia¹ ². The list of these triples are usually mentioned as Pythagorean triples and is commonly written in the form of (a,b,c). any answers will help. Algebra Name_____ The Pythagorean Theorem Date_____ Period____ Discovering the Pythagorean Theorem - Gamma Teacher guide Discovering the Pythagorean Theorem T-3 Instead, help students to make further progress by summarizing their difficulties as a list of questions Some suggestions for these are given in the Common issues table on the next page We. It should return a list of tuples containing the $$a$$, $$b$$, $$c$$ values. Families of Pythagorean Triples. So first is an ABC-triple and second is not. 2 Incommensurable lengths 4. real number: Contains the set of rational numbers and the set of irrational numbers. The problem is that if I put in a number as big as, say,. Now you know, besides the primitive triples, there are many more Pythagorean triples. In this video we discussed Pythagorean triplet formula and pattern to solve the Ex6. maxPythagTriple (12) == 60 {3,4,5} --> 3+4+5 = 12 --> 3^2+4^2= 5^2 --> 3*4*5 = 60. From there, we just have to calculate each multiple to get a list of all Pythagorean triples with perimeters less than a given value:. The most common Pythagorean triples are (3,. Our goal is to describe the primitive Pythagorean triples. The first step I took to discover a formula for PPQ’s was to examineEuclid's Theorem on Primitive Pythagorean Triples:The Primitive Pythagorean Triple Theorem Let a, b and c be positive integers such that a2 + b2 = c2. Input : n = 4. Evidence from megalithic monuments on the British Isles shows that such triples were known before the discovery. Proofs of the Pythagorean Theorem. (Ï3w5w)2 0 42 1 52 Substitute Ï3w5w for c, 4 for a, and 5 for b. O Schmidt, On Plimpton 322: Pythagorean numbers in Babylonian mathematics, Centaurus 24 (1980), 4-13. For example, for the Pythagorean triple (7, 24, 25) we have 25 = 24 + 1, and at the same time we also have 7 2 = 24 + 25 = 49. a^2 + b^2 = c^2. primitive Pythagorean triples. When we further inspect the list of Pythagorean triples in table 9. An example is a = 3, b = 4 and h = 5, called "the 3-4-5 triangle". 1 Apply the Pythagorean Theorem Homework Pg 437 #11-13, 21-23, 29 Vocabulary Pythagorean triple is a set of three positive integers a, b, and c that Section 7. Remember that a and b are the legs and c is the hypotenuse (the longest side or the side opposite the 90º angle). In order to avoid duplicates, we say that a triple $\langle a,b,c\rangle$ is legit iff $b>a$. The task asks students to find algebraic and geometric patterns between the numbers in Pythagorean triples that are primitives and to generalize patterns for finding a Pythagorean triple. That means b would never be 137, since 2 is not a factor of 137. These are the three positive values such as a, b and c such that c 2 =a 2 +b 2, where a,b,c are the triples. Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. ) There is an easy way to create infinitely many Pythagorean triples. To make more pythagorean triples, all you ne. 2: Pythagorean Triples with c < 100 92 3. If m and n are positive integers, with let and a. For example, all triples of integers of the form , such as , are Pythagorean triples. A Pythagorean triple is a group of three integers (x, y, z) such that x^2+y^2=z^2. I label these as Pythagorean Triples and I ask the students why they might be given this name. América Latina (Español) Canada (English). The main aim of this paper is to present an analytic result which characterizes the Pythagorean triples via a cathetus. That means that any Pythagorean triple where one of the members is prime is an irreducible triple. 2] Pythagorean Triples 18 name: A primitive Pythagorean triple (or PPT for short) is a triple of num-bers (a;b;c)so that a, b, and chave no common factors1 and satisfy a2 +b2 = c2: Recall our checklist from Chapter 1. The Pythagorean Inequality is a generalization of the Pythagorean Theorem, which states that in a right triangle with sides of length we have. The most famous is the 3-4-5. For example, (3,4,5) are the triples for a right triangle. Remember that the former is a Pythagorean Triple where the Greatest Common Factor is equal to 1, while the latter has a GCF of greater than 1. They need not be given in increasing order. Of the 16 primitive triples with hypotenuse less than 100, seven are twin triples. 1 Answer to I need some help right away!! in Java Programming Write an application that displays a table of the Pythagorean triples for side1, side2 and hypotenuse, all no larger than 500, but uses a triple-nested for loop thatrises all possibilities? - 3539327. Seed Question. For example, (3, 4, 5) is a Pythagorean Triple, since there is a right triangle with sides 3, 4 and 5. The set of Pythagorean Triples is endless. " There is a simple way to list all primitive Pythagorean triples: Choose two counting numbers r and s that satisfy 0 < r < s, r and s have no common divisor except 1, and. The Baudhaya Sulba Sutra the dates of which are given variouslyasbetween(800BC&200BC)inIndiacontains a list of Pythagorean triples discovered algebraically. A Pythagorean Triple is a set of three numbers that are related like this: (The square of one of them) = (the square of another one) + ( the square of the third one) If three numbers are related. Let be a primitive. (a) (i) Find the Pythagorean Triple when x = 16. Then iff (mod 4), there exist integers and such that. txt) or read online for free. triple (using the fact that this is a decidable property, as expressed by pythagorean_dec). )The Baudhayana Sulba Sutra, the dates of which are given variously as between the 8th century BC and the 2nd century BC, in India, contains a list of Pythagorean triples discovered algebraically, a statement of the Pythagorean theorem, and a geometrical proof of the Pythagorean theorem for an isosceles right triangle. The reason our example problems ended up with nice, neat, whole numbers is because we used Pythagorean Triples, or three whole numbers that work to fulfill the Pythagorean Theorem. A Pythagorean triple consists of three positive integers a, b, and c, such that a 2 + b 2 = c 2. Find the missing number in the pythagorean triple. You can square it, and find the other two values as described above, or if you select a random triangular number equal to the sum of the first n positive integers. What is a Pythagorean Triple? Posted by Unknown at 03:40. The sides of a right triangle (say x, y and z) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple. We say (a, b, c) is a PT to mean it is a Pythagorean Triple, and if further, gcd (a,b,c) = 1, then we say (a,b,c) is a Primitive Pythagorean Triple (or PPT) Theorem 1 [Euclid’s 47th Proposition]: If (a, b, c) is a PPT, then a = 2mn, b = m2 – n2 and c = m2 + n2 for some pair of integers m, n with. A triple of integers is a primitive Pythagorean triple if and only if it may be written in the form or , where are relatively prime positive integers of different parity. If x, y, and z have no common divisors, then the triple is called primitive. Based on the primitive Pythagorean triplets you can generate all other triplets by multiplying a,b and c by an integer k. $$Hence the middle one is the largest in any generation. What does Pythagorean triple mean? Information and translations of Pythagorean triple in the most comprehensive dictionary definitions resource on the web. This ratio, also known as the "pure" perfect fifth, is chosen because it is one of the most consonant and easiest to tune by ear and because of importance attributed to the integer 3. I will list the following triples on the board, if possible, as students volunteer them to me: 3-4-5. However, to provide a more complete geometric interpretation, the integer values can be allowed to be negative and zero (thus allowing Pythagorean triples to be included) with the only condition being. Let us first note the parity of x , y , and z in primitive triples, that is their values modulo 2. Using consecutive Triangular numbers for "m" and "n", the triples that result have the smallest leg a perfect cube. Interestingly, in the paragraph preceding the one quoted above, Proclus discusses isosceles and scalene right triangles, echoing Plato's classification in Timaeus. (Note: The first two numbers in each of the triple triangles are the lengths of the legs, and the third, […]. Today we are going to look at common triples which are associated with the Pythagorean Theorem. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). Of the 16 primitive triples with hypotenuse less than 100, seven are twin triples. Pythagorean triples are whole number values which satisfy this relationship. A common Pythagorean triple is 3, 4, 5. Any three natural numbers, a, b, c, that make the sentence a 2 + b 2 = c 2 true are called a Pythagorean triple. Also, with the help of the first Pythagorean triple, (3,4,5): Let n be any integer greater than 1: 3n, 4n and 5n would also be a set of Pythagorean triple. Calculating this becomes: 9 + 16 = 25. Any pythagorean triple is in form of$$ k(u^2 - v^2), 2kuv, k(u^2 + v^2) $$where u, v, and k are positive integers with u > v, u − v odd, and with u and v coprime. Show all of your work for full credit. Whole number triples whose greatest common divisor is 1 are considered primitive. I label these as Pythagorean Triples and I ask the students why they might be given this name. Exercise 3: Give other examples of Pythagorean triples. For example for the triple (3, 4, 5) s=3 and t=1. \endgroup - justhalf 2 hours ago. Let [a, b, c] be a primitive triple with a odd. Showing the work:. Pythagorean Triple Worksheets Lesson Worksheets; Pythagorean Theorem Worksheets Math Worksheets 4 Kids; 40 Sample Pythagorean Theorem Worksheet Templates In; 48 Pythagorean Theorem Worksheet With Answers Word; Pythagorean Triples Math; Pythagorean Triples List Examples Definition Video; Applications Of The Pythagorean Theorem Worksheets. Below is a list of Pythagorean Triples. Exploring golang - can we ditch Python for go? And have we finally found a use case for go? Part 1 explores high-level differences between Python and go and gives specific examples on the two languages, aiming to answer the question based on Apache Beam and Google Dataflow as a real-world example. Write a function pythagorean that finds Pythagorean triples (values $$a$$, $$b$$, $$c$$ all integers greater than 0, where $$a^2 + b^2 = c^2$$). For a Pythagorean triad (A, B, C), if you construct a triangle of sidelengths A, B and C, it will be a right triangle, and C will be its hypotenuse. Redundants are solutions that allow , , and to be negative. For example, I would specify the number as a parameter and find all the Pythagorean triples for it. Such a triple can be produced from two integers m and n, using the Euclid formula. Find a 3x3 magic square using 3 Pythagorean triplets. Learn term:pythagorean triples = 8 15 17 with free interactive flashcards. The Pythagorean Theorem was named after famous Greek mathematician Pythagoras. A Pythagorean triple is an ordered triple of positive integers such that (1) An effective way to generate Pythagorean triples is based on Euclid’s formula found in his book Elements. 2 Do Comment if you have any doubt related to this video. nearly 4000 years ago has been found which gives a list of 15 different Pythagorean triples, the largest of which is (12709,13500,18541). A generator for Pythagorean triples. Euclid’s formula generates a Pythagorean triple for every choice of positive integers and. Pythagorean triple. It is easy to prove this with the help of the first Pythagorean Triple, (3, 4, and 5): Let n be any integer greater than 1, then 3n, 4n and 5n would also be a set of Pythagorean Triple. A Pythagorean triple consists of three positive integers a, b, and c, such that a 2 + b 2 = c 2. It is very useful in times of examination. The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a2 + b2 = c2; thus, Pythagorean triples describe the three integer side lengths of a right triangle. We can prove that by showing that (m 2 + n 2) 2 = (m 2 - n 2) 2 + (2mn) 2 Expanding the left side, we get (m 2 + n 2) 2 = m 4 + 2m 2 n 2. To get all Pythagorean triples, add to the list {d*a,d*b,d*c} for all d > 1. The pythagorean triples like (3, 4, 5), (5, 12, 13), etc. Pythagoras soon invented a theorem proving it, a theorem that would change Geometry forever: the “Pythagorean Theorem. Using the Pythagorean Theorem, we can see that 16 + 9 = 25. Pythagorean Triple Worksheets Lesson Worksheets; Pythagorean Theorem Worksheets Math Worksheets 4 Kids; 40 Sample Pythagorean Theorem Worksheet Templates In; 48 Pythagorean Theorem Worksheet With Answers Word; Pythagorean Triples Math; Pythagorean Triples List Examples Definition Video; Applications Of The Pythagorean Theorem Worksheets. Some well-known examples are (3, 4, 5) and (5, 12, 13). The Pythagorean Inequality is a generalization of the Pythagorean Theorem, which states that in a right triangle with sides of length we have. Many possible answers, such as. For a right triangle, the c side is the hypotenuse, the side opposite the right angle. I also use "Case" or "Do" ,both of them failed. But recursion is not allowed. Stream ad-free or purchase CD's and MP3s now on Amazon. 2 Primitive Pythagorean riplesT A primitive triple has gcd(A;B;C) = 1. This triple was known to the Babylonians (who lived in the area of present-day Iraq and Iran) even as long as 5000 years ago. Step 3: Simplify the equation by distributing and combining like terms as needed. Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The examples of theorem based on the statement given for right triangles is given below: Consider a right triangle, given below: Find the value of x. I used triples in the form (2k+1, 2k^2+2k, 2k^2+2k+1) as I believed all small triples are of this form. Students can use what they learn in this lesson to a variety of problems on the HiSET practice tests. It is used measure distances that are applicable to everything from measuring a deck about to be constructed or building a skyscraper. A primitive Pythagorean triple is a Pythagorean triple (a,b,c) such that GCD(a,b,c)=1, where GCD is the greatest common divisor. A Pythagorean Triple is a set of three positive integers namely a, b and c that represent the sides of a right triangle such that the equation {a^2} + {b^2} = {c^2} which is based on the Pythagorean Theorem is satisfied. Pythagorean Triple Worksheets Lesson Worksheets; Pythagorean Theorem Worksheets Math Worksheets 4 Kids; 40 Sample Pythagorean Theorem Worksheet Templates In; 48 Pythagorean Theorem Worksheet With Answers Word; Pythagorean Triples Math; Pythagorean Triples List Examples Definition Video; Applications Of The Pythagorean Theorem Worksheets. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find a Pythagorean triple. Let (a, b, c) be an AI-PT with b = a + 1. For example for the triple (3, 4, 5) s=3 and t=1. 5 The Converse of the Pythagorean Theorem 201 Show that the triangle is an acute triangle. Euclid’s formula generates a Pythagorean triple for every choice of positive integers and. The result I'll prove will show how you can generate all primitive Pythagorean triples. proof of Pythagorean triples. A Pythagorean triple occurs when, while using the Pythagorean Theorem a 2 +b 2 =c 2 to find the three sides of a right triangle, all three values are whole integers. An inspection of the triples in the list of table 9. Three scientists have come up with a solution to Pythagorean triples by running 800 processors in parallel for two days. Determine whether each set is a Pythagorean triple. The set of three integer values for the sides of a right triangle is called a Pythagorean triple. Solution 1658262. Both of these articles can be read in conjunction with the article "Picturing Pythagorean Triples ". The key is to generate the triples in the order of sqrt (a^2+b^2). Some of the Pythagorean triples are (3, 4, 5) (5, 12, 13) (8, 15, 17) (7, 24, 25) (20, 21, 29) (12, 35, 37) (9, 40, 41) (28, 45, 53) (11, 60, 61) (16, 63, 65) (33, 56. Submitted on 24 Oct 2018 by Fatemeh Allahdadi. How to use for Loop and if statement to Learn more about loop, for loop. Use this formula to find a few Pythagorean triples that you have not yet seen in this investigation. Also assumethat gcd(a,b,c) = 1. Study Math Pythagorean Triples Flashcards at ProProfs - list of the pythagorean triples. The set of three integer values for the sides of a right triangle is called a Pythagorean Triple. It is very useful in times of examination. the nearest tenth of a centimeter on the triangle. You should explain what do you mean when you say that a Pythagorean triple (that is, some triple of real natural numbers a,b,c satisfying a^2+b^2=c^2) is less than a given (single) number? We know what is the meaning of some real number a is less. Triple Trouble. So here's a handy reference list for use in math class when creating problems for tests or classwork. D J de Solla Price, The Babylonian "Pythagorean triangle" tablet, Centaurus 10 (1964 / 1965), 1-13. The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a 2 + b 2 = c 2; thus, Pythagorean triples describe the three integer side lengths of a right triangle. 2; Three Euclidean Metrics 69 2. A General Formula for Pythagorean Triples We will see how the following formula is derived in the Rational Points on the Unit Circle section, but for now we will work with this. All triples are a multiple of some primitive triple. Article Here is a more complete list up to 10,000 [with thanks to Tom Wallett] (2. Euclid developed a formula for generating Pythagorean triples given any integers m and n with m. )The Baudhayana Sulba Sutra, the dates of which are given variously as between the 8th century BC and the 2nd century BC, in India, contains a list of Pythagorean triples discovered algebraically, a statement of the Pythagorean theorem, and a geometrical proof of the Pythagorean theorem for an isosceles right triangle. Euclid’s formula is altered a little and is expanded with a variable ‘x’. So, the set of Pythagorean triples is precisely the set of integer triples in the range of the function T:Z3 → Q3. The multiples of (a,b,c), (ie. 18, 24, 30 17. 8, 15, 17 4. Learn how to work with Pythagorean Triples instead of using the pythagorean theorem in this free math video tutorial by Mario's Math Tutoring. Such a triple can be produced from two integers m and n, using the Euclid formula. We obviously don't want to test a combination twice, and therefore we'll use a trick similar to the one we saw in the previous example:. Pythagorean Triples. They have variously interpreted the cryptic columns of numbers, written in the wedge-shaped script called cuneiform, as a trigonometric table or a sophisticated scheme for generating Pythagorean triples. The difference between c and b is 8 suggesting the modification-. Any Pythagorean triple with two numbers sharing a factor can be reduced to a primitive triple. Any triangle whose sides are in the ratio 3:4:5 is a right triangle. Step 3: Simplify the equation by distributing and combining like terms as needed. Some explanation of why these triples are called Pythagorean. Algebra Name_____ The Pythagorean Theorem Date_____ Period____ Discovering the Pythagorean Theorem - Gamma Teacher guide Discovering the Pythagorean Theorem T-3 Instead, help students to make further progress by summarizing their difficulties as a list of questions Some suggestions for these are given in the Common issues table on the next page We. Today's exercise feels like a Project Euler problem: A pythagorean triple consists of three positive integers a, b and c with a < b < c such that a2 + b2 = c2. What is the Pythagorean Theorem?(word form and algebraic form) A: The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides. the nearest tenth of a centimeter on the triangle. Born in 580 B. DA: 14 PA: 54 MOZ Rank: 75. Your program should prompt the user for given value and should provide a list of all the Pythagorean Triples in the given range. This is usually expressed as a 2 + b 2 = c 2. Next, 51 = 3 \times 17 and both 3 and 17 are primes; thus 255 = 3 \times 5 \times 17 and we say that 3, 5 and 17 are the prime factors of 255. KZN DEPARTMENT OF EDUCATION The Theorem of Pythagoras Grade 9 GENERAL EDUCATION AND TRAINING (GET) These groups of three numbers are called Pythagorean triples. Observing that (da,db,dc) is also. Pythagorean Triples are positive integers that satisfy the Pythagorean Theorem, and any multiples of these numbers also fulfill the Pythagorean Theorem. The first triangular numbers are 1, 3, 6 and 10. For example, (6, 8, 10) is a trivial triple because it's a multiple of the smaller triple (3, 4, 5). It can be proven that there are exactly eight Pythagorean triples for a right triangle with a perimeter of 840 units. The proof of the Flatiron building's right triangle nature is based on the Pythagorean theorem — the statement that for a right triangle with legs (shorter sides) of lengths a and b, and. There are 16 primitive Pythagorean triples with c ≤ 100: ( 3, 4, 5) ( 5, 12, 13) ( 7, 24, 25) ( 8, 15, 17) ( 9, 40, 41) (11, 60, 61) (12, 35, 37) (13, 84, 85) (16, 63, 65) (20, 21, 29) (28, 45, 53) (33, 56, 65) (36, 77, 85) (39, 80, 89) (48, 55, 73) (65, 72, 97) #include. 3-4-5 is an example of the Pythagorean Triple. The a side is the shorter of the two. Thus (8, 15, 17) must be a Pythagorean triple and 8^2 + 15^2 = 17^2 because of the identity (x^2+y^2)^2 = (x^2-y^2)^2 + (2xy)^2. The whole numbers a, b, c are a Pythagorean triple if a and b are the lengths of the two sides of a right-angled triangle with hypotenuse c, so by Pythagoras' Theorem, a² +b² =c². Your name: File: Open code-statistics: Language is selected by the extension of the file. Students will learn: how to use the Pythagorean Theorem to find the missing side lengths of a right triangle (legs and hypotenuse) using simplifying radical skills (6 problems)about Pythagorean Triples and list multiples of common triplesto determine if the. Even this exact triple may leave the gears able to slip past one another due to the possibility of axles wobbling in liftarm holes, etc. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). thagorean triple is again a Pythagorean triple, and that every Pythagorean triple is a multiple of a primitive one. Almost everyone knows of the "3-4-5 triangle," one of the right triangles found in every draftsman's toolkit (along with the 45-45-90). Solution 1371916. If the side lengths of a right triangle are all integers, we call them Pythagorean triples. For example, the (3, 4, 5) right triangle is a famous Primitive Pythagorean Triple. This study has very ancient origins. Pythagoras and the Mystery of Numbers. Adjust the sliders to change the generating integers and see which of the tests are satisfied by the triple generated. A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Got it Missed it. so a Pythagorean triple is in the form: a=m^2 - n^2. (b) Notice that 3 · 4 · 5 = 60. 27 An alternative characterisation of all primitive Pythagorean triples. If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. State if the missing side was a leg or the hypotnuse. A Pythagorean triple is a set of three natural numbers, a < b < c, for which. Thus, is a primitive Pythagorean triple if. Yes, it is a Pythagorean Triple! Triangles. All though the classical formulas produce all primitive triples, which do not generate all possible triples, specially non-primitive triples. a c b Example Problems 13 12 x From the list above, the missing side is “24” Show why the set “6,8. A "side based" right triangle is one in which the lengths of the sides form a whole number ratio, such. 28, 45, 53 9. If m and n are any integers, m > n, then {2mn, m² − n², m² + n²} is a Pythagorean triple. The Pythagorean Theorem says that for any right triangle, the square of the hypotenuse’s length is equal to the sum of the squares of the two legs. Definition of pythagorean triple in the Definitions. For example, 3² + 4²= 9 + 16 = 25 = 5². For example, 3 - 4 - 5. Choose from 500 different sets of term:pythagorean triples = 6 8 10 flashcards on Quizlet. Given a primitive Pythagorean triple a, b, c we show how to write the equations of the two. real number: Contains the set of rational numbers and the set of irrational numbers. Pythagorean triples with the help of a parametrized curve. apologiabiology +38 Kaneppeleqw and 38 others learned from this answer If the 2 legs are length a and b and hypotonuse is length c then. With the starting value (3,4,5), the first is the smallest. Since the number 101 is prime and the greatest member of a Pythagorean triple, then it must belong to a primitive pythagorean triple. Created: Oct Save for later. {9, 40, 41} since 1600+ 81 =1681. Solution Compare the side lengths. There exist infinitely many Pythagorean triples in which the two legs differ by exactly one. A Pythagorean triple consists of three positive integers a, b, and c, such that a 2 + b 2 = c 2. It can be used to locate Pythagorean Triples of significant size. There may be some way to cut down the solution space more easily than I did, but I still got this fairly quickly. What is the Pythagorean Theorem?(word form and algebraic form) A: The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides. This ratio, also known as the "pure" perfect fifth, is chosen because it is one of the most consonant and easiest to tune by ear and because of importance attributed to the integer 3. Determine whether each set is a Pythagorean triple. i'm trying to create a function of Pythagorean triples, i need to be able to input the sum of the sides (a,b,c) into my function and retrieve an output of all the different combinations of sides that add to that sum. (You may like to read about Pythagoras' Theorem or an Introduction to Pythagorean Triples first) A "Pythagorean Triple" is a set of positive integers, a, b and c that fits the rule: a2 + b2 = c2. The most common Pythagorean triples are (3,. There are no list comprehensions in Nim, but thanks to the strong metaprogramming capabilities we can implement our own: import macros type ListComprehension = object var lc*: ListComprehension. 4, 5 and 6 are not pythagorean triple. A Pythagorean triple consists of three positive integers a, b, and c, such that a 2 + b 2 = c 2. The first four Pythagorean triple triangles are the favorites of geometry problem-makers. (I did the latter and then checked it with the. For example, 3^2 + 4^2 = 5^2. Any Pythagorean triple with two numbers sharing a factor can be reduced to a primitive triple. Pythagorean Triples. For a complete lesson on Pythagorean Triples, go to https://www. Tell whether the side lengths form a Pythagorean Triple. BYJU'S online Pythagorean triples calculator tool makes the calculation faster, and it displays the result in a fraction of seconds. Use the method of the example in question 2. If the lengths of the legs in a right triangle are 7 and 8, what is the approximate length of the hypotenuse? (1 point) asked by Delilah on October 17, 2012. Use the method of the example in question 2. A Pythagorean triple is a set of three natural numbers, a < b < c, for which. , if no two of them. However, right triangles with non-integer sides do not form Pythagorean triples. It even lists Pythagorean Triples in columns. Given input n, output the nth PPT. A right triangle can have sides that are all integers. It improves the security and In order to construct all primitive Pythagorean triples (a, b, c) with a, c odd and b even are obtained by switching a, b. I used a computer to substitute in values for a and b and checked if a2 +b2. the entries as, in effect, Pythagorean triples: integer solutions of the equation a 2+b =c2. A "Pythagorean Triple" is a set of positive integers, a, b and c that fits the rule: a 2 + b 2 = c 2. In the list of the first few Pythagorean triples (a, b, c), we find (3, 4, 5), (5, 12, 13), (7, 24, 25), and (9, 40, 41). 36 + 64 = 100. The examples of theorem based on the statement given for right triangles is given below: Consider a right triangle, given below: Find the value of x. 1: A Sampling of Similar Areas 89 3. You can select whether you want all results shown, or just the non-trivial ones. Show that a multiple of a Pythagorean Triple is also a Pythagorean Triple. A triple of integers is a primitive Pythagorean triple if and only if it may be written in the form or , where are relatively prime positive integers of different parity. Remember that a and b are the legs and c is the hypotenuse (the longest side or the side opposite the 90º angle). Evidence from megalithic monuments on the British Isles shows that such triples were known before the discovery. I like "triplets," but "triples" seems to be the favored term. If both m and n are odd, then a, b, and c will be even, and so the triple will not be primitive; however, dividing a, b, and c by 2 will yield a primitive triple if m and n are. Check out Pythagorean Triple by Jesse Langen on Amazon Music. C# Pythagorean Triples) A right triangle can have sides whose lengths are all integers. If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. ” It stated that, in order to get the measure of the hypotenuse of any right triangles, the sum of the squares of the other sides (legs) had to be calculated. Trivial Pythagorean Triples are multiples of other triples. By definition, twin triplets are therefore primitive triples. We can check it as follows: 3 2 +4 2 = 9 + 16 = 25 = 5 2 so a 2 + b 2 = h 2. For example, (6, 8, 10) is a trivial triple because it's a multiple of the smaller triple (3, 4, 5). This lesson explores some patterns found in Pythagorean Triples. 18 18 14 85% of 500 2,316 elexie 4 Issues Reported. The general formula that can be derived to figure out when a triple occurs is: a= (A 2 -B 2) b= (2AB) c= (A 2 +B 2 ). 4 ⋅ 15 = 60 and 5 ⋅ 15 = 75. A primitive Pythagorean triple is one in which a, b and c are coprime (that is. The list only contains the first set (a,b,c) which is a Pythagorean triple (primitive Pythagorean triples). Brought to you by you: h. Ron Knott, Pythagorean Triples and Online Calculators. Yes, it is a Pythagorean Triple! Triangles. where u and v are coprime, positive integers. If a, b, and c are relatively prime in pairs then (a, b, c) is a primitive Pythagorean triple. I could not run my calculations long enough without hitting precision issues, but there is a theoretical basis to a belief that the calculated value tends to 3(3-2sqrt(2)) as this is the scale factor of a classical 4-vertex octahedral graph based on octahedral expansion, so by extension also the scale factor of a 'rolled' out one like the. For example, 3-4-5 is a Pythagorean Triple. For example, a right triangle may have angles that form a simple ratio, such as 45-45-90. The Pythagorean theorem, which could be tested in a more evidence-based model, states that the square of the hypotenuse of a right triangle is the sum of the squares of its two legs. Find a Pythagorean triple. Split pythagorean triples into two sets Why does BrickLink postpend a -1 to so many set numbers? Freely available translations of the Dhammapada. The formula and proof of this theorem are explained here with examples. Full text of "Pythagorean Triples and a New Pythagorean Theorem" See other formats Pythagorean Triples and A New Pythagorean Theorem H. (Pythagorean Triples) A right triangle can have sides that are all integers. If one begins with primitive triple [3, 4. Submitted on 24 Oct 2018 by Fatemeh Allahdadi. While c = sqrt (a^2+b^2). Integer triples which satisfy this equation are Pythagorean triples. If a Pythagorean triple is not a proper multiple of of another triple, it is said to be primitive. This triangle is different from most right triangles because it has three integer edges. pdf), Text File (. The Pythagorean Theorem can be usefully applied because the relationship between the lengths of the sides in any right triangle is consistent. A right triangle whose side lengths give a primitive Pythagorean triple is then known as a primitive right triangle. There are more than 300 proofs of the Pythagorean theorem. Stream ad-free or purchase CD's and MP3s now on Amazon. Explore patterns for triples of positive integers which satisfy $$x^2-xy+y^2=z^2$$. From there, we just have to calculate each multiple to get a list of all Pythagorean triples with perimeters less than a given value:. Triple" is a set of positive integers, a, b and c that fits the rule: a2+ b2= c2. Which also fits the formula a 2 + b 2 = c 2: 6 2 + 8 2 = 10 2. When we further inspect the list of Pythagorean triples in table 9. Let [a, b, c] be a primitive triple with a odd. In a lot of these scenarios, we might only know the value of c , and have to figure out what the value of a and b are. (2) Received: January 8, 2007 c 2007. As for your actual question the following should be an equivalent list comprehension to print out out the Pythagorean triples up til n:. Generate Pythagorean triples using Euclid's formula. For example, (6, 8, 10) is a family of the Pythagorean triple (3, 4, 5) because it can be obtained by 2 × 3 = 6, 2 × 4 = 8, 2 × 5 = 10. When a, b and c are whole numbers then the triangle is an integer right triangle and the triple (a, b, c) is called a "Pythagorean Triple," as you learned in Lesson 2. Suppose we have a set of three (3) positive integers, ( a, b, c) \left ( {a,b,c} \right) (a,b,c) they are Pythagorean Triples if it satisfies the equation, a 2 + b 2 = c 2. The main aim of this paper is to present an analytic result which characterizes the Pythagorean triples via a cathetus. So, for example a possible pythagorean triple would be (3, 4, 5) or (5, 12, 13) with respect to the Pythagorean theorem (x^2 + y^2 = z^2). All triples are a multiple of some primitive triple. Also, (12, 16, 20) is a Pythagorean Triple. hypotenuse. proof of Pythagorean triples. Since the number 101 is prime and the greatest member of a Pythagorean triple, then it must belong to a primitive pythagorean triple. In mathematics, a tree of primitive Pythagorean triples is a data tree in which each node branches to three subsequent nodes with the infinite set of all nodes giving all (and only) primitive Pythagorean triples without duplication. The sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse. numbers of same parity that will produce a given Pythagorean triple using Euclid’s construction. Email This BlogThis! Share to Twitter Share to Facebook Share to Pinterest. In general, once you have a triple, you can multiply this triple by any positive integer to generate another one. That means that any Pythagorean triple where one of the members is prime is an irreducible triple. 1 Pythagorean triples 4. Grade 8 - Unit 1 Square roots & Pythagorean Theorem Name: _____ By the end of this unit I should be able to: Determine the square of a number. A right triangle can also be isosceles if the two sides that include the right angle are equal in length (AB and BC in the figure above) A right triangle can never be equilateral , since the hypotenuse (the side opposite the right angle) is always longer than either of the other two sides. Find a Pythagorean triple. , 1, 3, 6, 10, 15, 21, etc. These four triangles are all members of the (3,4,5) family. (2) Received: January 8, 2007 c 2007. If the lengths of the legs in a right triangle are 7 and 8, what is the approximate length of the hypotenuse? (1 point) asked by Delilah on October 17, 2012. Fill in the blank to complete the definition of a Pythagorean Triple. Question: Instructions A "Pythagorean Triple" Is A Set Of Positive Integers, A, B And C That Fits The Rule: A2+ B2= C2 Here Is A List Of A Few Pythagorean Triples (3. Show all of your work for full credit. Solution 1206548. Though this classical formula. Pythagorean Triple Worksheets Lesson Worksheets; Pythagorean Theorem Worksheets Math Worksheets 4 Kids; 40 Sample Pythagorean Theorem Worksheet Templates In; 48 Pythagorean Theorem Worksheet With Answers Word; Pythagorean Triples Math; Pythagorean Triples List Examples Definition Video; Applications Of The Pythagorean Theorem Worksheets. Numbers that are not pythagorean triples are due to not working in the formula, or due to not being positive integers. This property of invariance under scaling is a characteristic feature of solutions. Here a=5,b=3 and c=4. You can select whether you want all results shown, or just the non-trivial ones. Take a look at the official python documentation for list comprehensions it explains how they work really well. The examples of theorem based on the statement given for right triangles is given below: Consider a right triangle, given below: Find the value of x. Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Ron Knott, Pythagorean Triples and Online Calculators. Any pythagorean triple is in form of$$ k(u^2 - v^2), 2kuv, k(u^2 + v^2) where u, v, and k are positive integers with u > v, u − v odd, and with u and v coprime. + n = (n (n+1))/2. A right triangle can also be isosceles if the two sides that include the right angle are equal in length (AB and BC in the figure above) A right triangle can never be equilateral , since the hypotenuse (the side opposite the right angle) is always longer than either of the other two sides. If there exists any such value, then there is a Pythagorean triplet. Now, we know that pythagorean triples (a,b,c) correspond to the set of rational points on the circle, 3. The example did put the rows of the matrix on (by Michael2_3B 20 Jun 2020 02:44, posts: 7). The most famous is the 3-4-5. One side may have two of these divisors, as in (8, 15, 17), (7, 24, 25), and (20, 21, 29), or even all three, as in (11, 60, 61). ; pythagorean_triples n = ; nubBy. ~ 400 BCE: Plato gave a method for finding Pythagorean triples that combined algebra and geometry. By an almost isosceles pythagorean triple (AI-PT), we mean an integer solution (a, b, c) of x 2 + y 2 = z 2 such that a and b differ by only 1. For initial positive integers hn and hn+1, if hn + hn+1 = hn+2 and hn+1 + hn+2 = hn+3, then is a Pythagorean triple. Pythagorean triples are the values of hypotenuse, base and perpendicular which tend to represent a right-angled triangle. Pythagorean triple. Also, with the help of the first Pythagorean triple, (3,4,5): Let n be any integer greater than 1: 3n, 4n and 5n would also be a set of Pythagorean triple. For a complete lesson on Pythagorean Triples, go to https://www. After his permission I post it here. ) There is an easy way to create infinitely many Pythagorean triples. Example: scale 3,4,5 by 2 gives 6,8,10. 2] Pythagorean Triples 18 name: A primitive Pythagorean triple (or PPT for short) is a triple of num-bers (a;b;c)so that a, b, and chave no common factors1 and satisfy a2 +b2 = c2: Recall our checklist from Chapter 1. Pythagorean Triples with Common Sides Raymond Calvin Ochieng , 1 Chiteng’a John Chikunji, 2 and Vitalis Onyango-Otieno 1 1 Strathmore Institute of Mathem atical Sci ences, Nairobi, Ke nya. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. REFERENCES: A. A Pythagorean Triple is a triple of positive integers a,b,c such that a 2 +b 2 =c 2. For example, the triple (6,8,10) is (3 x 2, 4 x 2, 5 x 2). So you have a, b, and c which are all positive integers. DA: 14 PA: 54 MOZ Rank: 75. In fact, all primitive Pythagorean triples can be generated in this way from the triple (3, 4, 5), and every triple is obtained exactly once. If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. Pythagorean Triplets generator. c 2 = a 2 + b 2 c 2 = 25 2 + 25 2. a triple of graphs obtained by gluing copies of a graph in some manner realize a Pythagorean triple. Whena and b are relatively prime, the triple is a primitive PT (PPT). Step 4: Solve the equation. A primitive Pythagorean triple is one in which a, b and c (the length of the two legs and the hypotenuse, respectively) are co-prime. Pythagorean Triple Worksheets Lesson Worksheets; Pythagorean Theorem Worksheets Math Worksheets 4 Kids; 40 Sample Pythagorean Theorem Worksheet Templates In; 48 Pythagorean Theorem Worksheet With Answers Word; Pythagorean Triples Math; Pythagorean Triples List Examples Definition Video; Applications Of The Pythagorean Theorem Worksheets. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. The proof is intuitively discussed below. However, Pythagorean. $\endgroup$ - justhalf 2 hours ago. Let (a, b, c) be an AI-PT with b = a + 1. If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. Determine 7 such triples. Making statements based on opinion; back them up with references or personal experience. Article Here is a more complete list up to 10,000 [with thanks to Tom Wallett] (2. The Pythagorean Inequality is a generalization of the Pythagorean Theorem, which states that in a right triangle with sides of length we have. Use the Pythagorean Theorem to confirm that your measurements are accurate. The smallest Pythagorean triple is a triangle in which a=3, b=4, and c=5. You can select whether you want all results shown, or just the non-trivial ones. The multiples of (a,b,c), (ie. Two other commonly used Pythagorean Triples are (8, 15, 17) and (7, 24, 25). Pythagorean triple. Solution 1387484. 7, 24 and 25 are also Pythagorean triples; so. In other words, a Pythagorean triple represents the lengths of the sides of a right triangle where all three sides have integer lengths. Submitted on 7 Dec 2017 by Remi Decorsiere. (e)Prove that your conditions in (d) really work. PythagoreanTriplesGrid. Let be a Pythagorean triple (PT), that is, , , and are positive integers such that. (Ï3w5w)2 0 42 1 52 Substitute Ï3w5w for c, 4 for a, and 5 for b. It is very useful in times of examination. So, x = 2(25) = 50. 6 Proof of Pythagorean Theorem (Indian). Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). An example of a Pythagorean Triplets is 3, 4 and 5 because 3² + 4² = 5², Calculating this becomes: 9 + 16 = 25 a Pythagorean Triple! But 5, 6 and 7 is not a Pythagorean Triplet because 5². Fill in the blank to complete the definition of a Pythagorean Triple. A Pythagorean triple is an integral solution (a, b, c) (a, b, c) to the Diophantine equation a 2 + b 2 = c 2 a^2 + b^2 = c^2. Or stated in other words a,b,c are coprimes. A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. It defines a Pythagorean triple (PT) as a sequence of three positive integers such that a2 + b2 = c2. Also assumethat gcd(a,b,c) = 1. I am puzzling about a way to do this. In India, the Baudhayana Sulba Sutra, the dates of which are given variously as between the 8th century BC and the 2nd century BC, contains a list of Pythagorean triples discovered algebraically, a statement of the Pythagorean theorem, and a geometrical proof of the Pythagorean theorem for an isosceles right. A Pythagorean triple consists of three positive integers a, b, and c, such that a 2 + b 2 = c 2. Any Pythagorean triple with two numbers sharing a factor can be reduced to a primitive triple. However, right triangles with non-integer sides do not form Pythagorean triples. Pythagorean Triple Worksheets Lesson Worksheets; Pythagorean Theorem Worksheets Math Worksheets 4 Kids; 40 Sample Pythagorean Theorem Worksheet Templates In; 48 Pythagorean Theorem Worksheet With Answers Word; Pythagorean Triples Math; Pythagorean Triples List Examples Definition Video; Applications Of The Pythagorean Theorem Worksheets. This is important since we know that all solution. Euclid's formula generates a Pythagorean triple for every choice of positive integers and. This is usually expressed as a 2 + b 2 = c 2. Algebra Name_____ The Pythagorean Theorem Date_____ Period____ Discovering the Pythagorean Theorem - Gamma Teacher guide Discovering the Pythagorean Theorem T-3 Instead, help students to make further progress by summarizing their difficulties as a list of questions Some suggestions for these are given in the Common issues table on the next page We. The whole numbers a, b, c are a Pythagorean triple if a and b are the lengths of the two sides of a right-angled triangle with hypotenuse c, so by Pythagoras' Theorem, a² +b² =c². Submitted on 16 Dec 2017 Size: 0; Leading solution size is 8. , a triple with no common factor greater than 1. A Pythagorean triplet is a set of three natural numbers, a < b < c, for which, a² + b² = c². Pythagorean Triples. German-English Dictionary: primitive Pythagorean triple » Tabular list of translations | always » List of translations starting with the same letters. Definition of pythagorean triple in the Definitions. Pythagorean Theorem AEL Math Prepared by Mary Jones OVERVIEW & PURPOSE This lesson will teach you about Pythagorean theorem. It lists all the primitive and non-primitive Pythagorean triples, sorted by the shortest side, from 3 to 50.
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## Abstract
Many features can describe a concept, but only some features define a concept in that they enable discrimination of items that are instances of a concept from (similar) items that are not. We refer to this property of some features as feature diagnosticity. Previous work has described the behavioral effects of feature diagnosticity, but there has been little work on explaining why and how these effects arise. In this study, we aimed to understand the impact of feature diagnosticity on concept representations across two complementary experiments. In Experiment 1, we manipulated the diagnosticity of one feature, color, for a set of novel objects that human participants learned over the course of 1 week. We report behavioral and neural evidence that diagnostic features are likely to be automatically recruited during remembering. Specifically, individuals activated color-selective regions of ventral temporal cortex (specifically, left fusiform gyrus and left inferior temporal gyrus) when thinking about the novel objects, although color information was never explicitly probed during the task. Moreover, multiple behavioral and neural measures of the effects of feature diagnosticity were correlated across participants. In Experiment 2, we examined relative color association in familiar object categories, which varied in feature diagnosticity (fruits and vegetables, household items). Taken together, these results offer novel insights into the neural mechanisms underlying concept representations by demonstrating that automatic recruitment of diagnostic information gives rise to behavioral effects of feature diagnosticity.
## INTRODUCTION
Any concept, such as a lion, can be described by a list of properties or features, and these features will vary in terms of how common they are among concepts (e.g., alive), how unique they are (e.g., king-of-the-jungle), how strongly associated they are with the concept (e.g., loud-roar), how behaviorally relevant they are (e.g., attacks-humans), and so on. For any given pair of concepts (e.g., lion and tiger), some features will be diagnostic for distinguishing between them (e.g., has-stripes) and others will not (e.g., has-fur). The goal of these studies is to understand the impact that these sorts of variables have on the representation of concepts, and our specific focus is on the notion of feature diagnosticity. The diagnostic feature in question is color, motivated in part by the growing literature showing that visual brain systems are recruited when thinking about concepts that have a specific visual feature (e.g., recruiting color-sensitive brain areas when participants remember colorful concepts like fruits; Hsu, Frankland, & Thompson-Schill, 2012; Hsu, Kraemer, Oliver, Schlichting, & Thompson-Schill, 2011; Simmons et al., 2007; Chao & Martin, 1999; Martin, Haxby, Lalonde, Wiggs, & Ungerleider, 1995).
There are a number of studies that describe the effects of diagnosticity on behavior; however, we do not believe that there currently exists a mechanism to explain how or why these effects arise. For example, although participants can perceive diagnostic features of an object as easily as nondiagnostic features, they selectively attend to those features that are most useful for discrimination (Schyns, 1998). Participants name objects with highly diagnostic colors faster and with fewer errors than for objects with nondiagnostic colors (Tanaka & Presnell, 1999), whereas children can be trained to attend to object shape in the context of naming, leading to faster object naming times (Smith, Jones, Landau, Gershkoff-Stowe, & Samuelson, 2002). Furthermore, feature verification tasks have shown that diagnostic features hold a privileged status in an object's overall representation, as participants' responses were faster when the feature was diagnostic of the concept than when the feature was shared among other category members (Cree, McNorgan, & McRae, 2006). We find these results intriguing, but lacking in providing a mechanism as to why feature diagnosticity affects behavior the way it does.
Similarly, there are a handful of neurophysiological findings that examine the impact of feature diagnosticity on neural measures. Single-unit and local field potential studies have shown selective tuning of neurons in response to relevant features. In macaque monkeys, inferotemporal (IT) neurons showed an increased response to diagnostic features, depending on the importance of those features for object categorization (Sigala & Logothetis, 2002). Neurons in the anterior IT cortex also responded similarly to images showing either 10% or 50% relevant information (Nielsen, Logothetis, & Rainer, 2006). This region-specific insensitivity to the stimulus image itself was coupled with a graded response to behaviorally relevant features in the posterior IT cortex. Thus, stimulus features can be preferentially represented if they are diagnostic for a behavior, and the neural representation of an object can be influenced by both visual experience and viewing history.
These studies provide descriptions rather than explanations of diagnosticity effects; in part, these effects are difficult to understand because so many variables are confounded in conceptual structure. To measure the impact of a single variable—feature diagnosticity—on concept representations, we created and taught participants a set of novel objects. In this way, we could control the structure of the conceptual space and thereby eliminate those confounds that are unavoidable with real-world objects (Kiefer, Sim, Liebich, Hauk, & Tanaka, 2007; Weisberg, van Turennout, & Martin, 2007; Grossman, Blake, & Kim, 2004; James & Gauthier, 2003). For example, “barks” is a diagnostic feature of dogs, but it is also an uncommon feature in the animal kingdom; the object concepts in our artificial world have features varying in diagnosticity while holding frequency constant.
The experiments described here employ both univariate and multivariate techniques to measure the impact of feature diagnosticity on concept representations. Recent neuroimaging studies utilizing multivariate methods have demonstrated that patterns of brain activation, as opposed to averaged overall regional activation, can carry meaningful information (Kamitani & Tong, 2005; Cox & Savoy, 2003; Haxby et al., 2001). Multivariate analyses have been used to decode categories of remembered stimuli (Polyn, Natu, Cohen, & Norman, 2005), compare similarity of disparate categories (O'Toole, Jiang, Abdi, & Haxby, 2005), and decode neural similarity within a single object category of abstract shape (Op de Beeck, Torfs, & Wagemans, 2008) or a single natural category of mammals (Weber, Thompson-Schill, Osherson, Haxby, & Parsons, 2009). These multivariate analyses add a complementary approach to the extant fMRI literature (Jimura & Poldrack, 2012).
In Experiment 1, participants learned a set of 12 novel objects. Half of the participants learned that the conjunction of color and shape was diagnostic of object category (henceforth referred to as the CS group); the other half of the participants learned that shape was sufficient to distinguish among the set of objects (the S group). Critically, we matched color variability among both sets (two objects were purple, two objects were green, etc.). Following training, we collected a variety of behavioral measures, and we measured fMRI responses during a test for memory of the shape of the objects. We hypothesized that accessing diagnostic feature information would result in group differences behaviorally and neurally; specifically, we would observe group differences in the activation of color-selective brain regions. Both behavioral and neural measures revealed effects of our manipulation of feature diagnosticity. Participants in both groups learned the colors of the objects equally well; however, compared with S participants, CS participants more frequently used color to describe the objects. Moreover, they activated ventral temporal cortex (specifically, left fusiform gyrus and left inferior temporal gyrus) even when color information was not explicitly probed. Furthermore, a multivariate measure of neural similarity predicted color similarity ratings for the CS group only. Experiment 2 examined relative color association in familiar object categories: fruits and vegetables (FV) and household items (HHI). In addition to providing a useful test of the generalization of the Experiment 1 results to a separate set of categories, Experiment 2 replicated many results from Experiment 1 and provided some interesting contrasts. Together, our results suggest that diagnostic features are more likely to be accessed automatically than are nondiagnostic features during remembering and that automatic recruitment of diagnostic information gives rise to the behavioral effects of feature diagnosticity. The features that we use to categorize objects—and not simply the features that we explicitly remember about objects—shape the neural representations of object concepts.
## METHODS
### Experiment 1
#### Participants
Sixty-three healthy individuals participated in the study (17 men, 46 women; average age = 22.8 years, range = 18–30 years). Thirty-two (n = 32) of these individuals participated in the subsequent fMRI portion of the study (9 men and 23 women; average age = 24.7 years, range = 18–30 years). All participants were right-handed, native speakers of English and were not taking any psychoactive medications over the course of the study. Those individuals participating in the fMRI portion had no history of neurological disorders and a healthy neurological profile. We paid participants $10/hr for behavioral portions of training and$20/hr for participating in the fMRI portion. Participants provided written informed consent, and the human subjects review board at the University of Pennsylvania approved all experimental procedures.
#### Training Materials and Procedure
In a between-subject design, participants were randomly assigned to learn one of two object sets. In the “color + shape” (CS) set, color is necessary for object identification, and shape information is not sufficient (e.g., objects have similar shapes but differ in color, like lemons and limes). In the “shape” (S) set, color is available for object identification, but shape information is sufficient (e.g., objects differ in both shape and color, like stop signs and yield signs). Participants learned one of these object sets over the course of four 30- to 60-min training sessions that took place over 7 days.
##### Stimuli
For either object set, as shown in Figure 1, participants were trained on a set of 36 exemplars of 12 distinct object basic level categories (three exemplars per category). Each category had a pseudoword name (Rastle, Harrington, & Coltheart, 2002). Stimuli were created from scratch in Blender 2.48 (www.blender.org). All objects were given the same surface texture and illuminated with the same single light source. For object shape, we created 4 shape variants for the CS set and 12 shape variants for the S set (four of these shape variants overlapped with those in the CS set: fulch, hinch, klarve, screll). For object size, we created two additional size variants for each exemplar by halving or doubling the scale of the object, thus creating three possible sizes for each object. Size was an irrelevant dimension for object identification but did serve to distinguish the individual exemplars within each basic category. For object color, we used Blender's HSV color space, in which color is determined from a set of three values, one each corresponding to hue, saturation, and value (or luminance). We held saturation and value constant, varying hue to create six distinct color categories for the objects.
Figure 1.
Exemplars from the CS and S objects, demonstrating set differences.
Figure 1.
Exemplars from the CS and S objects, demonstrating set differences.
The differences in the sets are summarized in Figure 1. Two properties are critical between the two sets. First, note that to identify successfully each object by distinguishing it from the others in the set (i.e., when P(object) = 1.00), the CS set requires the conjunction of shape and color information, whereas the S set only requires shape information. Second, color probability (i.e., that P(object|color) = 0.50) is matched between the two groups. Thus, the two groups differ in terms of fixed diagnosticity (with color for CS objects being relatively more diagnostic than color for S objects).
For each of the 36 exemplars, we created 10-sec videos of each exemplar rotating 360° counterclockwise on a raised, black platform against a gray background. For all behavioral tasks described below, we used PsyScope (psy.cns.sissa.it) to present stimuli and collect responses and RTs. The training schedule and list of tasks can be found in Table 1.
Table 1.
Participant Training Schedule
Session
12345
Training
Training videos ♦ ♦ ♦
Naming task ♦ ♦ ♦ ♦
Testing
Pairwise similarity ♦
Explicit color naming ♦
Session
12345
Training
Training videos ♦ ♦ ♦
Naming task ♦ ♦ ♦ ♦
Testing
Pairwise similarity ♦
Explicit color naming ♦
The specific combination of tasks is indicated for each session of the experiment.
##### Training, video exposure
Participants viewed a randomized sequence of videos, with each video individually presented. Each video was shown twice. This sequential presentation resulted in 72 videos that played for approximately 12 min. While each video played, the exemplar name appeared below, and participants were instructed to repeat aloud the name of the object currently being viewed. Participants watched the videos at the beginning of the first, second, and third sessions.
##### Training, naming
We assessed knowledge of the novel objects through a naming task. Immediately after viewing the object videos, participants saw a screenshot of each of the 36 exemplars. Upon typing that exemplar's name, they were given corrective feedback. Subjects participated in the naming task during each training session, viewing a total of 12 trials of each object category across all four sessions. We used four unique screenshots for each exemplar (at the 50th, 100th, 150th, and 200th frame of the video, counterbalanced across the size variants for each object), such that participants never viewed identical images for the same exemplar (or for the same object) during this task. Three participants who did not exceed 80% accuracy on recalling object names (measured via the naming task) during the fourth session were excluded from further analysis.
Feature listing has previously been used as a measure of diagnosticity (Tanaka & Presnell, 1999), where features considered to be diagnostic are listed earlier and more often than other features. For each trial of this task, we presented participants with an object name. They were instructed to list two to four adjectives describing the object. Participants could proceed at their own pace by pressing the ENTER key to proceed to the next trial. We administered this task last during the third session.
##### Testing, pairwise general similarity task
We assessed psychological similarity by having participants rate the general similarity of every pairing of the 12 learned novel objects, resulting in 66 pairwise ratings. For each trial of this task, we presented participants with a pair of object names, along with a scale numbered from 1 (very dissimilar) to 9 (very similar). Participants assigned each similarity rating at their own pace, and each response triggered the beginning of the next pairing. We administered this task during the fourth session, after the naming task but before the color naming task (see below). Note that participants were told to base their judgments on general similarity, and they were not asked to base their ratings on any particular object features.
At the end of the fourth session, the experimenter verbally named each of the objects individually. Participants were instructed to report the color that they associated with that object, and the experimenter recorded the response.
##### Untrained similarity rating
To assess the relationship between behavioral similarity and neural similarity, we obtained psychological similarity ratings based on perception (i.e., pictures) rather than memory (i.e., names) of the novel objects. Thus, we slightly modified the pairwise similarity task described earlier by having participants not previously trained on the objects (n = 32 total participants; n = 16 for each object set) view a pair of object images, side by side, along with a scale numbered from 1 (very dissimilar) to 9 (very similar). Participants performed two randomized block of 66 trials in which they based their ratings on either color or shape similarity. We randomized trial order within both blocks and counterbalanced block order of color or shape. Postexperiment debriefing revealed that the influence of the irrelevant feature on the current feature was minimal.
#### fMRI Procedure
This task was only given to the 32 participants who returned for the fifth and final session of the study. On each trial of the task, while undergoing fMRI, participants read a question about one of the learned objects (e.g., “If you flipped a YERTS over, would it stand up straight?”). There were 20 questions (see Table 2), and each set of 20 questions was asked about each of the 12 objects, resulting in 240 total questions asked of the objects.
Table 2.
Questions from the Shape Retrieval Task that Participants Performed while Undergoing fMRI
List of Questions for Experiment 1
Could you cut something with a CHULGE?
**Could you poke a hole with a CHULGE?
Could you roll a CHULGE down a hill?
Could you use a CHULGE as a weapon?
Does a CHULGE have corners?
**If you flipped a CHULGE over, would it stand up straight?
**Is a CHULGE bulging?
Is a CHULGE bumpy?
**Is a CHULGE cubic?
Is a CHULGE flimsy?
Is a CHULGE fragile?
Is a CHULGE made up of smaller parts?
Is a CHULGE rounded?
Is a CHULGE sharp?
Is a CHULGE symmetrical?
**Is a CHULGE tied together?
Would a CHULGE be easy to wrap up (e.g., as a present)?
Would you be able to spin a CHULGE?
Would you call a CHULGE curved?
**Would you consider a CHULGE to be flat?
List of Replacement Questions for Experiment 2
**Could you poke a hole in a piece of paper with a SPOON?
**Does a SPOON have any protrusions from its main body?
**If you flipped a SPOON upside down, would it stand up straight?
**Is a SPOON smooth?
**Is a SPOON square?
**Would you be able to pinch a SPOON with two fingers?
List of Questions for Experiment 1
Could you cut something with a CHULGE?
**Could you poke a hole with a CHULGE?
Could you roll a CHULGE down a hill?
Could you use a CHULGE as a weapon?
Does a CHULGE have corners?
**If you flipped a CHULGE over, would it stand up straight?
**Is a CHULGE bulging?
Is a CHULGE bumpy?
**Is a CHULGE cubic?
Is a CHULGE flimsy?
Is a CHULGE fragile?
Is a CHULGE made up of smaller parts?
Is a CHULGE rounded?
Is a CHULGE sharp?
Is a CHULGE symmetrical?
**Is a CHULGE tied together?
Would a CHULGE be easy to wrap up (e.g., as a present)?
Would you be able to spin a CHULGE?
Would you call a CHULGE curved?
**Would you consider a CHULGE to be flat?
List of Replacement Questions for Experiment 2
**Could you poke a hole in a piece of paper with a SPOON?
**Does a SPOON have any protrusions from its main body?
**If you flipped a SPOON upside down, would it stand up straight?
**Is a SPOON smooth?
**Is a SPOON square?
**Would you be able to pinch a SPOON with two fingers?
“Chulge” and “spoon” here are example items—we asked the same list of 20 questions of all 12 object categories in each experiment. The lists differ slightly across experiments to maintain plausibility. As such, for Experiment 2, we replaced questions from Experiment 1 that we did not think were suitable for the objects in Experiment 2. Those questions are indicated by **.
The trial structure was as follows: At the beginning of each trial, a “READY?” prompt appeared for 500 msec. A fixation cross then appeared for 500 msec, followed by the question about the object. While the question remained on the screen for 4500 msec, the participant was instructed to determine if the question referred to a plausible detail about the object's shape, responding “yes” or “no” via button press. At the end of the trial, a central fixation cross appeared for 500 msec, for a total trial duration of 6000 msec. Text was presented as white font on a black background.
Each participant completed four scanning runs of the shape retrieval task (approximately 9 min each) with 60 trials of the task per run. Using a rapid, event-related design, we presented a unique trial order to each participant, using Optseq2 (surfer.nmr.mgh.harvard.edu/optseq) to generate optimized pseudorandom stimulus presentation sequences. Experimental trials were intermixed with jittered fixation periods averaging 6 sec in length.
After completing the shape retrieval task, all participants completed the color perception functional localizer, which consisted of wheel-like visual stimuli that were made up of five smaller wedges and that were either colored or grayscale (Figure 4, top left). On any given trial, participants fixated on a dash at the center of the wheel and indicated whether the wedges making up the wheel proceeded in order from lightest to darkest (i.e., a luminance judgment). The methods used for this localizer were identical to those used previously (Hsu et al., 2011, 2012; Beauchamp, Haxby, Jennings, & DeYoe, 1999).
#### Image Acquisition
We acquired imaging data using a 3T Siemens Trio system with an eight-channel head coil and foam padding to secure the head in position. After we acquired T1-weighted anatomical images (repetition time [TR] = 1620 msec, echo time [TE] = 3 msec, inversion time [TI] = 950 msec, voxel size = 0.9766 mm × 0.9766 mm × 1.000 mm), each participant performed the shape retrieval task, followed by the color perception task, while undergoing BOLD imaging (Ogawa et al., 1993). We collected 870 sets of 42 slices using interleaved, gradient-echo, echoplanar imaging (TR = 3000 msec, TE = 30 msec, field of view [FOV] = 19.2 cm × 19.2 cm, voxel size = 3.0 mm × 3.0 mm × 3.0 mm). At least 9 sec of “dummy” gradient and radio-frequency pulses preceded each functional scan to allow for steady-state magnetization; no stimuli were presented, and no fMRI data were collected during this initial time period.
#### Neuroimaging Data Analysis
We analyzed the data offline using VoxBo (www.voxbo.org). Within VoxBo, we utilized a single scripting framework, which also called functions from SPM2 (www.fil.ion.ucl.ac.uk), and the FMRIB Software Library (FSL) toolkit (www.fmrib.ox.ac.uk/fsl). Anatomical data for each participant were processed using FSL to perform brain extraction (Smith, 2002), to correct for spatial inhomogeneities (Zhang, Brady, & Smith, 2001), and to perform nonlinear noise reduction (Smith & Brady, 1997). Using VoxBo, functional data were sinc interpolated in time to correct for the slice acquisition sequence, motion-corrected with a six-parameter, least squares, rigid body realignment routine using the first functional image as a reference. We then used SPM2 to normalize to a standard template in Montreal Neurological Institute (MNI) space. Using VoxBo, the fMRI data were smoothed using a 9-mm FWHM Gaussian smoothing kernel for univariate analyses, and with a 4-mm smoothing kernel for multivariate analyses. With VoxBo, following preprocessing for each participant, a power spectrum for one functional run was fit with a 1/frequency function, and this model was used to estimate the intrinsic temporal autocorrelation of the functional data (Zarahn, Aguirre, & D'Esposito, 1997).
We fit a modified general linear model (Worsley & Friston, 1995) to each participant's data, in which task trials were each modeled as separate event with a 6-sec duration and convolved with a standard hemodynamic response function. We included run effects (i.e., interrun scanner drift) and movement spikes (i.e., TRs wherein we detected >3.5 SD movement on a subject-by-subject basis) as covariates of no interest in the model. From this model, we computed parameter estimates for the task (compared with fixation baseline) at each voxel. These parameter estimates were included in the group-level random effects analyses described above.
### Experiment 2
#### Participants
Twenty-four (n = 24) healthy individuals participated in the study (8 men, 16 women; average age = 24.1 years, range = 20–34 years). Twelve individuals participated in both experiments.
#### Materials and Procedure
##### Stimuli
We selected 12 object categories from two taxonomies: FV and HHI. FV categories were apple, avocado, banana, beet, broccoli, carrot, cherry, lemon, lime, pumpkin, strawberry, and tomato. HHI categories were clock, comb, fork, knife, ladle, nail file, scissors, spatula, spoon, tongs, toothbrush, and tweezers. Just as the CS novel objects carried more diagnostic, associative color information relative to S objects, FV items carried more associative color information relative to HHI items. Note that FV and HHI taxonomies also differ in terms of relative diagnosticity (i.e., color vs. other semantic features), because other noncolor features also contribute to the overall representation.
In a parallel between-subject design as described in Experiment 1, participants were assigned to one of the two item sets. For the assigned item set, participants performed the adjective generation and pairwise similarity tasks, although we only describe the results of the adjective generation task here. When coding the descriptors from the adjective generation set, we included as color descriptors those that described surface properties (e.g., “shiny”). Unlike Experiment 1, for this experiment, we did not include the explicit color naming task nor did an independent set of participants perform the perceptual similarity task.
While participants underwent fMRI, we used the same shape retrieval task from Experiment 1. Of the 20 original questions, we modified those questions that would be implausible for any of the familiar object categories, replacing them with appropriate, plausible questions (see Table 2). The fMRI task procedure, followed by functional localizers, was otherwise identical to that described in Experiment 1.
## EXPERIMENT 1: NOVEL OBJECTS—RESULTS
### Effects of Feature Diagnosticity on Behavioral Measures
For naming task performance, we performed a mixed measures ANOVA (color + shape [CS], n = 29; shape [S], n = 34) on naming response accuracy, revealing a significant main effect of Stimulus Set, F(1, 61) = 11.42, p < .001, a significant main effect of Session, F(1.28, 78.00) = 98.53, p < .001, and a significant interaction of Stimulus Set and Session, F(1.28, 78.00) = 7.21, p < .01. Critically, by the end of training, both groups were equally proficient at correctly producing the names of the learned objects (CS: M = 97.4%, SE = 4.8%; S: M = 98.3%, SE = 2.9%; t(61) = 1.25, p > .2), such that any differences on subsequent tasks cannot be attributed to differences in how well both groups learned and knew the objects.
A similar ANOVA on RT revealed a significant main effect of Stimulus Set, F(1, 61) = 22.53, p < .001, a significant main effect of Session, F(1.11, 67.80) = 72.49, p = .001, but no interaction of Stimulus Set and Session, F(1.11, 67.80) = 1.49, p > .2. By the fourth session, the groups significantly differed in RT, with CS participants taking longer to produce the object names (average median RT for CS: 1417 msec, average median RT for S: 1077 msec; t(61) = 5.39, p < .001). The naming task results are shown in Figure 2.
Figure 2.
Behavioral performance on the naming task across training sessions. RT (left) and accuracy (right) performance are shown for both groups. The groups did not differ in accuracy by the end of training.
Figure 2.
Behavioral performance on the naming task across training sessions. RT (left) and accuracy (right) performance are shown for both groups. The groups did not differ in accuracy by the end of training.
### The Impact of Feature Diagnosticity on Conceptual Knowledge
We examined the effects of feature diagnosticity on three assessments of conceptual knowledge: (1) Did both groups of participants learn the colors of the novel objects? (2) Did both groups of participants prioritize color information equally? (3) Did both groups of participants use color information when considering the similarity of different objects to each other? When we asked participants to identify the color of a named object, both groups could do so equally well (CS: M = 93.4%, SE = 2.3%; S: M = 90.5%, SE = 1.9%; t(61) = 0.98, p > .3, ns). However, when we asked participants to describe the objects, CS participants offered a (correct) color adjective as their first response nearly twice as often as did the S participants (CS: M = 87.9%, SE = 4.0%; S: M = 44.6%, SE = 6.5%; t(61) = 5.44, p < .001) These results, shown in Figure 3, suggest that, although the groups remembered object color equally, they did not prioritize color information equally.
Figure 3.
The training groups differ in prioritization of color information. (Left) As measured by the frequency of listing color early in an adjective generation task, CS participants listed color as the first adjective earlier and more often than did S participants. (Right) In contrast, the groups could identify colors of the novel objects equally well when explicitly asked.
Figure 3.
The training groups differ in prioritization of color information. (Left) As measured by the frequency of listing color early in an adjective generation task, CS participants listed color as the first adjective earlier and more often than did S participants. (Right) In contrast, the groups could identify colors of the novel objects equally well when explicitly asked.
We also found that CS and S participants differed in how they used color information to evaluate the similarities of different objects to one another. Despite no explicit instruction to base the similarity rating on any particular feature, critically, CS participants assigned (on a 9-point scale) higher general similarity ratings to same-colored object pairs than did S participants, t(61) = 2.27, p = .03. We observed a similar pattern when only comparing stimuli shared across both training groups. In the shared stimuli analysis, although the groups did not significantly differ in rating the same-colored pair (C + S: 4.9; S: 4.4; t test across participants: t(31) = 0.99; p = .33), they did judge the items in the five differently colored pairs to be more dissimilar from each other (C + S: 1.5; S: 2.9; t test across items: t(8) = 7.03, p < .01).
### The Impact of Feature Diagnosticity on Neural Representations
#### ROI Univariate Analysis
To establish functionally defined ROIs (fROIs) in which we could assess any group differences in task effects, we first performed a group-level random effects analysis on the color perception data, comparing brain activity of colored stimuli to grayscale stimuli. This comparison is identical to previous work (Hsu et al., 2011, 2012; Simmons et al., 2007; Beauchamp et al., 1999). No regions responded more to grayscale than colored stimuli. From the set of fROIs that emerged, we identified the peak cluster of voxels from posterior and anterior visual regions (identified as cuneus and fusiform gyrus). Both sets of regions (i.e., posterior and anterior) have been documented previously for their involvement in color perception and color knowledge retrieval (Hsu et al., 2011; Martin, 2007; Simmons et al., 2007; Beauchamp et al., 1999). To create fROIs of comparable size across regions, we identified approximately 50 maximally responsive voxels in each region. Finally, within each of these fROIs, we calculated parameter estimates for each participant on the spatially averaged time series across the 50 voxels in the fROI, using these parameter estimates to assess shape retrieval task effects (relative to fixation baseline) between groups. Critically, there were no group differences in RT for the shape retrieval task (CS: average median RT: 2047 msec; S: average median RT: 2108 msec; t(30) = 0.37, p > .7). We used an independent samples t test to assess the difference between groups.
Activation in the left fusiform region (48 voxels, peak voxel t = 6.37, Talairach coordinates: −30, −56, −17, BA 37) during the shape retrieval task was significantly greater for the CS participants (mean percent signal change = 0.41%, SE = 0.07%) than for the S participants (mean percent signal change = 0.22%, SE = 0.06%; t(30) = 2.02, p = .05, see Figure 4). Performing the same analysis with individually defined ROIs yielded a similar pattern. In contrast, activation in the cuneus region (52 voxels, peak voxel t = 9.56, Talairach coordinates: 3, −92, 20, BA 19/17) did not show a significant Group difference in activity during the shape task (CS: mean percent signal change = 0.32%, SE = 0.08%; S: mean percent signal change = 0.19%, SE = 0.08%; t(30) = 1.11, p > .2, ns). The Region × Group interaction was not significant.
Figure 4.
Retrieval of a diagnostic feature automatically activates color-sensitive regions in ventral temporal cortex. During a shape retrieval task, the left fusiform gyrus, a region involved in color perception as defined by greater response to chromatic than achromatic visual stimuli, was more active for CS participants than for S participants. The cuneus region showed a similar pattern that did not reach significance. Exploratory analyses revealed that the left inferior temporal gyrus demonstrated a significant Task × Group interaction, with CS participants demonstrating more task activity than S participants (note: the means plotted in the bottom of this figure are intended to provide descriptive data about the ROI, not an independent inferential test, as they are taken from the voxels identified as having a reliable interaction in the Exploratory Analyses).
Figure 4.
Retrieval of a diagnostic feature automatically activates color-sensitive regions in ventral temporal cortex. During a shape retrieval task, the left fusiform gyrus, a region involved in color perception as defined by greater response to chromatic than achromatic visual stimuli, was more active for CS participants than for S participants. The cuneus region showed a similar pattern that did not reach significance. Exploratory analyses revealed that the left inferior temporal gyrus demonstrated a significant Task × Group interaction, with CS participants demonstrating more task activity than S participants (note: the means plotted in the bottom of this figure are intended to provide descriptive data about the ROI, not an independent inferential test, as they are taken from the voxels identified as having a reliable interaction in the Exploratory Analyses).
To rule out a task difficulty explanation (i.e., attributing greater fusiform activity to the task being harder for CS participants), we examined “accuracy” on the memory task. Although there were no “correct” answers for the shape questions, we derived a consensus measure for each question by counting the number of “yes” and “no” responses, calculating the absolute value of their difference, and dividing by the total number of responses. Lower consensus values would approach 0, and higher consensus would approach 1. If CS participants found the task more difficult, a task difficulty hypothesis would predict lower consensus on their answers. However, CS participants had higher consensus than S participants on the memory task (CS: M = 0.66, SE = 0.02; S: M = 0.55, SE = 0.02, t(478) = 4.05, p < .001).
#### Multivariate Neural Similarity Analysis
We next adopted a measure of neural similarity from Weber and colleagues (2009) to see if activation patterns in the left fusiform fROI (48 voxels) predicted behavioral similarity ratings. First, we preprocessed data for this analysis with a smaller smoothing kernel (4 mm, rather than 9 mm) than for the univariate analyses, as larger smoothing kernels can be destructive for multivariate analyses. Then, for each item, we identified a pattern of activation of vector length equal to the number of voxels in the fROI. Although voxel order in the vector was arbitrary, it remained consistent across all patterns. Some voxels within the fROI were, on average, more active than others; thus, to prevent mean activation of voxels from driving our similarity measure (a Pearson correlation of neural similarity), we mean-centered each voxel's response to its average response across all items. We calculated neural similarity by correlating each of the 66 vector pairs (averaged over participants) and then assessed whether these values could predict two sets of behavioral ratings of similarity: the general similarity ratings obtained by the participants (by memory) as well as the similarity ratings obtained by an independent group of participants (by perception; see Methods: Untrained Similarity Rating for details on obtaining feature-specific behavioral similarity ratings).
We conducted these analyses with both sets of behavioral similarity ratings for specific reasons. First, we used the logic behind theories of embodied cognition—namely, that color-sensitive brain systems are recruited when thinking about color—as the motivation for our decision to use perceptual similarity judgments from an independent group of participants. Specifically, we wanted perceptual judgments from an untrained set of participants for two reasons: (a) previous knowledge about the objects (e.g., object name) would not influence the similarity ratings and (b) we could probe participants on specific and critical perceptual features (i.e., color or shape). We could then correlate this relatively clean set of perceptual similarity ratings with the neural similarity data. Second, because we were also interested in correlating the neural similarity data with the (memory-based) general similarity data from the trained participants (i.e., a test for within-subject similarity correlations), we used this second set of behavioral ratings as well.
Because we could not assume a linear relationship for the behavioral ratings of similarity, we used the Spearman rank correlation coefficient to assess the relationship between neural and behavioral similarity. Finally, we ran a Monte Carlo simulation to arrive at the appropriate p values for the similarity correlations.
#### Perceptual Similarity
As shown in Figure 5, color similarity ratings approached significance in predicting neural similarity for the CS participants (rs = .23, p = .06; 95% CI [−0.01, 0.45], but not for the S participants (rs = −.17, p = −.18; 95% CI [−0.39, 0.08]). These predictions were significantly different from each other (Z = 2.27, p < .05). Shape similarity ratings did not predict neural similarity in this region for either group (CS: rs = .19, p = .13; S: rs = −.02, p > .8), and the two groups did not differ from each other (Z = 1.17; p > .2).
Figure 5.
Behavioral color similarity predicts neural similarity in the left fusiform gyrus. Behavioral ratings of color similarity (derived from a set of untrained participants) approach significance in predicting neural similarity of novel object activation patterns in the left fusiform gyrus, but only for the CS participants, shown in gray. S participants are shown in white. Each data point represents a pairwise combination of novel objects, averaged across all participants.
Figure 5.
Behavioral color similarity predicts neural similarity in the left fusiform gyrus. Behavioral ratings of color similarity (derived from a set of untrained participants) approach significance in predicting neural similarity of novel object activation patterns in the left fusiform gyrus, but only for the CS participants, shown in gray. S participants are shown in white. Each data point represents a pairwise combination of novel objects, averaged across all participants.
#### General Similarity
In the localizer-defined left fusiform gyrus ROI that showed a Group effect, we correlated the average behavioral general similarity rating with the average neural similarity measure. The general similarity ratings predicted neural similarity for CS participants (rs = .29, p = .02; 95% CI [0.05, 0.50]) and not for S participants (rs = −.07, p = .57; 95% CI [−0.31, 0.18]), and the correlations were significantly different from each other (Z = 2.06, p = .04).
#### Exploratory Analyses
To assess the specificity of our effect, we examined other regions of the left ventral temporal cortex other than those used for our primary a priori analyses. In line with previous work, we expanded our search to left ventral temporal cortex in line with left-lateralized brain regions involved in knowledge retrieval (cf. Chao, Haxby, & Martin, 1999; Martin et al., 1995). In an anatomically defined left ventral temporal cortex region (∼5500 voxels), we looked for voxel clusters (>50 voxels) showing a Task (task vs. baseline) × Group (CS vs. S) interaction at a cluster-corrected, permuted threshold of α < 0.05 (t = 2.92). Only the left inferior temporal gyrus (Talairach coordinates of peak voxel: −56, −53, −12, BA 20) surpassed this threshold, both within the anatomically defined region, and when we unmasked the rest of the brain to examine whether other regions demonstrated this interaction.
Here (see Figure 4, bottom), we found significantly greater activity during the shape retrieval task for CS participants than for S participants (note: the means plotted in the bottom of this figure are intended to provide descriptive data about the ROI, not an independent inferential test, as they are taken from the voxels identified as having a reliable interaction in the Exploratory Analyses). Moreover, as shown in Figure 6, we also found that the extent to which participants prioritized color during the adjective generation task (i.e., how often they listed object color first) predicted activity in this region (C + S: r = −.18, p = .49; S: r = .30, p = .24, combined: r = .50, p < .01). We observed similar trends in the left fusiform gyrus (C + S: r = .21, p = .42; S: r = −.07, p = .79; combined: r = .30, p = .09) and the cuneus (C + S: r = .19, p = .47; S: r = .09, p = .73; combined: r = .23, p = .20), the two regions identified from the color perception functional localizer. This result suggests that during object knowledge retrieval, diagnostic features may be automatically activated.
Figure 6.
Color prioritization predicts task activity in ventral regions. Prioritizing color during the adjective generation task only correlated significantly with activity in the left inferior temporal gyrus, a second region active during the shape retrieval task that was identified through secondary exploratory analyses. Patterns in the same direction were observed in the left fusiform gyrus and cuneus. Each data point represents the BOLD response from a given participant, averaged across all items.
Figure 6.
Color prioritization predicts task activity in ventral regions. Prioritizing color during the adjective generation task only correlated significantly with activity in the left inferior temporal gyrus, a second region active during the shape retrieval task that was identified through secondary exploratory analyses. Patterns in the same direction were observed in the left fusiform gyrus and cuneus. Each data point represents the BOLD response from a given participant, averaged across all items.
Finally, in a second exploratory analysis, we assessed the specificity of the shape retrieval task effect (relative to baseline) by conducting a whole-brain analysis. Using a permuted threshold (t > 6.22; α < 0.005), we identified the local maxima that surpassed this threshold and derived the corresponding brain regions, which are now reported in Table 3. As seen in the table, activation focuses on color-selective regions (e.g., left fusiform gyrus, left lingual gyrus, cuneus, precuneus) in addition to other regions.
Table 3.
Regions Identified from the Whole-brain, Permuted Analysis of the Shape Retrieval Task
RegionxyzPeak t Value
L inferior frontal gyrus −42 23 16.44
L insula −45 15 16.44
L precuneus −27 −62 36 16.19
R middle occipital gyrus 21 −96 15.17
R lingual gyrus −93 14.14
L fusiform gyrus −45 −68 −14 14.04
L cingulate gyrus −3 16 37 13.80
R cingulate gyrus 11 40 13.79
L thalamus −9 −20 13.68
L inferior occipital gyrus −27 −85 −13 13.20
L lingual gyrus −9 −93 12.97
L putamen −21 −3 12.95
L precentral gyrus −36 −6 56 12.51
R fusiform gyrus 21 −88 −11 12.25
L inferior parietal lobule −42 −30 39 12.07
L cuneus −24 −96 11.90
R parahippocampal gyrus 21 −32 −3 11.32
R inferior frontal gyrus 33 20 −4 11.05
R putamen 21 10.92
L parahippocampal gyrus −24 −29 −4 10.87
L supramarginal gyrus −36 −42 37 10.74
L superior frontal gyrus −18 −8 66 10.35
R cuneus 12 −75 10.28
R thalamus 12 −17 9.88
L posterior cingulate −9 −31 22 9.76
L postcentral gyrus −39 −23 59 9.48
R inferior occipital gyrus 39 −96 −5 8.66
R precentral gyrus 36 −12 61 8.48
R hippocampus 33 −44 7.39
R superior frontal gyrus 21 −8 66 7.34
L uncus −33 −13 −32 7.08
R precuneus 27 −65 31 7.07
R caudate (tail) 30 −43 12 6.98
RegionxyzPeak t Value
L inferior frontal gyrus −42 23 16.44
L insula −45 15 16.44
L precuneus −27 −62 36 16.19
R middle occipital gyrus 21 −96 15.17
R lingual gyrus −93 14.14
L fusiform gyrus −45 −68 −14 14.04
L cingulate gyrus −3 16 37 13.80
R cingulate gyrus 11 40 13.79
L thalamus −9 −20 13.68
L inferior occipital gyrus −27 −85 −13 13.20
L lingual gyrus −9 −93 12.97
L putamen −21 −3 12.95
L precentral gyrus −36 −6 56 12.51
R fusiform gyrus 21 −88 −11 12.25
L inferior parietal lobule −42 −30 39 12.07
L cuneus −24 −96 11.90
R parahippocampal gyrus 21 −32 −3 11.32
R inferior frontal gyrus 33 20 −4 11.05
R putamen 21 10.92
L parahippocampal gyrus −24 −29 −4 10.87
L supramarginal gyrus −36 −42 37 10.74
L superior frontal gyrus −18 −8 66 10.35
R cuneus 12 −75 10.28
R thalamus 12 −17 9.88
L posterior cingulate −9 −31 22 9.76
L postcentral gyrus −39 −23 59 9.48
R inferior occipital gyrus 39 −96 −5 8.66
R precentral gyrus 36 −12 61 8.48
R hippocampus 33 −44 7.39
R superior frontal gyrus 21 −8 66 7.34
L uncus −33 −13 −32 7.08
R precuneus 27 −65 31 7.07
R caudate (tail) 30 −43 12 6.98
Coordinates are in Talairach space and are given for the peak voxel (local maximum) with corresponding t value. Note that these t values correspond to regions identified in the shape retrieval task, whereas the t values reported in the text for the ROI analyses refer to regions identified in the color perception localizer task.
## EXPERIMENT 2: FAMILIAR OBJECTS—RESULTS
### Effects of Familiar Object Feature Diagnosticity on Behavioral Measures
A repeated-measures ANOVA revealed significant main effects of both Condition, F(1, 21) = 21.14, p < .001, and Adjective Order, F(1, 21) = 13.56, p < .001, but no interaction, F(1, 21) = 0.32, p > .5. Even when including surface descriptors in the adjectives as colors, such as “shiny,” “metallic,” “plastic,” and “wooden,” participants describing FV items listed color first more often than participants describing HHI items (FV: M = 54.9%, SE = 10.3%; HHI: M = 24.2%, SE = 5.4%; t(21) = 2.56, p < .02). These results are comparable to Experiment 1, supporting the idea that within the context of this particular task, both novel and familiar object categories share commonalities.
### The Generalization of Feature Diagnosticity Effects to Familiar Object Categories
One of the main strengths of novel object studies (i.e., experimenter-manipulated control) is also a constraint: It is often unclear to what extent the results will generalize to familiar objects for which there is natural variation in stimulus characteristics. Thus, Experiment 2 asked whether familiar, real-world objects that varied in relatively diagnostic color association (i.e., FV vs. HHI) would yield findings in line with those of Experiment 1. In an item-based analysis using all three ROIs (i.e., the functional color localizer-identified fusiform gyrus and cuneus; the exploratory analysis-identified inferior temporal gyrus) from Experiment 1, we compared item responses from both experiments as a function of color prioritization. For all 48 items, within each ROI from Experiment 1, we obtained the response to each individual item across all 20 questions, averaged across all participants. This analysis allows us to compare item responses across conditions and across experiments.
As observed in Figure 7, color prioritization varied across both experiments. Across conditions, the distribution of items does not overlap for novel objects, but does for familiar objects. In the cuneus, comparing item responses across the two common object categories reveals significantly greater percent signal change for FV items (M = 0.40, SE = 0.03) relative to HHI items (M = 0.28, SE = 0.01; t(22) = 3.79, p < .007). Because the FV items are color-associated, but the HHI items tend to not be color-associated, this result parallels previously reported chromaticity effects in memory (Hsu et al., 2012). Notably, the same pattern was also observed in the left fusiform gyrus, the region where we had discovered a group effect of feature diagnosticity in Experiment 1 (FV: mean percent signal change = 0.26; SE = 0.01; HHI: mean percent signal change = 0.22; SE = 0.01; t(22) = 2.25, p < .05). Furthermore, both regions demonstrated positive correlations between color prioritization and BOLD signal in Experiment 2 (cuneus: r = .58, p = .003; fusiform: r = .44, p = .03). The latter fusiform region replicates a similar pattern observed in Experiment 1 (fusiform: r = .83, p < .001), but not in the cuneus (r = .28, p = .18). That color prioritization predicted responses for both novel and common object categories in the left fusiform gyrus suggests some commonalities in the relative role of feature diagnosticity regardless of stimuli type. Interestingly, we observed different patterns in the left inferior temporal gyrus across experiments. Whereas color prioritization positively correlated with BOLD signal for items in Experiment 1 (r = .87, p < .001), color prioritization negatively correlated with BOLD signal for items in Experiment 2 (r = −.46, p < .05). We discuss possible reasons for this divergence in the General Discussion.
Figure 7.
Item-based analyses reveal that feature diagnosticity effects generalize across stimulus sets. Across the three ROIs (posterior cuneus and anterior fusiform identified from the color perception localizer, inferior temporal gyrus identified from the exploratory analysis), we analyzed averaged item-level responses in signal change and color prioritization for Experiment 1 (left) and Experiment 2 (right). Each data point represents the BOLD response to a given item, averaged across all participants.
Figure 7.
Item-based analyses reveal that feature diagnosticity effects generalize across stimulus sets. Across the three ROIs (posterior cuneus and anterior fusiform identified from the color perception localizer, inferior temporal gyrus identified from the exploratory analysis), we analyzed averaged item-level responses in signal change and color prioritization for Experiment 1 (left) and Experiment 2 (right). Each data point represents the BOLD response to a given item, averaged across all participants.
## GENERAL DISCUSSION
We report several behavioral and neural results indicating that feature diagnosticity affects concept representations. In ventral temporal cortex, and specifically in the left fusiform gyrus and left inferior temporal gyrus, we found greater activity for participants who had learned color was a useful, diagnostic feature when performing a task that did not explicitly require color retrieval. We also found that behavioral ratings of color similarity predicted neural similarity for CS participants only and that color prioritization predicted activity in color-selective fusiform gyrus; this latter effect was also evident in the set of familiar objects. Together, these results provide evidence that the behavioral effects of feature diagnosticity (measured at least in part by color prioritization) arise from varying degrees of automatic recruitment of the diagnostic feature; this brain–behavior correlation was evident across both stimulus sets. To our knowledge, this study is the first to explain rather than describe the importance of feature diagnosticity, both when the diagnostic feature (here, color) is systematically manipulated and in a more familiar real-world context.
Although both training groups were equally able to identify the color of the object when explicitly asked to, the CS participants listed color first more frequently when naming features. This result is particularly interesting in light of some previous work (Connolly, Gleitman, & Thompson-Schill, 2007), which used an implicit similarity measure to demonstrate that, although both sighted and congenitally blind participants were equally proficient at knowing the colors of FV, only sighted participants used color as the primary basis for their judgment. The authors suggested that visual experience (or lack thereof) had contributed to a fundamental group difference in how conceptual representations for these categories were structured. Our design matched the training stimuli in terms of color uniqueness and probability of occurrence (i.e., for both sets, it was always the case that P(object|color) = 0.5). Despite a fixed level of absolute diagnosticity, we found fundamental differences in how participants used color, which was relatively more diagnostic (compared with shape). We can stipulate color knowledge of a klarve for both groups of participants from the color naming task, but the adjective generation task yields information about the usefulness of color in distinguishing a klarve from the other objects in the set.
Furthermore, the shapes were deliberately created such that they bore no resemblance to familiar objects and thus would not be easily named. Participants tried—and often struggled—to generate descriptors, sometimes resorting to shape adjectives that were easily verbalized (e.g., a klarve is “curved”) or likening shapes to ones that they knew (e.g., a klarve is “football-like”). Given this observed difficulty, one might have predicted the participants to produce color descriptors, which are easily named. Despite this difference in likely ease of production, S participants did not produce color descriptors before noncolor descriptors, and, for some S participants, color was never mentioned at all. This result strengthens our argument that the object set differences, together with subsequent differences in visual experience, contributed to fundamental differences in how the groups represented the novel objects.
The pairwise similarity data provided a complementary method for investigating conceptual knowledge; according to some theories of concepts, similarity among instances of a category is critical for category (Murphy, 2004). The data here demonstrate a fundamental difference in how the CS participants considered the general similarity of same- versus different-color object pairs. Given the unavoidable heterogeneity in constructing the two object sets, restricting the analysis to shared stimuli between the groups (klarve, hinch, fulch, screll) replicated our initial findings (specifically in terms of dissimilarity), demonstrating that diagnostic features can be regarded in the context of long-term experience with other objects in the set. Not only does use of feature knowledge affect a conceptual representation, but our data show that the learned context of the objects can also affect conceptual representations.
Turning to the neuroimaging data, we hypothesized a group difference in accessing color as a diagnostic feature during a shape retrieval task in the left fusiform gyrus. Our findings were in line with our initial hypothesis, in that the left fusiform gyrus, which is known to be a region involved in color perception (Hsu et al., 2011; Simmons et al., 2007; Beauchamp et al., 1999), was indeed more active during the shape retrieval task for CS participants than for S participants. These results are all the more compelling given than the shape retrieval task never explicitly probed participants about object color. In fact, color was irrelevant to the task. This result, suggesting automatic retrieval of diagnostic features even when retrieving other object features, is consistent with temporal information revealed in a related ERP study: Participants categorizing novel objects showed ERP patterns as early as 117 msec when remembering diagnostic features of the learned objects. However, this early effect was only seen in occipitoparietal electrodes when participants had pantomimed actions with the novel objects, rather than pointing to them (Kiefer et al., 2007). Although we did not find a significant group effect in the cuneus region (i.e., the other region identified in the functional color localizer), the results were numerically in the same direction. This was a slightly surprising but not an undocumented finding, as previous work has demonstrated differential activation of color perception in posterior versus anterior regions (e.g., Beauchamp et al., 1999). Finally, our multivariate analyses revealed that neural similarity of patterns in left fusiform gyrus were linked to general (i.e., from trained participants) and perceptual (i.e., from untrained participants) similarities for the CS participants only (i.e., when color had relatively high diagnosticity). Because color did not yield the same relatively diagnostic information for S objects, this may explain the elimination of the correlation between behavioral and neural similarity for these participants.
Furthermore, our follow-up exploratory analyses revealed an unexpected pattern in the left inferior temporal gyrus. Previous work has shown this region—lateral and anterior to the medial fusiform region—to be involved in color knowledge retrieval; it is more active when participants name colors (of achromatically presented object drawings) than when they name the objects themselves (Chao & Martin, 1999). We find that color prioritization is correlated with activity in this region (with a similar pattern in other color perception regions). This brain–behavior correlation indicates that the behavioral effect of feature diagnosticity arises from differing degrees of automatic recruitment of color information. However, we wish to mention one caveat to this particular exploratory analysis. Specifically, the within-group assessments of these data were not significant, and effects only emerged when combining the groups together; yet, within-group assessments are challenging. That is, it was difficult for us to assess the same relationship within both groups because the two groups demonstrated differing patterns of data distribution in terms of color prioritization. Within the S group, the correlation was positive (r = .30)—although not significant, it was numerically in the direction that we would expect (given values that are a bit more normally distributed), but might be underpowered. Despite this caveat, we note that this study is unusual in the fMRI literature in that it involves a between-subject manipulation, which has considerably less power than more typical within-subject designs. The between-subject design was a necessity in this case, but one consequence is that we had less statistical power than desired. We urge readers to consider the overall body of conclusions reported here as a broader demonstration of how behavioral effects of feature diagnosticity can arise from the recruitment of color information.
In considering the results across all three regions, the composition of the novel object sets, in a sense, forced participants to categorize objects according to strict color–shape conjunctions. Thus, our experimental design may have been more amenable toward group differences in an anterior region involved in feature integration, but it does not preclude similar group differences in a posterior color region. Group differences in the shape task showed the same directional effect in the cuneus as in fusiform gyrus, although not significantly so. Because the magnitude of this difference increased from posterior to anterior regions of ventral temporal cortex, this result suggests an increased sensitivity to diagnostic features in regions tuned to object categorization. In line with this theory, macaque IT cortex differentially responded to diagnostic features along a posterior–anterior axis, with only the anterior portion of the recording area responded with diagnostic local field potential activity (Nielsen et al., 2006).
Finally, Experiment 2 allowed us to compare between novel and familiar object categories. In both color perception regions, color prioritization correlated with brain activity during the shape task, suggesting automatic retrieval of diagnostic features, and in particular, a neural basis for the taxonomy differences in relative color association. The reversal of this trend in the left inferior temporal gyrus in Experiment 2 suggests a different role for this region in concept representations. One possibility is that the region represents the contribution of an object feature, in light of all other known object features. Whereas color information constituted 50% of the features known about novel object categories, it likely constituted a smaller percentage of all known features of HHI object categories (where other features might include function, texture, etc.) and an even smaller percentage for FV object categories (where other feature might include taste, size, etc). However, there may be other explanations that better explain this seemingly contradictory reversal in correlation patterns across both experiments, and future research should address this finding. Taken together, this comparison demonstrates the utility of training studies, in that they allow amplification of an otherwise muddied gradient of information that is of interest.
We have argued here that the retrieval of diagnostic features can automatically activate color-selective brain regions, but some of these brain regions—particularly the fusiform gyrus—are also involved in shape processing (e.g., Gerlach, Law, & Paulson, 2006; Bar et al., 2001; Op de Beeck, Béatse, Wagemans, Sunaert, & Van Hecke, 2000). As such, there remains the possibility that the diagnostic feature in question may not have been color per se, but the conjunction of shape and color. The data in our study cannot rule out this possibility. However, a recent MVPA study (Coutanche & Thompson-Schill, in press) demonstrated that, within a region often associated with color processing, a classifier could decode meaningful information about color and about shape but could not decode the conjunction of the two features (in that study, only in the anterior temporal lobe could the classifier decode feature conjunction information). We believe that this result makes it less likely for a color processing region to carry feature conjunction information, but this is an intriguing idea that the field should pursue further. That is, which brain regions carry information about independent conceptual features, and which brain regions carry information about conjoint features? One promising method for addressing this question is to compare metrics that measure independent (i.e., city-block) or conjoint (i.e., Euclidean) featural information (Drucker, Kerr, & Aguirre, 2009). Future explorations of conjunctive feature coding might also benefit from potential links to the literature on learning of conjunctive versus nonconjunctive rules in categorization tasks (e.g., Ashby & Maddox, 2011; Ell, Weinstein, & Ivry, 2010; Ashby, Alfonso-Reese, Turken, & Waldron, 1998). Finally, we emphasize that whether a singular feature or conjunction of multiple features is the diagnostic component of the concept, in either case, we observe automatic retrieval of information that is seemingly task-irrelevant, but only in cases when that information is diagnostic.
Collectively, the results of the current work are the first to provide a neural explanation for the behavioral effects of feature diagnosticity, namely that these effects arise from automatic recruitment of the diagnostic information. Our findings suggest that neural representations may not be stable and fixed but may instead be far more flexible than previously thought (Binder & Desai, 2011; Kiefer & Pulvermüller, 2011; Hoenig, Sim, Bochev, Herrnberger, & Kiefer, 2008). More broadly, our results point to the notion that feature diagnosticity is one of many sources contributing to variation in concept representations, the neural bases of which underlie our ability to describe and define characteristics of the massive variety of objects that we encounter on a daily basis.
## Acknowledgments
This work was funded by R01-MH070850 to S. L. T.-S. and F31-AG034743 to N. S. H. We thank Matt Weber for help with data analysis, Emily Kalenik and Lauren Hendrix for help with data collection, members of the Thompson-Schill lab for generous feedback and discussion, and two anonymous reviewers for comments on an earlier version of this manuscript.
Reprint requests should be sent to Nina S. Hsu, 7005 52nd Avenue, University of Maryland, College Park, MD 20742, or via e-mail: ninahsu@umd.edu.
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The first round of Stanley Cup Playoffs finished with a crazy game between the Leafs and the Bruins. It was the seventh match of the series and Boston celebrated this scoring 7 goals. Toronto answered with just 4. Good game anyway.
I discovered that my forecasting skills suck — I correctly predicted only 50% of teams who’d advance to the second round. Golden Knights, Lightning, Sharks and Penguins were bound to lose according to my predictions. Haha. It’s funny that NHL 18 is way more precise — so far they’re absolutely correct:
https://www.nhl.com/news/winnipeg-wins-stanley-cup-in-ea-sports-nhl-18-playoff-simulation/c-297863906
# Animelog: Spring 2018, Dropped
Persona 5 The Animation
Despite the fact that I enjoyed the game a lot the same plot in animation format looks rather silly. For people who haven’t played Persona 5 this anime’s description unlikely will be especially tempting — a bunch of school students led by a guy whose parents don’t care for him at all trying to change the “rotten world built by corrupt adults”. Those damn adults, they always corrupt everything! Out of curiosity we checked out the first episode, saw that it wasn’t filmed any better than in-game animated cutscenes and dropped it.
Megalo Box
I don’t watch sports anime but visual of Megalo Box is so old-school that I couldn’t resist. However, other than unusual graphics it’s very difficult to find any reasons to keep on watching this show. (Note for the future self — megalo box is just like regular box but when sportsmen wear exoskeletons).
3D Kanojo: Real Girl
An otaku falls in love with a girl who supposedly does this and that with anyone who’s closer than 5 meters to her. To add up, the first episode was rather poorly animated. I might’ve continued watching this anime if we didn’t have a better one about otaku-in-love this season. To drop without a trace of remorse.
Golden Kamuy
We’re going to watch how an “immortal” Japanese deserter accompanied by an ainu girl is looking for stolen gold, killing humans (decently drawn) and 3D bears (they look terrible). Interesting character design and unbeaten period of time but somehow this anime didn’t impress me much, maybe because of that war-and-prison vibes it has.
Gurazeni
I think that this anime is going to be covered in bad reviews and eventually forgotten. For sports anime fans (and baseball fans in particular) it’s too slow and too concentrated on everything except actually matches and characters who, hm, overbear all the time. For others — it has too much baseball in it. But again — character design is really nice.
Survived so far:
Steins;Gate 0
Wotaku ni Koi wa Muzukashii
Tada-kun wa Koi wo Shinai
Hinamatsuri
Mahou Shoujo Ore
Comic Girls (actually, this one can be considered pretty much as dropped)
Ginga Eiyuu Densetsu: Die Neue These – Kaikou
Piano No Mori
Akkun to Kanojo
Hisone to Maso-tan
Fumikiri Jikan
Cutie Honey Universe
Space Battleship Tiramisu
Recently discovered that Dave Lombardo isn’t only one of the best drummers we’ve ever seen but also responsible for some (questionable, I must admit) art.
The website dedicated to his collection is: http://davelombardoart.com/
Just to get an idea what the collection looks like:
Actually, I wouldn’t mind having one of his artworks at home but prices are not especially friendly =(
Misc stuff.
Guys at work rarely ask me something about Russia but a couple of days ago were curious whether it’s true that the Russian government managed to block a hellish amount of websites in attempts to stop Telegram. I didn’t know for sure so my answer was full of “apparently” and “as far as I know” — but some food for thought they definitely got.
Finally figured out how the coefficients in Sloan’s “Stupid SH tricks” irradiance calculations are, hm, calculated. For me this stuff looked slightly magical
const float fC0 = 1.0f/(2.0f*s_fSqrtPI);
const float fC1 = (float)sqrt(3.0f)/(3.0f*s_fSqrtPI);
const float fC2 = (float)sqrt(15.0f)/(8.0f*s_fSqrtPI);
But as usual turned out that it’s just stupid me. If we take a coefficient we use to project onto SH basis and then multiply it with coefficient used for convolution — we’ll get exactly this fC0 and so on. For example, for the first band:
$A1 = \dfrac{2\pi}{3}; c1 = \sqrt{\dfrac{3}{4\pi}};$
$A1 \cdot c1 = \dfrac{2\pi\sqrt3}{3 \cdot 2\sqrt\pi} = \dfrac{\sqrt3}{3\sqrt\pi} \cdot \pi$
As a final step we divide by $\pi$ to get irradiance.
And the last but not least:
Discovered a beautiful band — Grandpa’s Cough Medicine. These guys and girls play bluegrass and probably are not known anywhere expect the town they proudly reside in. So far the band released 3 albums and I have to say that “The Murder Chord” is definitely worth listening.
website
Official video
My favourite song (Julianne):
A bunch of new screenshots from Ni No Kuni 2.
I’ve played about 20 hours and somewhere in the middle of the game I guess. Locations in the game is its best part (this and simple but nice jokes) — Goldpaw is my favourite place now. Gameplay-wise everything is more complicated, there is a lot of mechanics and honestly I don’t care about virtually all of them. Weapons or armor? Once in a few hours I check out what I have a equip the best ones. Spells? Don’t even know if I got any new. Higgledies (or Funya) are so sweety-cutie that it’s even annoying. Kingdom building is a big part of the game and you have to do it whether you want it or not because the story requires some improvements that can be made only when the level of your kingdom is at least 2 (to level it up you need to finish 2/3 of available side quests because that’s apparently the only way to recruit new citizens the certain number of citizens is one if the level-up requirements). The same goes for skirmishes — you have to play them because at least one quite a high-level combat is an unavoidable part of the story.
In general — the game is super-relaxing and a lot of fun to play (despite my complaining).
# Animelog: Violet Evergarden, Fate Extra
Violet Evergarden
I wrote that a couple of times before and I’m ready to write this again but Violet Evergarden is beautiful. It basically yells at you “Look, I’m not your typical low-budget TV garbage”. The only downside of the anime’s visual is sometimes questionable rim light but it’s bearable. However, if you removed that great appearance you’d be left with nothing. Primitive story that can be described in one sentence. Bland characters doing useless things. Shallow and laughable sometimes world (yep, of course we need Dolls to write the declaration of peace). And on top of everything is Violet herself who evolves at a pace even Bulbasaur would be proud of, jumps from planes and has eyes as sharp as a hawk’s. Oh, I forgot to mention that you’re supposed to wring out streams, rivers and sometimes even oceans of tears during every episode. I wish Violet Evergarden wasn’t that gorgeous and I would’ve dropped it instead of cursing during all 13 episodes.
Fate Extra Last Encore
Well, sometimes even Shaft makes mediocre anime. To be honest, all Fate shows so far have been rather boring to me (I watched the original Fate Stay Night and Zero) but Extra turned out to be not only boring but also lacking a logical plot. All those SE.RAPHs, Angelic Cages — I honestly couldn’t get what’s going on. The strongest Shaft’s selling points, animation and direction, also were not the top notch this time. Either the studio didn’t have enough money or they were too concentrated on finishing “March Comes In Like a Lion” — anyways, first 5 episodes looked cheap. I had a feeling that before episode 6 the team had changed and the second part of Fate Extra was almost flawless in terms of direction — however, it was too late (not all people are patient Shaft fans) and, what’s more important, the plot hadn’t become more sensible. Obviously, this anime’s going to have a second season because the last episode finished abruptly, with bare minimum of explanations, I’m not sure though that Shaft will be the studio filming the second one.
The ending in the anime is really good though.
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The genome is diploid at the end of which phases of a human mitotic cell cycle?
1. $\text{G2 & S}$
2. $\text{G1 & M}$
3. $\text{M & S}$
4. $\text{G1 & G2}$
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# 1993 technical reports
CS-93-60
Title OPTIMUM LOGIC ENCODING AND LAYOUT WIRING FOR VLSI DESIGN: A GRAPH-THEORETIC APPROACH
Authors Chuan-Jin Shi
Abstract This thesis addresses two problems in VLSI design: constrained via minimization — which aims at minimizing the number of vias between routing layers — and constrained logic encoding — a problem fundamental to the design of synchronous, and hazard-free asynchronous, circuits. We show that these two problems have the same combinatorial structure, which can be captured by a new graph-theoretic model, called signed hypergraph. They can be formulated as two new optimization problems, namely maximum balance and minimum covering, related to a balance property of signed hypergraphs.
On the theoretical side, we establish a structural characterization of balanced signed hypergraphs. We then prove that both maximum balance and minimum covering are NP-complete. We present an integer linear programming formulation for maximum balance of signed hypergraphs, and a polynomial-size linear programming formulation for the case of planar signed graphs. We show that maximum balance in a planar signed hypergraph reduces to the minimum hypergraph $T$-join in its planar dual. We address the problem of modeling signed hypergraphs by real-weighted hypergraphs or graphs. We settle a conjecture of Lengauer which states that a clique is a best approximate model for a hyperedge, even if dummy vertices are allowed. We present a local search algorithm for the maximum balance problem, with one pass running in linear time. We describe a simple greedy peeling heuristic for minimum covering. We prove that greedy peeling has a guaranteed performance bound for solving a class of VLSI optimization problems of the so-called cluster-cover structure.
On the practical side, our work on constrained via minimization breaks new ground for the case of $k$-way splits ($k \leq 3$) with a compact reduction to graph $T$-joins and a polynomial-size linear programming formulation. For the case of multi-way splits ($k >3$), it provides a direct and efficient local search for timing-driven layer assignment and an optimal modeling scheme for good approximation algorithms. For logic synthesis, we present a unified approach to optimum state assignment for synchronous and hazard-free asynchronous circuit design. We have implemented our results as two experimental CAD tools. As demonstrated on a set of industry benchmarks, our tools outperform existing tools in terms of both solution quality and CPU time.
Comments A thesis presented to the University of Waterloo in fulfilment of the thesis requirement for the degree of Doctor of Philosophy in Computer Science.
Report OPTIMUM LOGIC ENCODING AND LAYOUT WIRING FOR VLSI DESIGN: A GRAPH-THEORETIC APPROACH (PDF) Compressed PostScript:
OPTIMUM LOGIC ENCODING AND LAYOUT WIRING FOR VLSI DESIGN: A GRAPH-THEORETIC APPROACH (PS.Z)
CS-93-57
Title A Rationale for Both Nesting and Inheritance in Object-Oriented Design
Authors L.M.F. Carneiro, D.D. Cowan, and C.J.P. Lucena
Abstract It has been observed that design of complex objects such as software requires both decomposition by form (atomic objects) and decomposition by function (nesting) in order to reduce the design to a set of manageable components. However, the object-oriented design paradigm mostly supports decomposition by form. This paper uses a simple example to motivate the need for nesting (decomposition by function) and illustrates how nesting might be incorporated into a design language. We then demonstrate how the introduction of nesting into software specification and design significantly increases reusability. ADVcharts, a new visual formalism, and VDM are used to provide a semantics for nesting.
Date December 1993
Comments This paper was published in the Proceedings of the VII Software Engineering Symposium - Rio de Janeiro - RJ - Brazil - Pages: 223-237
Report A Rationale for Both Nesting and Inheritance in Object-Oriented Design (PDF) Compressed PostScript:
A Rationale for Both Nesting and Inheritance in Object-Oriented Design (GZIP)
CS-93-55
Title Sequential and Parallel Algorithms for Embedding Problems on Classes of Partial k-Trees
Authors A. Gupta and N. Nishimura
Abstract We present sequential and parallel algorithms for various embedding problems on bounded degree partial k-trees and k-connected partial k-trees; these include subgraph isomorphism and topological embedding, known to be NP-complete for general partial k-trees. As well as contributing to our understanding of the types of graphs for which these problems are tractable, this paper introduces new methods for solving problems on graphs. In particular, we make use of a tree-like representation of the graph (the tree-decomposition of the graph) to apply techniques used to solve problems on trees to solve problems on more general classes of graphs.
Date February 1994
Report Sequential and Parallel Algorithms for Embedding Problems on Classes of Partial k-Trees (PDF) Compressed PostScript:
Sequential and Parallel Algorithms for Embedding Problems on Classes of Partial k-Trees (PS.Z)
CS-93-54
Title Towards Automated Detection of Feature Interactions
Authors K.H. Braithwaite and J.M. Atlee
Abstract The feature interaction problem occurs when the addition of a new feature to a system disrupts the existing services and features. This paper describes a tabular notation for specifying the functional behavior of features. It also describes how four classes of feature interactions can be detected when features are specified in this new notation. Our goal is to develop a tool that can automatically analyze feature specifications and detect interactions at the specification stage of development.
Date February 1994
Comments Appeared in the Second International Workshop on Feature Interactions in Telecommunications Software Systems.
Report Towards Automated Detection of Feature Interactions (PDF) Compressed PostScript:
Towards Automated Detection of Feature Interactions (GZIP)
CS-93-52
Title Abstract Data Views: A Module Interconnection Concept to Enhance Design for Reusability
Authors D.D. Cowan and C.J.P. Lucena
Abstract The Abstract Data View (ADV) design model was originally created to specify clearly and formally the seperation of the user interface from the application component or Abstract Data Type (ADT), and to provide a systematic design method that is independent of specific application environments. Such a method should lead to a high degree of reuse of both interface components and their associated ADTs. The material in this paper extends the concept of ADVs to encompass the general specification of interfaces between objects in the same or different computing environments. This approach to specifying interfaces clearly seperates objects from each other, since objects do not need to know how they are used, or how they obtain services from other objects. Thus, objects which are designed to minimize knowledge of the environment in which they are used, are more amenable to reuse.
Date March 1994
Report Abstract Data Views: A Module Interconnection Concept to Enhance Design for Reusability (PDF) Compressed PostScript:
Abstract Data Views: A Module Interconnection Concept to Enhance Design for Reusability (GZIP)
CS-93-49
Title A spectral algorithm for envelope reduction of sparse matrices
Authors A. Pothen, S.T. Barnard and H.D. Simon
Abstract The problem of reordering a sparse symmetric matrix to reduce its envelope size is considered. A new spectral algorith for computing an envelope-reducing reordering is obtained by associating a Laplacian matrix with the given matrix and the sorting the components of a specified eigenvector of the Laplacian. This Laplacin eigenvector solves a continuous relaxation of a discrete problem related to envelope minization called the minimum 2-sum problem. The permutaion vector computed by the spectral algorith is a closest permutation vector to the specified Laplacian eigenvector. Numerical results show that the new reordering algorithm usually computes smaller envelope size than those obtained from the current standards such as the Gibbs-Poole-Stockmeyer (GPS) algorithm or the reverse Cuthill-McKee (RCM) algorithm in SPARSPAK, in some cases reducing the envelope by more than a factor of two.
Date October 1993
Report README A spectral algorithm for envelope reduction of sparse matrices (PDF) Compressed PostScript:
A spectral algorithm for envelope reduction of sparse matrices (PS.Z)
CS-93-48
Title A Goal-Directed Functionally-Based Style Analyzer
Authors P. Hoyt
Abstract If sophisticated natural language systems are to handle the full range of communication, then they must be able to account for the nuances and subtleties of linguistic style. A computational treatment of style would be highly advantageous to natural language understanding and generation, with particular relevance to intelligent computer-assisted language instruction and machine translation. These systems would be able to understand more complex and expressive language, produce text suitable for a specific occasion, help a second-language learner develop a more natural and appropriate style, and produce higher quality translations of text.
A foundation for AI-based computational style has been laid by DiMarco, with extensions by Green, Makuta-Giluk, Mah, and Payette in generation, rhetoric, comparative stylistics, and intelligent computer-aided language instruction, respectively. These researchers found that DiMarco's work, while an important step in computational stylistics, was limited due to the lack of a theoretical foundation. DiMarco and Hirst provided a preliminary theoretical foundation and Green extended their work. This thesis unifies these complementary, and sometimes contradictory, theories of syntactic style. A definitive grammar of style, based on this revised theory, is developed and used to implement a stylistic analyzer, Asset. The revised theory of syntactic style and its implementation show that human-independent computer analysis of style is a feasible goal for computational linguistics.
Date Sept 1993
Report A Goal-Directed Functionally-Based Style Analyzer (PDF) Compressed PostScript:
A Goal-Directed Functionally-Based Style Analyzer (PS.Z)
CS-93-46
Title Performing Group-by Before Join
Authors P. Yan and P.-A. Larson
Abstract Assume that we have an SQL query containing joins and a group-by. The standard way of evaluationg this type of query is to first perform all the joins and then the group-by operation. However, it may be possible to perform the group-by early, that is, to push the group-by operation past one or more joins. Early grouping may reduce the query precessing cost by reducing the amount of data participating in joins. We formally define the problem, adhering strictly to the semantics of NULL and duplicate elimination in SQL2, and prove necessary and sufficient conditions for deciding when this transformation is valid. In practice, it may be expensive or even impossible to test whether the conditions are satisfied. Therefore, we also present a more practical algorithm that test a simple, sufficient condition. This algorithm is fast and detects a large subclass of transformable queries.
Date November 1993
Comments The major part of this paper will appear in the Proceedings of the 10th International Conference on Data Engineering(1994).
Report Performing Group-by Before Join (PDF) Compressed PostScript:
Performing Group-by Before Join (PS.Z)
CS-93-43
Title Constraint-Based Rendering for Scenes with High Dynamic Ranges
Authors L. Fang
Abstract Many researchers have examined rendering techniques with a focus on realistic image synthesis. Ray tracing and radiosity, which are the most successful current methodologies, are based on the physics of light and surfaces. Neither considers display device limitations or properties of human visual perception. Furthermore, the synthetic camera model has shown its deficiency in rendering scenes with high dynamic ranges onto display devices with lower dynamic ranges.
A new rendering framework is proposed. Human visual properties are incorporated into the framework to increase the effective visual contrast. It is known in visual perception that brightness is not a monotonic function of intensity. The perceived brightness is affected by the intensities of the surrounding area. It is also known that human vision is insensitive to low frequency spatial intensity variation. In the proposed framework, to preserve the visual contrast in one image, the contrasts across edges are maintained while the intensities in large areas are slowly varied.
Based on the proposed framework, a modified rendering pipeline is presented and a prototype system is implemented. The system generates the contrast constraints by invoking a modified visible surface algorithm. Then, the problem of satisfying the constraint hierarchy is transformed into a bounded linear least squares (BLLS) problem. Numerical algorithms are employed to solve the BLLS problem.
Date October 1993
Report Constraint-Based Rendering for Scenes with High Dynamic Ranges (PDF) Compressed PostScript:
Constraint-Based Rendering for Scenes with High Dynamic Ranges (PS.GZ)
CS-93-42
Title A Query Sampling Method of Estimating Local Cost Parameters in a Multidatabase
Authors Q. Zhu and P.-A. Larson
Abstract In a multidatabase system (MDBS), some query optimization information related to local database sys- tems may not be available at the global level because of local autonomy. To perform global query optimization, a method is required to derive the necessary local information. This paper presents a new method that employs a query sampling technique to estimate the cost parameters of an autonomous local database system. We introduce a classification for grouping local queries and suggest a cost estimation formula for the queries in each class. We present a procedure to draw a sample of queries from each class and use the observed costs of sample queries to determine the cost parameters by multiple regression. Experimental re- sults indicate that the method is quite promising for estimating the cost of local queries in an MDBS.
Report A Query Sampling Method of Estimating Local Cost Parameters in a Multidatabase (PDF) Compressed PostScript:
A Query Sampling Method of Estimating Local Cost Parameters in a Multidatabase (GZIP)
CS-93-41
Title Weighted Graph Based Ordering Techniques for Preconditioned Conjugate Gradient Methods
Authors S.S. Clift and W.-P. Tang
Abstract We describe the basis for a matrix ordering heuristic for improving incomplete factorization for preconditioned conjugate gradient techniques applied to anisotropic PDE's. Several new matrix ordering techniques, derived from well-known algorithms in combinatorial graph theory, which attempt to implement this heuristic, are described. These ordering techniques are tested against a number of matrices arising from linear anisotropic PDE's, and compared with other matrix ordering techniques. A variation of RCM is shown to generally improve the quality of incomplete factorization preconditioners.
Date August 1993
Report Weighted Graph Based Ordering Techniques for Preconditioned Conjugate Gradient Methods (PDF) Compressed PostScript:
Weighted Graph Based Ordering Techniques for Preconditioned Conjugate Gradient Methods (PS.Z)
CS-93-40
Title The Sparse Basis Problem and Multilinear Algebra
Authors A. Pothen, R.A. Brualdi and S. Friedland
Abstract Let A be a k by n underdetermined matrix. The sparse basis problem for the row space W of A is to ,nd a basis of W with the fewest number of nonzeros. Suppose that all the entries of A are nonzero, and that they are algebraically independent over the rational number field. Then every nonzero vector in W has at least n - k + 1 nonzero entries. Those vectors in W with exactly n - k + 1 nonzero entries are the elementary vectors of W. A simple combinatorial condition that is both necessary and suficient for a set of k elementary vectors of W to form a basis of W is presented here. A similar result holds for the null space of A where the elementary vectors now have exactly k + 1 nonzero entries. These results follow from a theorem about nonzero minors of order m of the (m -1)st compound of an m by n matrix with algebraically independent entries) which is proved using multilinear algebra techniques. This combinatorial condition for linear independence is a first step towards the design of algorithms that compute sparse bases for the row and null space without imposing arti,cial structure constraints to ensure linear independence.
AMS(MOS) subject classifications: primary 65F50, 65K05, 15A96.
Keywords: elementary vector, matrix compound, null-space basis, row-space basis, sparse matrix, wedge product.
Date September 1993
Report README The Sparse Basis Problem and Multilinear Algebra (PDF) Compressed PostScript:
The Sparse Basis Problem and Multilinear Algebra (PS.Z)
CS-93-38
Title On Correctness and Efficiency for Advancing Front Techniques of Finite Element Mesh Generation
Authors S. Farestam and R.B. Simpson
Abstract Advancing front techniques are a family of methods for finite element mesh gener- ation that are particularly effective in dealing with complicated boundary geometries. In the first part of this paper, conditions are presented which ensure that any planar aft algorithm that meets these conditions terminates in a finite number of steps with a valid triangulation of the input domain. These conditions are described by specifying a framework of subtasks that can accommodate many aft methods and by prescribing the minimal requirements on each subtask that ensure correctness of an algorithm that conforms to the framework.
An important efficiency factor in implementing an aft is the data structure used to represent the unmeshed regions during the execution of the algorithm. In the second part of the paper, we discuss the use of the constrained Delaunay triangulation as an efficient abstract data structure for the unmeshed regions. We indicate how the cor- rectness conditions of the first part of the paper can be met using this representation. In this case, we also discuss the additional requirements on the framework which en- sure that the generated mesh is a constrained Delaunay triangulation for the original boundary.
Classifications: AMS(MSC) 65N50, 65Y25; CR G.1.8, I.3.5
Keywords:unstructured meshes, finite element method, Delaunay triangulation
Date July 1993
Report On Correctness and Efficiency for Advancing Front Techniques of Finite Element Mesh Generation (PDF) Compressed PostScript:
On Correctness and Efficiency for Advancing Front Techniques of Finite Element Mesh Generation (GZIP)
CS-93-33
Title Preconditioned Conjugate Gradient Methods for Three Dimensional Linear Elasticity
Authors J.K. Dickinson
Abstract A finite element modelling of three dimensional elasticity problems gives rise to large sparse matrices. To improve upon direct solution methods, various new preconditioning methods are developed and examined, as well as some generally standard techniques, for use in preconditioned conjugate gradient iterative solution techniques. Developments of incomplete factorizations based on levels of fill, drop tolerance, and a two level hierarchical basis are used to build the preconditioning matrices. The problem of non-positive pivots occurring during factorization is also addressed by the use of several techniques. Computational tests are carried out for problems generated using unstructured tetrahedral meshes with quadratic basis functions. The performance of the iterative methods is compared to a standard direct sparse matrix solver. Various problems with up to 70,000 degrees of freedom are considered during which the effect of a range of average element aspect ratios, including small (<< 1) aspect ratios, on the performance of the PCG method is examined. A brief review is also made of stopping criteria for conjugate gradient solvers. One method based on the norm of the residual and an estimate of the smallest eigenvalue of the matrix system was implemented and tested with poor results.
Date June 1993
Report Preconditioned Conjugate Gradient Methods for Three Dimensional Linear Elasticity (PDF) Compressed PostScript:
Preconditioned Conjugate Gradient Methods for Three Dimensional Linear Elasticity (PS.Z)
CS-93-31
Title Computing Values and Derivatives of Bezier and B-spline Tensor Products
Authors S. Mann, T. DeRose and G. Windenback
Abstract When evaluating tensor product surfaces it is often necessary to calculate both the position and the normal to the surface. We give an efficient algorithm for evaluating Bezier and B-spline tensor products for such information. The algorithm is an extension of a method for computing the position and tangent to a Bezier curve, and is asymptotically twice as fast as the standard bilinear algorithm.
Date May 1993
Report Computing Values and Derivatives of Bezier and B-spline Tensor Products (PDF) Compressed PostScript:
Computing Values and Derivatives of Bezier and B-spline Tensor Products (PS.Z)
CS-93-30
Title An Illustration Technique for Unstructured 3-D Meshes
Authors N.P. Konrad and R.B. Simpson
Abstract Geometric relations in an irregular 3-D polyhedron or tetrahedral mesh are often difficult to comprehend, even for relatively few vertices. A technique for illustrating such meshes which aids this comprehension is described in terms of several independent components, i.e. edge representation, viewpoint and perspective projection, and lighting. These images are suitable for embedding in dynamic displays, or in publications.
Heuristics for the effective use of these components are discussed and the technique is demonstrated on three small configurations from the recent literature.
Date November 1993
Comments Submitted, 29/09/1993, to Graphics Interface '94 Conference.
Report An Illustration Technique for Unstructured 3-D Meshes (PDF) Compressed PostScript:
An Illustration Technique for Unstructured 3-D Meshes (PS.Z)
CS-93-29
Title The Design and Analysis of Asynchronous Up-Down Counters
Authors J.P.L. Segers
Abstract The goal of this report is to investigate up-down counter implementations in the framework of delay-insensitive circuits. An up-down counter is a counter on which two operations can be performed: an increment by one and a decrement by one. For N larger than zero, an up-down N-counter counts in the range from zero through N. In the counters we design, the value of the counter, or its count, cannot be read, but it is possible to detect whether the counter's value is zero, N, or somewhere in between. Up-down counters have many applications. For example, they can be useful in implementing queues or stacks.
Various implementations for up-down N-counters are presented for any N larger than zero. All counter designs are analyzed with respect to three performance criteria, namely area complexity, response time, and power consumption. One of the designs is optimal with respect to all three performance criteria. Its area complexity grows logarithmically with N, and its response time and power consumption are independent of N.
Date May 1993
Report The Design and Analysis of Asynchronous Up-Down Counters (PDF) Compressed DVI:
The Design and Analysis of Asynchronous Up-Down Counters (DVI)
CS-93-28
Title Skip Lists and Probabilistic Analysis of Algorithms
Abstract This thesis is concerned with various forms of skip lists, and with probabilistic analyses of algorithms. We investigate three topics; one topic from each of these two areas, and another topic common to both of them.
First, we consider Pugh's skip list. We derive exact and asymptotic expressions for the average search costs of a fixed key and of an average key. Our results improve previously known upper bounds of these two average search costs. We also derive exact and asymptotic expressions for the variance of the search cost for the largest key.
Next, we propose several versions of deterministic skip lists. They all have guaranteed logarithmic search and update costs per operation, they lead to an interesting "bridge" structure between the original skip list and standard search trees, they are simpler to implement than standard balanced search trees, and our experimental results suggest that they are also competitive in terms of space and time.
Finally, we consider the elastic-bucket trie, a variant of the standard trie, in which each external node (bucket) has precisely as many key slots as the number of keys stored in it. We examine the number of buckets of each size, and we derive exact and asymptotic expressions for their average values, as well as asymptotic expressions for their variances and covariances under the closely related "Poisson model" of randomness. Our experimental results suggest that maintaining only two bucket sizes may be a very reasonable practical choice.
Date May 1993
Report Skip Lists and Probabilistic Analysis of Algorithms (PDF) Compressed DVI:
Skip Lists and Probabilistic Analysis of Algorithms (DVI)
CS-93-27
Title A Clique Tree Algorithm for Partitioning a Chordal Graph
Authors A. Pothen, B.W. Peyton and X. Yuan
Abstract A partitioning problem on chordal graphs that arises in the solution of sparse triangular systems of equations on parallel computers is considered. Roughly the problem is to partition a chordal graph G into the fewest transitively orientable subgraphs over all perfect elimination orderings of G, subject to a certain precedence relationship on its vertices. In earlier work, a greedy scheme that solved the problem by eliminating a largest subset of vertices at each step was described, and an algorithm implementing the scheme in time and space linear in the number of edges of the graph was provided. Here a more efficient greedy scheme, obtained by representing the chordal graph in terms of its maximal cliques, which eliminates a subset of the leaf cliques at each step is described. Several new results about minimal vertex separators in chordal graphs, and in particular the concept of a critical separator of a leaf clique, are employed to prove that the new scheme solves the partitioning problem. We provide an algorithm implementing the scheme in time and space linear in the size of the clique tree.
AMS(MOS) subject classifications: primary 65F50, 65F05, 68R10.
Keywords:chordal graph, clique tree, critical separator, directed acyclic graph, perfect elimination ordering, sparse triangular solution, vertex separator, transitive closure, transitive perfect elimination ordering.
Date May 1993
Report README A Clique Tree Algorithm for Partitioning a Chordal Graph (PDF) Compressed PostScript:
A Clique Tree Algorithm for Partitioning a Chordal Graph (PS.Z)
CS-93-26
Title Enhancing Software Design Reuse: Nesting in Object-Oriented Design
Authors D.D. Cowan and C.J.P. Lucena
Abstract It has been observed that design of complex objects such as software requires both decom- position by form (atomic objects) and decomposition by function (nesting) in order to reduce the design to a set of manageable components. However, the object-oriented design paradigm mostly supports decomposition by form. This paper uses a simple example to motivate the need for nesting (decomposition by function) and illustrates how nesting might be incorporated into a design language. We conclude that the introduction of nesting into software specification and design significantly increases reusability.
Keywords: programming languages, program specification, software design and implementa- tion, software engineering
Date March 1994
Report Enhancing Software Design Reuse: Nesting in Object-Oriented Design (PDF) Compressed PostScript:
Enhancing Software Design Reuse: Nesting in Object-Oriented Design (PS.Z)
CS-93-25
Title Model Checking Timing Requirements
Authors J.M. Atlee and J. Gannon
Abstract Model checking has been used successfully to analyze concurrent, finite-state systems. In this paper, we extend the Software Cost Reduction (SCR) requirements notation to specify systems' timing requirements. We describe an analysis tool that transforms timed SCR specifications into timed reachability graphs, and show how some real-time properties can be verified with a model checker for branching-time temporal logic. In addition, we compare our system for analyzing SCR requirements with other model checkers that verify properties of real-time systems.
Date February 1994
Comments Submitted to TOSEM for publication.
Report Model Checking Timing Requirements (PDF) Compressed PostScript:
Model Checking Timing Requirements (PS.Z)
CS-93-24
Title Conflict-Free Accedss to Rectangular Subarrays in Parallel Memory Modules
Authors D. Erickson
Abstract In a parallel computing environment, we consider conflict-free access to constant-perimeter rectangular subarrays, using a natural formulation in terms of latin squares. For parallel matrix computations, there are frequently portions of data, referred to as templates, that one desires to be stored and retrieved in such a way that one can operate on the data simultaneously with each processor working on one element of the template. If more than one processor attempts to retrieve data from a single memory module during the same memory cycle, there is a memory conflict. When the array is stored to allow the desired templates to be accessible from the memory modules without memory conflicts, it is conflict-free for that set of templates. In this thesis, we examine a set of structured templates where the number of template instances defined by template grows with respect to the maximum size of a template. In particular, we examine the set of constant-perimeter rectangular subarrays.
A square is perimeter rectangular conflict-free' (p_rcf) if it is conflict-free for all rectangular subarrays whose perimeter is less than or equal to 2p. If p is even, the problem is to provide conflict-free access to all rectangular subarrays of size ((p/2)-i)*((p/2)+i) for -(p/2) < i <(p/2). We show that the necessary number of memory modules is ((p/2)^2) - p+1. Furthermore, ((p/2)^2) - p+1 memory modules are sufficient, and there is a linear skewing scheme to realize this bound. If p is odd, the problem is to provide conflict-free access to all rectangular subarrays of size (floor(p/2)-i)(ceiling(p/2)+i) for -floor(p/2)< i < floor(p/2). We show that the necessary number of memory modules is floor(p/2)^2, and there is a linear skewing scheme that realizes this bound. We also provide bounds and constructions for subsets of constant-perimeter rectangular subarrays, in particular all (x-i)(y+i) rectangular subarrays of an (n)(n) array for all nonnegative i where p=x+y. The linear results for the constant-perimeter rectangular subarrays hold when the subarrays are stretched by a factor of v where v is relatively prime to the number of memory modules. A subarray is stretched by v if every vth element in a row and every vth row is selected. In this situation, the perimeter includes only those elements in the rectangular subarray and not those elements skipped because of the stretch. Thus, the perimeter of a given rectangular subarray is the same regardless of its stretch.
In addition, the perimeter results provide a lower bound for conflict-free access to constant-area rectangular subarrays. An upper bound is found using a technique of relating conflict-free access to the chromatic number of a graph. In addition to bounds for constant-area rectangular subarrays, some computational results are provided. Finally, we propose a new method for defining skewing schemes, in particular, skewing schemes defined by permutations.
Date May 1993
Report Conflict-Free Accedss to Rectangular Subarrays in Parallel Memory Modules (PDF) Compressed PostScript:
Conflict-Free Accedss to Rectangular Subarrays in Parallel Memory Modules (GZIP)
CS-93-23
Title Threshold Schemes with Hierarcical Information
Authors D. Erickson
Abstract Consider the problem of n trustees, any k of which are needed to be in agreement to make an action x. In addition, if only (k-1) are in agreement, we would like to ensure that the action can not be made. Solutions to this type of problem have been independently proposed by Shamir (1979) and Blakley(1979). The solution is commonly referred to as a threshold scheme.
Numerous uses for threshold schemes are presented. These uses range from protecting encryption keys to preventing military and management actions without proper authority. Several general methods for implementing such schemes are examined in the literature. In this thesis we look at methods based on polynomial interpolation, on the intersection properties in finite geometries, and, more generally, Steiner systems, on those utilizing error correcting codes, and on those employing the Chinese Remainder Theorem.
Some of the threshold schemes in the literature present variations to the general scheme including the detection and the prevention of cheating. Others explore the implementation of threshold schemes that permit a hierarchy of authority for the participants in the scheme. The aim of this thesis is to present and explore variations and expansions of existing methods for threshold schemes to accommodate hierarchical information. Some of the proposed schemes not only provide hierarchical information but also implement hierarchical authority.
Date May 1993
Report Threshold Schemes with Hierarcical Information (PDF) Compressed PostScript:
Threshold Schemes with Hierarcical Information (PS.Z)
CS-93-22
Title On Object Layout for Multiple Inheritance
Authors W. Pugh and G.E. Weddell
Abstract We consider the problem of encoding objects for object-oriented programming languages that allow subtyping and multiple inheritance among class definitions. This is an important problem since a choice of encoding will determine the implementation for a number of common operations: extracting a property value from an object, comparing two object references for equality, and expression retyping.
We expand on earlier work in [9] in which we proposed a new algorithm for obtaining an object encoding that assigns a fixed o set to each property. This allows property values to be extracted with the same efficiency as in systems that do not provide multiple inheritance. We present both analytic and experimental evidence that suggests that this is an important performance issue and that our method works well in practice.
Keywords:object-oriented programming languages, object encoding, compilation.
Date May 1993
Report On Object Layout for Multiple Inheritance (PDF) Compressed PostScript:
On Object Layout for Multiple Inheritance (GZIP)
CS-93-21
Title Pointers versus Arithmetic in PRAMs
Authors P. Dyment, F.Fich, N.Nishimura, P.Ragde and L.Ruzzo
Abstract Manipulation of pointers in shared data structures is an important communication mechanism used in many parallel algorithms. Indeed, many fundamental algorithms do essentially nothing else. A Parallel Pointer Machine, (or PPM) is a parallel model having pointers as its principal data type. PPMs have been characterized as PRAMs obeying two restrictions — first, restricted arithmetic capabilities, and second, the CROW memory access restriction (Concurrent Read, Owner Write, a commonly occurring special case of CREW).
We present results concerning the relative power of PPMs (and other arithmetically restricted PRAMs) versus CROW PRAMs having ordinary arithmetic capabilities. First, we prove lower bounds separating PPMs from CROW PRAMs. For example, any step-by-step simulation of an $n$-processor CROW PRAM by a PPM requires time $\Omega(\log\log n)$ per step. Second, we show that this lower bound is tight — we give such a step-by-step simulation using $O(\log\log n)$ time per step. As a corollary, we obtain sharply improved PPM algorithms for a variety of problems, including deterministic context-free language recognition.
Date May 1993
Report No report
CS-93-20
Title ADV Charts: a Visual Formalism for Describing Abstract Data Views
Authors L.M.F. Carneiro, D.D. Cowan and C.J.P. Lucena
Abstract This paper introduces a new visual formalism, called ADVcharts, for specifying the behaviour of interactive systems (including multi-modal interactive systems) using a state-machine-based approach. ADVcharts combine concepts from Abstract Data Views (ADVs), with notations from Objectcharts, Statecharts, and Petri-nets. ADVcharts are part of the ADV specification approach. In this paper, we abbreviate the ADV specification approach'' term to ADVspec. The ADVspec allows the designer to express visually both the relationship among the user-interface objects and the flow of control of an interactive system using a single integrated approach. It is intended that the ADVspec will serve as a foundation for a future design methodology for interactive systems.
In particular, we show some aspects of design specific to interactive systems, such as the association of input and output events with particular Abstract Data Views, the concurrency of the components of a user interface, and the representation of various modes (input and output) in the design of an interactive system.
The semantics of ADVcharts are presented through the specification of some examples, and we demonstrate that ADVcharts can be used as a visual specification language to represent highly interactive systems from the perspective of the user interface.
We conclude this paper by demonstrating that VDM-like specifications can be derived directly from ADVcharts, thus providing the ADV concept with complementary visual and textual formalisms.
ADV Charts: a Visual Formalism for Describing Abstract Data Views (PS.Z)
CS-93-17
Title Towards CAAI: Computer Assisted Application Integration
Authors D.D. Cowan, R.G. Veitch and C.J.P. Lucena
Abstract As the manipulation and use of information forms the base of our economic structure, knowledge workers will become software application integrators. That is, knowledge workers who are experts in their specific domain and its related software, will need to "glue" together databases, analysis, simulation, modelling and visualization tools in order to produce timely information for their organization. In order to perform application integration easily we first need to define a coherent supporting architecture and a programming model. This paper outline this architecture and the programming model and indicates that many of the components to implement this model are available. Unfortunately, the design of many of these components is not consistent, thus, making it difficult for a knowledge worker to integrate applications without a large amount of "inside" technical information. Through the definition of these models we have highlighted the problems that need to be resolved. The architecture and programming model described in this paper are based on a large number of experimental systems developed as part of our research program.
Date February 1994
Report Towards CAAI: Computer Assisted Application Integration (PDF) Compressed PostScript:
Towards CAAI: Computer Assisted Application Integration (PS.Z)
CS-93-16
Title Program Design & Implementation with Abstract Data Views
Authors A.B. Potengy, C.J.P. Lucena, D.D. Cowan and R. Ierusalimschy
Abstract Creating new applications by integrating user interface and application components is a relatively new idea which is currently of wide interest. A significant part of this problem is clearly defining the separation between user interface and application components. This paper uses simple examples to illustrate a new design and implementation approach based on the concept of an abstract data view (ADV), a structuring method which cleanly defines this separation.
Date February 1994
Report Program Design & Implementation with Abstract Data Views (PDF) Compressed PostScript:
Program Design & Implementation with Abstract Data Views (PS.Z)
CS-93-15
Title Information Repository Requirements of the CORDS Multidatabase Service
Authors N. Coburn and P.-A. Larson
Abstract A multidatabase is a virtual database. As such, it requires support for the storage and retrieval of its operational data. That is, it requires the equivalent of the data dictionary or catalogue found in traditional relational databases. The CORDS project is a collaborative effort between several IBM laboratories and several North American universities. The goal of the CORDS project is to investigate and prototype a distributed environment which supports the development and operation of distributed applications. The CORDS Multidatabase project is one component within the CORDS environment. A second component of this environment is an Information Repository. We are investigating the viability of using the Information Repository as a means of implementing the Multidatabase catalogue. This report states the (current) Multidatabase data requirements on the Information Repository. We have attempted to outline our future requirements as clearly and broadly as possible. However, since we are creating a research prototype the requirements may change as we gain experience and understanding.
Date March 1993
Report Information Repository Requirements of the CORDS Multidatabase Service (DVI) Information Repository Requirements of the CORDS Multidatabase Service (PDF)
CS-93-14
Title User Interface High-Order Architectural Models
Authors L.M.F. Carneiro, M.H. Coffin, D.D.Cowan and C.J.P.Lucena
Abstract Many user-interface design models (usually expressed through architectural designs), expressed at different levels of abstraction, have been proposed in the literature. These models have been classified according to several criteria. The various design models are explicitly or implicitly derivable from a high order model which constitutes its specification. Existing classification schemes do not reflect this derivation process.
A new classification scheme for user-interface architectural designs is presented in this paper. This new classification scheme is based on derivations of designs. We analyze the initial specification and the high-order design models which correspond to models proposed in the literature at various levels of abstraction. The goal of the present study is to discuss issues such as relevant properties of design families'' (related to design trajectories), specification notations to be used as initial design steps, and `implementation biases'' induced by different design families. In particular, we put the Abstract Data View model in perspective by reviewing its specification, presenting its high-order architecture, and comparing it with architectures at similar and lower levels of abstraction.
Date February 1993
Report User Interface High-Order Architectural Models (PDF) Compressed PostScript:
User Interface High-Order Architectural Models (GZIP)
CS-93-13
Title Preconditioned Conjugate Gradient Methods for Three Dimensional Linear Elasticity
Authors J.K. Dickinson and P.A. Forsyth
Abstract Finite element modelling of three dimensional elasticity problems gives rise to large sparse matrices. Various preconditioning methods are developed for use in precon- ditioned conjugate gradient iterative solution techniques. Incomplete factorizations based on levels of /ll, drop tolerance, and a two level hierarchical basis are developed. Various techniques for ensuring that the incomplete factors have positive pivots are presented. Computational tests are carried out for problems generated using unstruc- tured tetrahedral meshes. Quadratic basis functions are used. The performance of the iterative methods is compared to a standard direct sparse matrix solver. Problems with up to 70,000 degrees of freedom, and small (<< 1) element aspect ratio are considered.
Keywords:Three dimensional elasticity, preconditioning, hierarchical basis
Running Title:PCG methods for 3-d elasticity
AMS Subject Classification:65F10, 65N30
Date February 1993
Report Preconditioned Conjugate Gradient Methods for Three Dimensional Linear Elasticity (PDF) Compressed DVI:
Preconditioned Conjugate Gradient Methods for Three Dimensional Linear Elasticity (DVI.Z)
CS-93-05
Title Mathematical Output Presentation in User Interfaces for Computer Algebra Systems
Authors T. R. Tyhurst
Abstract In recent years, the evolution of user interfaces for Computer Algebra Systems has lagged behind both the advances in the algebra engines which they serve, and the general developments seen in user interface principles as a whole. The increased availability of bitmapped display devices and the graphical user interface software running upon them has served to demonstrate the limitations of existing computer algebra system interfaces.
This thesis discusses some of the design and implementation issues inherent in the construction of an effective user interface for computer algebra systems. The emphasis is upon the efficient handling of the output of algebra systems, and effective techniques for presenting the mathematical content to the user, particularly when the expressions are large. A new user interface for the Maple system is described in light of the issues discussed, and a new variation on an algorithm for breaking long mathematical expressions over multiple lines is presented.
Date October 1992
Report Mathematical Output Presentation in User Interfaces for Computer Algebra Systems (PDF) Compressed PostScript:
Mathematical Output Presentation in User Interfaces for Computer Algebra Systems (PS.Z)
CS-93-03
Title On Lambert's W Function
Authors R.M. Corless, G.H. Gonnet, D.E.G. Hare and D.M. Jeffrey
Abstract The Lambert W function is defined to be the multivalued inverse of the function w→we^w It has many applications in pure and applied mathematics, some of which are briefly described here. We present a new discussion of the complex branches of W, an asymptotic expansion valid for all branches, an efficient numerical procedure for evaluating the function to arbitrary precision, and a method for the symbolic integration of expressions containing W.
Date January 1993
Report On Lambert's W Function (PDF) Compressed PostScript:
On Lambert's W Function (PS.Z)
CS-93-02
Title Linear and Non-linear Methods for the Incompressible Navier-Stokes Equations
Authors Simon S. Clift and Peter A. Forsyth
Abstract In this study, the discretized finite volume form of the two dimensional, incompressible Navier Stokes equations is solved using both a frozen coefficient and a full Newton nonlinear iteration. The optimal method is a combination of these two techniques. The linearized equations are solved using a conjugate-gradient-like method (CGSTAB). Various different types of preconditioning are developed. Completely general sparse matrix methods are used. Investigations are carried out to determine the effect of finite volume cell anisotropy on the preconditioner. Numerical results are given for several test problems.
Date January 1993 Revised August 1993
Comments Submitted to: International Journal for Numerical Methods in Fluids
Report Linear and Non-linear Methods for the Incompressible Navier-Stokes Equations (PDF) Compressed PostScript:
Linear and Non-linear Methods for the Incompressible Navier-Stokes Equations (PS.Z)
CS-93-01
Title GRAIL: Enginering Automata in C++
Authors D. Raymond and D. Wood
Abstract Grail is a package for computing with finite automata and regular expressions, written in C++. Grail supports input and output of textual descriptions of automata and regular expressions, conver- sions between automata and regular expressions, and other opera- tions. Grail can be used as a set of shell-callable processes, a library of functions, or as individual C++ classes. This docu- ment describes the history, design, and organization of Grail; the appendix contains a list of all classes and a short descrip- tion of each function.
Date January 1993
Report GRAIL: Enginering Automata in C++ (PDF) Compressed PostScript:
GRAIL: Enginering Automata in C++ (GZIP)
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# Probability and statistics ques
1. Jun 22, 2008
### sstudent
QUES: the yield of a chemical process is bieng studied. the past 5 days of plant operation have resulted in :91.6, 88.75, 90.08, 89.95, 91.3. Find a 95% two-sided confiendce interval. Thanks folks
2. Jun 22, 2008
### rootX
3. Jun 22, 2008
### sstudent
i tried using the eqautaion "Confiendnce interval on the mean, varaiance known" but i am not sure how to get the variance. thanks
4. Jun 23, 2008
### konthelion
Let $$\bar{x}$$ be the sample mean, what is $$\bar{x}$$?
What is n, the sample size?
What is s, the sample standard deviation?
What distribution should you use(based on n)? Then find the 95% confidence interval.
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Torque3d Features - Issues - Wishlist
Friendly conversations, and everything that doesn't fit into the other forums.
• 1
• 2
Torque3d Features - Issues - Wishlist
Bloodknight
Posts: 94
Joined: Tue Feb 03, 2015 8:58 pm
[/size]Torque 3D MIT Uservoice Wishlist[/size]
This is the complete list of wishes from the garage games uservoice, I intend to relist them in some orderly fashion.
Some are done, some are works in progress, some despite wishful thinking are never likely to happen, especially with the current manpower issues, these along selected items from the other places where features are requested can form the goto list if you want to work on the engine, or users can add their own to the list and start work.
If you are working on one of these and wish to say so, I can put your @link next to them so people who want to help with specific parts
Also I've no idea how this clashes with jeffs new posts, if it does then... I've prepared a list for him :p
• Add full support for Linux Operating Systems to Torque 3D
• Multiple CPU Core Usage (for skinned meshes especially)
• A new scripting language
• Shader Composer / Material Editor
• Open GL 4.x support for Torque3D
• Add full support for Mac OS X to Torque 3D
• AI System - Navgraph, planner, fuzzy state machine
• A system like kismet from unreal engine 3
• DX11 Support
• Global Illumination
• Update the Terrain System
• Inverse Kinematics for character animation
• Export to mobile platforms
• weather system
• Create an Open Source Alternative to Torsion
• GUI system Overhaul for Torque 3D
• Terrain Streaming or Paging
• Wind animation and collision support for groundcover objects
• 3d skybox
• Multiple Viewports in World Editor
• Better support for MinGW compilers
• hitboxes aka locational damage
• KEY FEATURE - Please keep Torque-3D-Linux Generic (Non-Os and Non-Version specific! )
• Animation Blending
• Add Torque3D to Steam Greenlight
• Steps in the FPS Tutorial for how to compile Torque3D for the first time.
• Use a Plug-in Architecture so all the Add-ons could work together
• Add full support for Linux Operating Systems to Torque 2D
• Convert data serialization over to use TAML
• In game cinematics
• More Full Featured templates/Starter kits
• Forest Editor to support multiple forest objects per mission
• Play through web page, with streaming capabilities
• Support for Intel Graphics Cards
• Displacement map option.
• Core Engine refactor with Core Plus modules
• PhysX vehicle
• C# implemented
• Light animation for the emissive material
• wetness PostFX and wetness custom material
• Torque Smart ptr: Shared, Weak, and Scoped
• Seperate Sever from Client
• XMLVM toolchain for cross compiling to .Net, iOS, Android and Java
• A scripting language like GML (Game Maker Language)
• screenspace lightning
• Elevation mask for terrain-painting and new filling function
• Add placement of physicsForce objects to the World Editor
• More efficient / intuitive handling of the editor
• Additional options for forest/mesh painting
• Phong Tesselation
• More Simgroups/better managing (forest items, terrain materials...)
• Bigger brushes
• Marble Class
• Vehicle steering return-to-centre
• Better Zip file functionality
• Occlusion Volume
• RayInfo distance with ContainerRayCast
• Database: Simple and Complex
• MVC Design Pattern (Component System?)
• An unreal mesh paint like editor hooked into shadergen
• SetDPIAware()
• Add terrain layer sensitivity to the forest
• Enable looping for GuiTheoraCtrl.
• Zone Update
• Support for exporting game to the Flash platform
• Ai poses and ContactTimer Pack/Unpack update fix (already in resources)
• T2D Style Toybox System
• beefing up the sketch tool
• Jitter in terrain system between terrain and models
• Feature: "externalCommand" for Torque 3D
• GuiHealthHud - a C++ replacement for the scripted numerical health hud
• Improved Color Picker
• Add new GuiBitmapStringCtrl that strings a number of images
Art and level development
*Interior/structure designer like Constructor
*Prefab object that combines models and scripts
*Improve forest editor
*Beefing up the sketch tool
*Beef up the material editor
*Jitter in terrain system between terrain and models
*Better snapping system
*Better Zip file functionality
*Add terrain specular, and if needs be, remove parallax from the terrain pass to make way for it, but retain parallax for shapes.
*Add the ability to set a kind of 'alpha mask' for the terrain tools, so you can set the strength & shape of the tools a bit more specifically.
*Add more flexibility in the noise tool again, maybe being able to set a tiled heightmap mask to it so you can again control the behaviour of it better depending on design requirements.
*Water... although I haven't played around with it in recent builds, and it may have been changed since I have used it properly, the settings for water could really be simplified down to make it more user-friendly, a lot of the settings are awkwardly named considering their effects on the water blocks.
*A basic precipitation and particle library
*Better terrain materials manager
*Add a semi "auto-zone" widget kinda thing. for example selecting a building shape, and at the click of a button, create a "zone" item matching its bounds etc.
*Ground Cover needs collision support
*Add terrain layer sensitivity to the forest
*Improve character import
*Light bleeding through the seems
*Possibly change the ground cover and forest editor to be 2 more generalized editors
*when standing outside of a zone, particles and lights are visible that are created inside of it. the only way that they should be visible is by looking inside the zone through a portal.
*Occlusion Volume. It should have a switch that allows it to effect the terrain behind it or not. As it stands, it causes the terrain to disappear behind it, which u don't always want.
*More 3D imports
*Artist friendly - add sliders along w numbers input
*SKYBOX and SCATTER SKY should work together somehow
*Better animation blending
everything that says 'improve' or one of its 20 million gazillion alternative ways to say improve need moving to a separate list, since clearly, the feature exists in some form, also to some extent they are the most pointless and irritating *wishes* in list form, they need to be discussed.
if you believe this is an important area of work, take an item and create its own thread, make sensible suggestions and notes about what is missing of needs adding/enhancing.
TODO Note: Rework to new thread with appropriate separation.
Last edited by Bloodknight on Mon Jul 11, 2016 1:25 pm, edited 1 time in total.
Re: Torque3d Features - Issues - Wishlist
Steve_Yorkshire
Posts: 205
Joined: Tue Feb 03, 2015 10:30 pm
A new scripting language
Bloodknight
confirmed for iterally worse thanStarfish Hitler
Re: Torque3d Features - Issues - Wishlist
rlranft
Posts: 298
Joined: Thu Feb 05, 2015 3:11 pm
Bloodknight wrote:
• A new scripting language - vague
• C# implemented - available
• A scripting language like GML (Game Maker Language) - why?
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• AI System - Navgraph, planner, fuzzy state machine - vague, I'm guessing just some basic tools? Navigation is already present with recast/detour. State machine is already there, how the end user decides to trigger state transitions it is up to the end user.
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• GUI system Overhaul for Torque 3D - vague
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• 3d skybox - "skybox" is by definition 3D
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• Animation Blending - I think you mean "improvements" - animation blending has been a thing for over a decade, it's just not great
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• Steps in the FPS Tutorial for how to compile Torque3D for the first time. - this doesn't belong in the FPS Tutorial, It's about making an FPS, not building the engine. A link to this information (which already exists elsewhere) would be more appropriate.
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• Use a Plug-in Architecture so all the Add-ons could work together - Which add-ons? ALL the add-ons? Because some are redundant and some are mutually exclusive....
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• Convert data serialization over to use TAML - pros and cons
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• In game cinametics - I thought GMK was part of the engine now....
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• Forest Editor to support multiple forest objects per mission - but it already supports multiple brushes, and brushes can contain multiple meshes. What need does this address?
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• Support for Intel Graphics Cards - this is backwards. Intel graphics cards have poor support for the features T3D provides. Or do we want T3D to reduce feature usage to allow running on inferior hardware?
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• wetness PostFX and wetness custom material - puppy shader confirmed.
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• Torque Smart ptr: Shared, Weak, and Scoped - where? Rewrite the engine using these? or make them available script side (and how)?
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• More efficient / intuitive handling of the editor - using whose opinion as the metric?
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• More Simgroups/better managing (forest items, terrain materials...) - vague
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• Marble Class - What? One can create a sphere with mass using any of the available physics systems - what does a "marble" do that any other sphere does not?
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• Database: Simple and Complex - which DBMS?
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• Support for exporting game to the Flash platform - Under what license?
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- redundant
• beefing up the sketch tool
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• Jitter in terrain system between terrain and models - Need to add jitter? Remove it? What jitter specifically? This sounds odd - how reproducible is this? Never seen it before....
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• Feature: "externalCommand" for Torque 3D - Again, in what context? Engine-side you can do this at will. You want a script command that will allow execution of third-party code outside of the game? Ever hear the phrase "recipe for disaster"? "Your game deleted my C:\ drive!" "Your game sent my credit card information to a bank in Tunisia!"
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• GuiHealthHud - a C++ replacement for the scripted numerical health hud - Okay, but it's crazy simple to use a GuiBitmapCtrl and resize it to show reduced health....
• Add new GuiBitmapStringCtrl that strings a number of images - guessing we're talking about some sort of animated bitmap control like the old IFL-animation system, but this is also a little vague.
I know, I'm being obnoxious. Consider this my wish list:
"Be careful what you wish for" and for Pete's sake be specific and detailed. And filter for redundant wishes - I'm sure many of these are already on the roadmap. Much of what is in that list is either available, available with a little thought, or project-specific and therefore inappropriate for inclusion in the engine (I suppose examples would be nice, sure, but don't put your AI solution in there because I'll just have to remove it).
I like all of the "improvement" items, except where vague. Some items are too open to interpretation or too subjective - how do we make the editor "more intuitive?" The only really "counter-intuitive" thing off the top of my head is GUI placement and resizing constants - they're poorly named and when you look at it it's hard to think of "better" names, so they stay poorly named (I mean, once you see what they do they describe it correctly, but until you see what they do they make no sense).
Stuff like "Intel graphics cards" gets me. "This looks like crap on my Intel graphics card." "Yeah? Well at least it runs on it...." is where we're headed with that one. Unless we're still just bailing because it's Intel. This used to be an issue because the Intel cards reported no support for power management features that the engine needs to prevent screen saver activation and monitor shutoff. Do we want to remove this? Should we just allow the game to run and then listen to the users cry because their monitor goes to sleep in the middle of a game? Sounds to me like that's a developer decision - if I want that headache over the "This won't run on my Intel card" headache then that's my choice.
So, tldr, some are vague, some are redundant, many are subjective.
Re: Torque3d Features - Issues - Wishlist
Azaezel
Posts: 383
Joined: Tue Feb 03, 2015 9:50 pm
rlranft wrote:[*]In game cinametics - I thought GMK was part of the engine now....
Nope. Last word on that (still) was the things fatal in spots.
rlranft wrote:[*]Forest Editor to support multiple forest objects per mission - but it already supports multiple brushes, and brushes can contain multiple meshes. What need does this address?
[*]More Simgroups/better managing (forest items, terrain materials...) - vague
Will note there's an opengl bug with multiple meshes per forest brush casing corruption. Different brushes per forest is a thing that does work iirc. would need to tripplecheck.
Of more concern (or at least more often mentioned is the fact it writes the brush definitions all to one file.
rlranft wrote:[*]wetness PostFX and wetness custom material - puppy shader confirmed.
James Stanley actually threw us a partial I've been keeping a copy of https://github.com/Azaezel/Torque3D/tre ... teness_bbq though as you'll see https://www.youtube.com/watch?v=-y6s73A8TqY the math still needs work and I haven't had time to follow up. Someone wants to swtich from asking to doing, by all means.
rlranft wrote:[*]Torque Smart ptr: Shared, Weak, and Scoped - where? Rewrite the engine using these? or make them available script side (and how)?
Engine actually already has weak and strong pointer divides, so theres 1/3rd of that request already.
[*]beefing up the sketch tool
Being worked on by JeffR
rlranft wrote:[*]Jitter in terrain system between terrain and models - Need to add jitter? Remove it? What jitter specifically? This sounds odd - how reproducible is this? Never seen it before....
https://github.com/GarageGames/Torque3D/issues/914
https://www.youtube.com/watch?v=IFmp9sX8xRM done a little research there. needs proper action classes and some math reworking vs the quickie-hax, but the baseline noise class still seems to work.
bloodknight wrote:Add full support for Linux Operating Systems to Torque 3D
KEY FEATURE - Please keep Torque-3D-Linux Generic (Non-Os and Non-Version specific! )
Last thing* needs doing that's been reported is file save dialogues. either native gui via sdl plugin, or go the torque gui route.
* (barring glew replacement down the road for some non'standard' linux distros)
bloodknight wrote:Shader Composer / Material Editor
This would be the part where I start binge-drinking, right?
bloodknight wrote:Add full support for Mac OS X to Torque 3D
Export to mobile platforms
Play through web page, with streaming capabilities
Oh, wait, no, this is.
bloodknight wrote:Multiple CPU Core Usage (for skinned meshes especially)
Better to fix the remaining flaws in the hardware skinning fork from James.
Do we reeeeely need a third language to maintain?
bloodknight wrote:Add placement of physicsForce objects to the World Editor
That anything like the physicszones that are already A Thing?
bloodknight wrote:Bigger brushes
Is literally a oneliner. That shouldn't be a request. That should be a PR. C'mon now...
Open GL 4.x support for Torque3D -check it off.
RayInfo distance with ContainerRayCast - The capability of getting this has been a thing for more than a decade...
DX11 Support - viewtopic.php?f=40&t=473 -check it out.
Better Zip file functionality - https://github.com/GarageGames/Torque3D/pull/1466 -check it out.
Improved Color Picker - https://github.com/GarageGames/Torque3D/pull/1334 -check it out.
Create an Open Source Alternative to Torsion - http://wiki.torque3d.org/introduction:scripting-ides - should clarify what further integration is needed.
hitboxes aka locational damage - part of E/C
Re: Torque3d Features - Issues - Wishlist
rlranft
Posts: 298
Joined: Thu Feb 05, 2015 3:11 pm
Azaezel wrote:
rlranft wrote:[*]In game cinametics - I thought GMK was part of the engine now....
Nope. Last word on that (still) was the things fatal in spots.
Darn.
Azaezel wrote:
rlranft wrote:[*]Forest Editor to support multiple forest objects per mission - but it already supports multiple brushes, and brushes can contain multiple meshes. What need does this address?
[*]More Simgroups/better managing (forest items, terrain materials...) - vague
Will note there's an opengl bug with multiple meshes per forest brush casing corruption. Different brushes per forest is a thing that does work iirc. would need to tripplecheck.
Of more concern (or at least more often mentioned is the fact it writes the brush definitions all to one file.
Hmm. I have yet to have an actual problem with this. Does it still munge up the forest saves occasionally?
Azaezel wrote:
rlranft wrote:[*]Torque Smart ptr: Shared, Weak, and Scoped - where? Rewrite the engine using these? or make them available script side (and how)?
Engine actually already has weak and strong pointer divides, so theres 1/3rd of that request already.
Yeah, but the rest of this is just odd anyway - while VS2015 acts up when using T3D's current template stuff, VS2013 is fine with it and you can use the STL smart/strong/weak/scoped pointers at need when adding new stuff. Do we really need to go and rework thousands of lines of code for this? Or create a custom set of templates for them? This entire request just seems odd because these are language extension features in C++ (if we're talking engine-side, of course) and not really engine features (because T3D's weak and strong pointer implementations predate solid STL implementations).
Azaezel wrote:
[*]beefing up the sketch tool
Being worked on by JeffR
Was just pointing out the redundant requests and subjective nature thereof.
Azaezel wrote:
rlranft wrote:[*]Jitter in terrain system between terrain and models - Need to add jitter? Remove it? What jitter specifically? This sounds odd - how reproducible is this? Never seen it before....
https://github.com/GarageGames/Torque3D/issues/914
Huh. Nope, never had that problem either.... Nasty, though.
Last edited by rlranft on Sun Dec 20, 2015 6:20 pm, edited 2 times in total.
Re: Torque3d Features - Issues - Wishlist
chriscalef
Posts: 332
Joined: Mon Feb 09, 2015 7:48 pm
bigger brushes
I don't know the one line fixes all solution, but here's an example one liner for forest brushes...
Code: Select all
void ForestBrushTool::setSize( F32 val ){ mSize = mClampF( val, 0.0f, 15000.0f );//instead of 150.0f... Con::executef( this, "syncBrushToolbar" );}
Re: some of the other items, I know it's not production ready but I'm definitely working on the terrain paging thing, and have PhysX vehicles on my roadmap although I can't commit to a date for them yet. Also interested in several of the other items. But unless it means moving over to C#, which is already pretty well established, good luck with pushing another scripting language.
Re: Torque3d Features - Issues - Wishlist
JeffR
Steering Committee
Posts: 750
Joined: Tue Feb 03, 2015 9:49 pm
rlranft wrote:
Bloodknight wrote:
• 3d skybox - "skybox" is by definition 3D
Most of the other stuff has been pretty well covered, but I thought I'd comment on this:
This is referring to what the UT99 engine or GoldSrc/Source did for skyboxes, where you basically have the skybox read from a dynamic cubemap probe in a little sub-area in the map. That way, you could model your terrain and add other details/models, and it would act as a dynamic skybox rather than a static image. This is useful for dynamic situations, such as, say, a huge distant forest fire and having the smoke from that animated, while very much perceptually being in the distance.
It would also come with the advantage of playing very uniformly with dynamic lighting from the sun/sky.
So yeah, pretty legit request, actually. It'd definitely have it's uses.
Re: Torque3d Features - Issues - Wishlist
chriscalef
Posts: 332
Joined: Mon Feb 09, 2015 7:48 pm
Well that does sound quite interesting!
Say, while we're on the subject, can anyone tell me anything about what might be involved in order to implement a skydome instead of a skybox? I searched around on this site and garagegames, and didn't find much, but apparently this guy has done it.
Not sure off the top of my head how to create a hemispherical image, but it's obviously a problem that's been thoroughly solved by now. Beyond that wouldn't it just mean drawing a spherical object in place of the box, and inserting it at the same place in the render?
Re: Torque3d Features - Issues - Wishlist
JeffR
Steering Committee
Posts: 750
Joined: Tue Feb 03, 2015 9:49 pm
This may act as a decent starting point:
https://msdn.microsoft.com/en-us/library/bb464016.aspx
And yeah, could probably just copy the skybox object, rename it to skysphere, have it render in the same order the skybox does now and just have it use the skysphere shader.
Re: Torque3d Features - Issues - Wishlist
Azaezel
Posts: 383
Joined: Tue Feb 03, 2015 9:50 pm
By and large once you peel off the proceedural colorization and account for the foreshortening, that's scattersky in a nutshell. https://github.com/GarageGames/Torque3D ... y.cpp#L755 for instance would be one to manipulate if working off of that as a base to turn into a full sphere*.
*Disclaimer, Oversimplification. just doing so to that will lead to (admittedly hilarious but) useless results due to the aforementioned shader-side procedural colorization.
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Math Emeritus Sci Advisor Thanks PF Gold P: 39,568 Velocity w/axis vs without If the force is applied perpendicular to the motion of the ball then its speed is constant. The distance around the circle in time t is $v_it$.
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225 posts
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Question water ocean
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Question water physics
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# 8. Visibility Rules¶
## 8.1. Declarative Region¶
No extensions or restrictions.
## 8.2. Scope of Declarations¶
No extensions or restrictions.
## 8.3. Visibility¶
No extensions or restrictions.
### 8.3.1. Overriding Indicators¶
No extensions or restrictions.
## 8.4. Use Clauses¶
Legality Rules
1. Use clauses are always in SPARK, even if the unit mentioned is not completely in SPARK.
## 8.5. Renaming Declarations¶
### 8.5.1. Object Renaming Declarations¶
Legality Rules
1. [An expression or range occurring as part of an object_renaming_declaration shall not have a variable input; similarly, the access-valued prefix of a dereference occurring as part of an object_renaming declaration shall not have a variable input. See Expressions for the statement of this rule.] [The first part of this rule can apply to an index of an indexed_component and the range of a slice.]
### 8.5.2. Exception Renaming Declarations¶
No extensions or restrictions.
### 8.5.3. Package Renaming Declarations¶
No extensions or restrictions.
### 8.5.4. Subprogram Renaming Declarations¶
From the point of view of both static and dynamic verification, a renaming-as-body is treated as a one-line subprogram that “calls through” to the renamed unit.
Legality Rules
1. The aspect_specification on a subprogram_renaming_declaration shall not include any of the SPARK-defined aspects introduced in this document.
### 8.5.5. Generic Renaming Declarations¶
No extensions or restrictions.
## 8.6. The Context of Overload Resolution¶
No extensions or restrictions.
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Why use linux to dev games?
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Mindwarp 122
Hello everyone, For about the past year or so I have been running linux as my primary operating system. Previously I had only windows experience. I am currently running windows 2000. I recently switched to windows this week because I was hoping to find direction in programming (It always seems to me like there isn''t much money in programming free software or selling software in a market where everything is free). I would just like to share some of my thoughts for those who havent tried linux as to its advantages and disadvantages for programmers looking to make games (Primarily win32 platform). Some benefits of linux are that it is free. To get my win2k box up to speed I have to attempt to attain a copy of Visual C++ 6.. god only knows how much that costs if your not a student. Then I want to make a logo or 2 for my game, so I need to find a suitable editor. Seems either fireworks or photoshop. Both costing alot of money (I prefer photoshop). Then I figure I want some 3d stuff in my games, so I need to go purchase some 3d editor like 3ds max.. point is by the time I am done I have probably spent more money than I have, which is a bad thing. With linux you have the gcc compiler which is free. It does not come bundled with a IDE (I know what most people are saying right now, they can just use borland in windows without paying for the above visual C++.. bah), but it is command line driven, and is very easy to use. (ex. gcc mygame.c -o mygame.exe) There are several very good editors (vim for console mode and xemacs and gvim for xwindows). As for picture editing gimp is great, and for 3d work blender is excellent also. So how do you make games on Linux that do both linux and win32? Libsdl (http://www.libsdl.org).. lets you do both.. slap in a good api like opengl and your ready to go. Give linux about a month or 2 months of moderate use and you will be flying. Point is.. even though the free applications I mentioned are all available on windows also, they may not be as well supported since they were designed for linux. Also linux itself is free, which is a big benefit with XP costing as much as it does. Not to mention you can then serve a webpage, host your own email server etc. all for free.. As a coder I actually enjoy alot of the command line-ness of linux, as it really helps me get stuff done faster than trying to work through some GUI (which probably explains why apache is the #1 webserver. Just simply edit the apache.conf file and your rocking). Related links: www.mandrake.com - Mandrake linux - Good distrobution to start out with www.debian.org - the distribution you will use once you know what your doing www.linuxnewbie.org - where I first learned how to use linux www.libsdl.org - the library your application will use so you dont need to fuss with winapi nehe.gamedev.net - Just about all examples available in SDL cone3d.gamedev.net - SDL examples there also www.gimp.org - Graphic editor www.blender.nl - 3d editor www.vmware.com - Lets you run windows from inside linux ($) www.winehq.org - Lets you run windows applications from inside linux (ex. half-life, the sims etc. all run pretty decent) www.slashdot.org - Tons of linux related news, one-sided stories on how linux rules www.lokigames.com - a example of games ported using SDL www.enlightenment.org - my favorite windows manager Hope this helps anyone who is bored with their current operating system, sick of paying too much$, sick of bad business tactics, or if your a hippie.. Mindwarp
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Null and Void 1088
Although I don''t know his reason for posting this, a lot of his points are valid . SDL is so cool (spred the word ). Here''s the link for GIMP for Windows if anyone wants it: http://user.sgic.fi/~tml/gimp/win32/. The Win32 version is a little buggy, it is much better in *nix.
[Resist Windows XP''s Invasive Production Activation Technology!]
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Guest Anonymous Poster
Also remember, the main reason Linux hasn''t become hugely popular yet is because there hasn''t been as much development and support for it. Once more people (like you coders out there) start supporting and developing on Linux, it will quickly get much more popular.
Monolith 122
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pwd 122
Umm. Why are you switching back to Windows again?
Oh well, I''ll post a few random thoughts. The last time I had to do a Windows app (for a job interview), I whipped out my ancient Win95 cd, pulled the Borland compiler off the net, and was ready to go within 20 minutes. I only needed to show a garbage collecting/compacting algorithm, and some other random stuff, so it was all console. Did the coding under Linux w/Vim tested/debugged with gcc/gdb and then just copied it over to the Windows stagin area and recompiled. Who needs Visual Studio?
Way back when, when I still used Windows regularly, I used Paint Shop Pro for 2d graphics stuff (www.jasc.com). It suited my needs well enough. Don''t knock it either, the game dev company I worked at used it right alongside Photoshop. For light graphics (ie, if your abilities rank as "Programmer Art", or if all you need to do is some scaling, format conversion or color correction), it is a viable, cheaper alternative to Photoshop. That was a few major versions ago, though, so not sure how well it has matured. If you can have the artists on your team using Photoshop, and leave the programmers with Paint Shop Pro for emergency touch ups, that might be an ideal solution.
I have yet to be impressed with what I''ve seen of the Windows Gtk port, so avoiding the GIMP under Windows is probably wise.
VMWare (www.vmware.com) is your friend. If you can afford the full version, you can run any number of versions of Windows or other OSs. Cheaper than a dedicated machine for different Windows versions, but you''ll want at least 256MB of RAM... Also great for testing installs, you can set up virtual machines that "roll back" to a clean state whenever you want them to. I use this daily at my current job, and it is worth every penny.
Or... Go Mac. A platform with a less saturated market for games. Perhaps an indie developer would have a better chance of getting notice. Mac OS X rocks, and the dev tools are free (Project & Interface Builder, gcc, etc) + the familiar *nix command line tools are available. And Macheads are probably more used to paying for their software. iBooks can be had fairly cheaply and are nice (the iBook and OS X combo are what finally got me to switch )
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Martee 476
I tend to disagree (not with Linux being a great OS, but with everything in the Windows world being expensive). My hard drive is filled with free Windows software. MinGW, Mozilla, Winamp, ICQ, Apache, J2SDK, JCreator, SSH, Leech FTP, Editor ''99, QWS3270, Cygwin, and so on. These aren''t just crappy ports of Linux apps, they are high-quality native Windows applications which I use every day.
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Kwizatz 1392
ok, Here is my 2 cents,
I code for Windows inside Linux, mostly because of the money factor, even when I code under Windows I do it with Linux(ish) tools, that is Gimp for Win32, Xemacs for NT, Mingw32, AC3d (not really free, but worth paying for), I have to say that it is a really good environment to work with, and I am staying with it.
The Fact That I can Actually Email the authors of the programs I use, and tell them how great their software is, or tell them hey there is a bug in there! or even fix the bug myself and send them the patch feels great, as you get to be where the action is
My goal is to write a comercial game (its on its way), I know it doesn't very well fit with being developed with open source technologies, but, I want to turn this into a way of life, and the plan is to make donations once the game generates revenue, The GIMP,Mingw,SDL and RedHat are on top of my list, so I see it as a use now, pay later kind of thing.
By The Way, SDL IS great!
Edited by - kwizatz on November 5, 2001 10:39:32 PM
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amreshr 122
Use Kylix or Delphi6. They are both free and u can download it from http://www.borland.com
The code is X-platform for both Win32 and Linux. It has a great IDE and good debugging facilities.
For api header translations, you can find it at www.delphi-jedi.org
For OpenAL header translations you can wait for the jedi release or find it at http://amresh09.tripod.com
Amresh
ramresh@dsqsoft.com
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GoofProg 127
I have been an avid windows user for some time now and I wanted to learn something new.. so I bought a box for \$200 and converted it to OpenBSD (not linux) I installed Mandrake and Suse before.. but I didn''t like them.. To be honest I have not developed anything for **nux yet, but it does look promising.. setting up config files with VI was quite interesting.
Windows is good for games because of DirectX. Linux is free, but still requires you to set aside HD partitions to install (except for stuff like loadlin)..
I feel that people keep dancing around the problem.. why not just create an whole OS for game development. Or remember the old days.. the game WAS the OS! The problem is imagine writing driver code for 2000 different devices. Also you could use legacy stuff VESA.. SB compatible code...etc.. but you lose hardware acceleration..
maybe writing a game OS is not a good idea..
sorry i was writing in "real time" so my writing contradicts itself =P
that''s my half a pennies worth
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Tracy 122
Anonymous Poster-I don''t know anything about Linux (although I''ve thought about using it because it sounds like a really cool OS), but from what I understand it''s a prompt driven OS (sort of like DOS). Is that right? If so, that''s the reason it will never be hugely popular. Most PC users aren''t really what you call ''geeks'', what they''ll want is an OS that is an event driven type with a visual interface. Personnally, I like that sort of stuff. But I know a little (I said ''alittle'') about programming. Most PC users aren''t programmers and don''t wanna be. They want something that''s easy to use and they don''t care about technical stuff.
Of course, those of us here who are serious about this stuff are an exception to the rule.
Who agrees? disagrees?
"A man can''t just sit around." ''Lawn Chair'' Larry Walters (1982)
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Martee 476
quote:
Original post by Tracy
but from what I understand it''s a prompt driven OS (sort of like DOS).
http://www.kde.org/screenshots/kde2shots.html
Yes, the console is extremely important in the Linux world, but it''s quite possible to use Linux without touching a console. Some distributions (such as Mandrake) will automatically configure your system to start a graphical environment on boot.
Of course, the console is an extremely useful tool, and in many ways, it''s much more powerful than a GUI could ever be
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Kwizatz 1392
Tracy,
XWindows is the Graphic interface for Linux, it doesnt has to be command prompt driven unless you want it to be, dont think of it as something like 16 bit DOS, because it is not, although if I had to give you an idea of how it works, I would have to say it is like when you had to boot in DOS and run Windows with WIN, of course there are methods (XDM) so you can start in graphics mode right away.
try too look for Linux desktop screenshots, I remember that after being so used to the Windows Look and feel I was impresed seeing those.
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Dauntless 314
I''m still debating whether I should devote the majority of my time learning to develop for windows or Linux. The realistic part of me says that Windows is the more profitable venture and will make me more marketable, but the more curious and pioneering side of me wants to learn Linux.
What little I do know about Linux programming seems very interesting. What I find most interesting is how open things are. I think I could learn more quickly with Linux despite its (seemingly) higher complexity because source code is so readily available. IT lets me see the nuts and bolts of how real programming works. So even though Windows stuff seems more enscapsulated (no need to worry about X windows, file managers, and wondering if your audience has all the dependencies), Linux just seems like the tinkerers paradise.
However, Linux has another nasty downfall. Namely that I see Windows outperforming it graphically come DirectX9. And going along with that, in Windows programming, all it seems you really need to know is the DirectX API and some Win32 stuff. With Linux, you have to know the Linux kernel, SDL, OpenGL (and or Mesa), X windows, and potentially GUI toolkits/Desktop stuff like GTK gnome or Kde/Qt. That''s what I mean by the learning curve.
So for a beginner like me, what would people recommend I learn first? If I study windows/directX programming first, will it make the transition to Linux easier? Or would it be the other way around, and should I study Linux first and then move on to Windows?
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Famine 100
Two words: DRIVER SUPPORT
Until linux can woo manufacturers into developing drivers for video cards, printers, lah di dah, linux will go nowhere. I agree, its a great platform, and could be the best in terms of a development platform, but, they need to get some support. I''ll agree its grown in popularity, and some manufacturers are developing drivers now, but its still pretty weak. Second problem, standard user interface.....Fix those two major situations, and linux will grow much faster.
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Kwizatz 1392
Dauntless,
if you are confident enought, learn both, some people put it as "if I learn WinApi, I will never learn GTK+" as if they were both so hard to learn that only one fits in your head, as it comes up, its not really all that different, if you know standard C/C++, you already know how to program in both Windows and Linux, its just a matter of getting used to the tools available to you on eighter platform, I code in/for both, I learned WinApi first, cos Windows was what was available to me at the time, but learning different Linux API''s its not as hard as it might seem (my first Linux program was a FLTK app, and I found it to be a lot easier than WIN32_LEAN_AND_MEAN).
Of course you will be more likelly to find a job sooner if you know Windows, but if its a 70%/30% chance, wouldnt you want to learn both, and have a 100% chance?
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Oluseyi 2107
quote:
Original post by Famine
Two words: DRIVER SUPPORT
Actually, there''s a whole bunch more words. Standard directories. Standard definitions of dependencies (which versions of which libraries link against which other versions of which other libraries). Defined installation procedures. Improved user interface (if Linux ever wants to go mainstream).
There''s also the fact that commerce and Linux haven''t gone too well together - from the succession of cutbacks and closures of Linux companies (most notably VA''s hardware operations) to Linux users'' lack of support for commercial Linux software (note the dismal sales of the boxed Linux Quake3/Arena). Put your moeny where your mouth is, Linux faithful.
I wanna work for Microsoft!
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Mindwarp 122
Well you guys seem to enjoy smashing linux.. feel good?
I was not saying linux should replace windows, nor its superiority. But when you can design games that work on both platforms, and for free no less, I figured I would help pass along the world. Thats all. I didn''t say linux owns the desktop or has superior driver support. It doesn''t. But in many cases, such as mine, it has proven to be a very productive environment for my development. Thought I would share, thats all
Mindwarp
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Oluseyi 2107
I don''t think anybody was smashing Linux. People simply aired their views on the pros and cons of Linux development. Don''t be so overprotective; the Linux community bashes Windows all the time... what goes around, comes around.
And I love Linux.
I wanna work for Microsoft!
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chiuyan 122
your arguments are pretty bogus. gcc (that free compiler you love for linux) runs on windows. borland has a free compiler too. for your image editing, you got paint (just as good a bitmap editor as any other). Gimp runs on windows too (and is still free). most of your cool imaging effects will most likely be done by your own tools anyway (building alpha maps and such). For 3d modeling, blender runs on windows too.
all these free tools run on windows too, so the only thing you have to pay for is the OS.
--michael
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Null and Void 1088
quote:
Original post by chiuyan
Your arguments are pretty bogus... All these free tools run on Windows too, so the only thing you have to pay for is the OS.
How does that make his ''arguments'' bogus? He even points out that most of those programs run in Windows. His ideas still can potentially save money. Saving money is the point, isn''t it? Why are you trying to ''disprove'' his tips for saving money?
[Resist Windows XP''s Invasive Production Activation Technology!]
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Rube 122
Nah, the origional point wasn''t saving money, but why develop on Linux. By proving that most of the free software you want to use also runs on Windows, then you''re back to the point of which OS to use to develop. =)
Personally, I''m a Linux advocate. I think it''s a great OS. I''m also a so-so Open Source Software(OSS) advocate. I think OSS is great in an ideal world, but unfortunately, we''re not in an ideal world. I wish we were. =(
I think the biggest barrier to Linux isn''t that it''s open source, but that most Linux users won''t pay for applications. Companies are willing to pay for support contracts and software licensing on OSS, but end users aren''t ready to go there yet. Until then, there just isn''t the drive to create robust, stable software.
Personally, I wish Microsoft would develop their applications to run on Linux and even build their own GUI shell. But, again, not an ideal world we live in =)
I hope in the future companies will invest in OSS programmers and just hire them to adapt OSS packages to a company''s specific needs. But so far, most companies are still willing to pay for their own development from scratch. Though IBM is making some positive changes in that regard.
We''ll have to see how it all plays out. But the great thing about OSS is their willingness to port to Win32. I''m glad the spirit behind OSS continues beyond the OS Religion Wars!
Rube.
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Null and Void 1088
quote:
Original post by Rube
Nah, the original point wasn't saving money, but why develop on Linux. By proving that most of the free software you want to use also runs on Windows, then you're back to the point of which OS to use to develop. =)
I think it was to save money (maybe I interpret arguments differently ), and Linux happened to be one of the options to turn to. There's no reason NOT to use Windows if you already have paid for it, unless it can't do something you want it (doesn't have the feature, doesn't have the software, technically lacking, whatever).
I personally still refrain from writing any single OS (whether that single OS is Windows, Linux, or whatever) only software, I like to give people options. I try not to enforce those boundaries external to what I have control over .
[EDIT: Fixing typos. Stupid quarks in the English language, heh]
[Resist Windows XP's Invasive Production Activation Technology!]
Edited by - Null and Void on November 6, 2001 6:28:44 PM
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A. Buza 122
Bleh... just stick to writing pure DirectX/Win32 code. Those linux hippies won''t pay for your games anyway! They''re not at all like windows users, who pay for all the software they have! Linux users are the type who would trade copyrighted/commercial products over filesharing systems and IRC! Not windows users, no sir! The evil GPL gnomes will steal your source code, too! And everyone knows that by letting other people look at your code, the blind idiot God Azathoth will spread chaos throughout time and space, and great Cthulhu will awaken from his sleep of death in R''lyeth!! Don''t let that happen! Cross OS/Platform software is bogus! Everyone uses windows anyways! When is the last time you''ve seen someone use something other than windows!? ..
No, macOS doesn''t count. Thats for trendies and soccer moms!
..
UNIX derivatives? Those are only used on stodgy 40-year old monotlithic servers! What kind of nerd are you!?
..
Linux is for peacenicks and hippies, man. They don''t pay for stuff anyway.
..
Consoles!? You can''t develop for those on computers!
..
See what I mean! Everyone uses windows! We should all write 100% windows code from now until eternity! MFC forever! Down with standards! Microsoft is the only standard you need!
Whats a "pozicks"?
...bleh.. I needed that little rant..
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# Electromagnetic induction
Electromagnetic induction is the production of an electrical potential difference (or voltage) across a conductor situated in a changing magnetic flux.
Michael Faraday discovered the induction phenomenon in 1831. He found that the electromotive force (EMF) produced along a closed path is proportional to the rate of change of the magnetic flux through any surface bounded by that path. In practice, this means that an electrical current will flow in any closed conductor, when the magnetic flux through a surface bounded by the conductor changes. This applies whether the field itself changes in strength or the conductor is moved through it. Electromagnetic induction underlies the operation of generators, induction motors, transformers, and most other electrical machines.
For a coil of wire in a changing magnetic field, Faraday's law of electromagnetic induction states that
[itex] \epsilon= - N{{d\Phi} \over dt}[itex] or [itex] U= {-{d\Phi} \over dt}[itex]
where
[itex]\epsilon[itex] is the electromotive force (emf) in volts
N is the number of turns of wire
Φ is the magnetic flux in webers
U is the induced voltage
Further, Lenz's law gives the direction of the induced emf, thus:
The emf induced in an electric circuit always acts in such a direction that the current it drives around the circuit opposes the change in magnetic flux which produces the emf.
Lenz's law is therefore responsible for the minus sign in the above equation.
## Applications
• Art and Cultures
• Countries of the World (http://www.academickids.com/encyclopedia/index.php/Countries)
• Space and Astronomy
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• # question_answer ) A and B are friends. A is elder to B by 5 years. B's sister C is half the age of B while A's father D is 8 years older than twice the age of B. If the present age of D is 48 years, find the present ages of A, B and C respectively. A) 50 years, 25 years, 20 yearsB) 40 years, 20 years, 15 yearsC) 20 years, 15 years, 10 yearsD) 25 years, 20 years, 10 years
Let the present ages of A, B, C and D are $x,y,z$and t respectively. Since, present age of D = t = 48 years. According to question, $x=y+5$ ?(i) $z=\frac{1}{2}y$ ?(ii) $t=2y+8$ ?(iii) From (iii), $48=2y+8$ $\Rightarrow$ $2y=40\Rightarrow y=20$years From (ii), $x=\frac{1}{2}\times 20=10$years From (i), $x=20+5=25$years So, present ages of A, B and C are 25 year, 20, years and 10 years respectively.
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### Help Support The Rocketry Forum:
#### manixFan
##### Not a rocket scientist
Magnetic switches and wifi are back.
Thank you TRA board!!!!
Tony
#### Cameron Anderson
##### Well-Known Member
Magnetic switches and wifi are back.
Thank you TRA board!!!!
Tony
#### manixFan
##### Not a rocket scientist
The link shows up as a login screen. It is on the prefects forum on the TRA website.
Tony
#### cerving
##### Owner, Eggtimer Rocketry
TRF Supporter
The Official notice...
Sent: Sunday, October 18, 2020 6:01 PM
Subject: [TRA Prefects Forum] Rule revision regarding wireless remote switches October 2020
A message was posted to Prefects Forum, on the Tripoli member's forum.
Gerald Meux Jr Posted:18 Oct 2020 10:00 AM Subject: Rule revision regarding wireless remote switches October 2020 In February 2020, the Tripoli BoD adopted a rule requiring a physical disconnection from power for any electronics controlling energetics. At the time they felt this was required by NFPA 1127. After further discussion during its September meeting, the board of directors has concluded that additional physical disconnects are not required and the February 2020 rule has been canceled. The rule requiring that energetics and firing circuits be inhibited until the rocket is in firing position remains in place. Thanks, Gerald Meux
Thank you, Tripoli Rocketry Association
#### manixFan
##### Not a rocket scientist
Thanks for posting that. I know the thread heading is a bit cryptic but I figured someone from TRA might also post about it. I’m no longer a prefect so I was a little obtuse about it. But anyone who followed the thread announcing the original decision will understand how I feel!
I sincerely appreciate the TRA board revisiting their decision. Thanks to the TRA board.
Tony
#### rharshberger
##### Well-Known Member
Funny it took TRA so long to announce the change to the public, I received notice of it from my clubs Prefect on Oct 1, and TRA posted it to FB yesterday.
#### timbucktoo
##### Well-Known Member
Staff member
TRF Supporter
Global Mod
Funny it took TRA so long to announce the change to the public, I received notice of it from my clubs Prefect on Oct 1, and TRA posted it to FB yesterday.
TRA only made it public on their website yesterday.
#### Charles_McG
##### Ciderwright
Praise be. Hopefully NAR will follow suit and I won’t worry anymore with my Protons if I’ve remembered to turn on deployment power - because they read closed circuit with deployment power off.
#### timbucktoo
##### Well-Known Member
Staff member
TRF Supporter
Global Mod
Praise be. Hopefully NAR will follow suit and I won’t worry anymore with my Protons if I’ve remembered to turn on deployment power - because they read closed circuit with deployment power off.
I will see if I can find the newsletter with their official statement but they were careful in their wording and didn't say you were required to use a switch but something like "recommended".
#### Charles_McG
##### Ciderwright
I understand that with greater risk, better controls should be in place. And ‘recommended’ is fine.
But I, personally, fly G-H impulse and sub gram charges, which seems to me to be at the low end of the HPR risk scale.
#### markg
##### Well-Known Member
Thank you to TRA. Since I didn't fly any HPR this year due to launch restrictions I hadn't yet made any changes to my wifi av-bays. Turns out procrastination paid off again!
#### ksaves2
Sooooooo, Does that mean I am perfectly legal with wiring up my charges, plugging in the battery and indeed the Featherweight switch defaults to “on” and I swipe the magnet immediately to turn it off? Or is that still a “no-no”?
Same thing with my Eggtimer TRS. I plug in the battery with charges attached and swipe to turn off at the bench before taking it out to the pad. Mind you with newly built or obtained deployment products I test them with contained ematches without powder to be certain I can plug the battery in, turn off the mag switch without any anomalies occurring. I also do the test with contained ematches before every flight to make sure the electronics perform the turn on/off process nominally before every flight.
Look, I usually do a “one shot” deal. Fly the rocket, turn off the deployment electronics after recovery and go on and fly another rocket. Too much of a pain in the a to re-prep an already flown rocket for another flight. I‘d rather have several rockets pre-prepped and ready to go to fly as many as possible during a flying session. It’s easy to do the safety checks when getting ready for the next launch down the road.
With minimum diameter rockets it can be difficult to have an external switch outside of twist and tape. Easier to have the charges in place and use a Mag switch to activate at the pad. Connect the battery at the prep area, usually the back of my SUV, turn the Mag switch off and get ready to go to the pad.
If there has been a change in the rules, great. If not well, will try to get by or maybe retire a bunch of rockets.
Kurt Savegnago
#### cerving
##### Owner, Eggtimer Rocketry
TRF Supporter
Remote arming is now considered to be "inhibited", as it was prior to the rule change. However, since the TRS does not have remote DISARMING, we recommend a switch on the deployment power so you can shut it off in case you have to take the rocket off the rack. The Quantum and Proton DO have remote disarming, plus a built-in switch for the deployment power that is not activated until launch-detect, so they do not require an external switch (which was the original TRA position).
If you read the TRA rule change, " additional physical disconnects are not required and the February 2020 rule has been canceled" pretty much says it all. Off is off... regardless of what interrupts the current flow.
#### ThirstyBarbarian
##### Well-Known Member
TRF Supporter
Awesome! I didn't do anything about retrofitting my egg timers with switches, because by the time the rule was announced, we were in lockdown, and all my launches were canceled, and I'm never one to take advantage of downtime to get things done. My "life-hack" of putting things off to the very last minute has worked yet again! Woohoo!
#### ttabbal
##### Well-Known Member
Nice! I'm in the middle of a small build and finding a way to get the switch mounted was bugging me. I really like the Quantum and Proton and think they are plenty safe with the two level switching required to trigger. Of course, between fire danger and virus danger there haven't been any launches lately, but I'm sure we'll get there eventually.
#### Wayco
##### Desert Rat Rocketeer
I'm glad that the Tripoli board members I voted for fixed this problem. Now I can fly all 24 of my high power rockets with magnetic switches at Tripoli launches again. I did build a couple of rockets with pull pin switches, but the Frenzy XL I'm building now will be with the new and improved Featherweight mag. switches.
#### Tobor
TRF Supporter
Hmm, I never received a Tripoli email announcement regarding this reversal.
Anyhoot, I'm glad I procrastinated finishing my MC Pike build...
#### Cameron Anderson
##### Well-Known Member
Nice to see common sense and acceptance of current technology prevailed.
#### sl98
##### Well-Known Member
Praise be. Hopefully NAR will follow suit and I won’t worry anymore with my Protons if I’ve remembered to turn on deployment power - because they read closed circuit with deployment power off.
One might argue that NAR never prohibited electronic switches in the first place. In the March 2020 Electronic Rocketeer, NAR states in part:
WiFi or magnetic non-contact switches should be backed up with physical breaks in either the power or energetic circuits whenever the rocket is being transported, handled, or inspected. Rocket preparation areas, vehicles, and check-in areas can be electromagnetically "noisy" areas that can increase the possibility of an inadvertent firing circuit or energetic operation.
"Should be" sounds more like a recommendation than a mandate.
#### Banzai88
##### Lvl 1,Wallet....Destroyed
TRF Supporter
"Should be" sounds more like a recommendation than a mandate.
Never thought I would say it, but I sometimes miss the LACK of ambiguity in military manuals that use the terms SHALL, MAY, and MUST, and the attendant definitions provided for such.
Last edited:
#### Steve Shannon
##### Well-Known Member
TRF Supporter
One might argue that NAR never prohibited electronic switches in the first place. In the March 2020 Electronic Rocketeer, NAR states in part:
WiFi or magnetic non-contact switches should be backed up with physical breaks in either the power or energetic circuits whenever the rocket is being transported, handled, or inspected. Rocket preparation areas, vehicles, and check-in areas can be electromagnetically "noisy" areas that can increase the possibility of an inadvertent firing circuit or energetic operation.
"Should be" sounds more like a recommendation than a mandate.
It was a recommendation for NAR. Neither organization prohibited electronic switches. Tripoli required that they be disconnected from power until after inspection. NAR never did.
Now Tripoli doesn’t.
#### gna
##### average joe-overbuild member
Thanks for posting that. I know the thread heading is a bit cryptic
So Hero used wifi, but it's ok with Claudio now? What will Beatrice and Benedick say?
#### Rob702Martinez
##### Zip-Tie Oversight Committee
TRF Supporter
I just ordered a ton of those fingertech switches too.
BTW have to repost this as I saw it in the original thread. Too good to let this one go...
#### cerving
##### Owner, Eggtimer Rocketry
TRF Supporter
I just ordered a ton of those fingertech switches too.
BTW have to repost this as I saw it in the original thread. Too good to let this one go...
View attachment 435447
Bueller? Anyone?...
#### Rob702Martinez
##### Zip-Tie Oversight Committee
TRF Supporter
But now I can resume ordering eggtimer wifi switches and using protons and quantums!!!
#### dvdsnyd
##### Well-Known Member
Remote arming is now considered to be "inhibited", as it was prior to the rule change. However, since the TRS does not have remote DISARMING, we recommend a switch on the deployment power so you can shut it off in case you have to take the rocket off the rack. The Quantum and Proton DO have remote disarming, plus a built-in switch for the deployment power that is not activated until launch-detect, so they do not require an external switch (which was the original TRA position).
If you read the TRA rule change, " additional physical disconnects are not required and the February 2020 rule has been canceled" pretty much says it all. Off is off... regardless of what interrupts the current flow.
Cris,
Is remote disarming on the roadmap of the TRS?
#### cerving
##### Owner, Eggtimer Rocketry
TRF Supporter
Hopefully... it's not a simple as it is with the WiFi stuff, because once you arm it the TRS is no longer "listening" to the LCD receiver.
#### g.pitts
##### Well-Known Member
TRF Supporter
What a cluster this whole thing has been. I trust that TRA internal processes will be looked at to ensure that decisions are better vetted before rollout in the future. Just my \$0.02.
#### HHaase
##### Well-Known Member
On a lighter note......
The whole discussion did get me to start re-examining how I handle my electronics mounting though, and my next generation of avionics bays are going to be a lot better for it. Still a few things to refine but the core concept I'm moving to is quite solid.
-Hans
#### Charles_McG
##### Ciderwright
The whole discussion did get me to start re-examining how I handle my electronics mounting though, and my next generation of avionics bays are going to be a lot better for it. Still a few things to refine but the core concept I'm moving to is quite solid.
I examined my preflight setup as a result, and changed a couple of things for the better. (I believe.)
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Dave the Most Horrid and Foul Necromancer
Dave the Most Horrid and Foul Necromancer lives in an underground chamber beneath an enormous dead tree in the swamp southwest of Escrow in Uberwald.
The underground chamber looks like this:
Thick roots weave along the roof and walls, encircling this small chamber with their massive girth. Moist earth makes up the rest of the walls, in stark contrast to the black granite floor. In the centre of the room squats a large black stone slab, carved with silvery runes and heaped with a massive mound of decaying flesh and bones. One or two quite fresh-looking human corpses dangle gruesomely from hooks driven into a couple of the roots that form the walls, while piled up against the remaining wall space are several caches of well-stripped bones. A few eerie lights, balls of greenish gas, illuminate this insalubrious place. A narrow tunnel leads up above ground and into the marsh.
There is one obvious exit: up.
A skeleton warrior and Dave the Most Horrid and Foul Necromancer are standing here.
A skeleton warrior.
A walking corpse. Bits look like they're about to fall off, or already have. It looks slightly
out-of-touch with the world, and very fierce.
It is in good shape.
It is standing.
Holding : a long sword (left hand).
Wearing : a pair of hobnailed boots, a pair of black wool trousers and a white cotton shirt.
(under) : thick black socks that can kick through walls
Dave the Most Horrid and Foul Necromancer.
He is a young man with a thick crop of bright red hair. He is very pale with not even the glimpse of a muscle underneath his white flesh. Something in the way that he stands, however, seems to give him the appearance of being quite sure of his own superiority.
He is in good shape.
He is standing.
He is surrounded by a hazy glow containing intense bands of red.
He has a large wooden shield floating around him.
Holding : a blackened iron staff (left hand and right hand).
Wearing : a pair of ornate black boots, a pair of ornate bone greaves, a pair of plaid breeches, a black tunic, a small satchel, an ornate bone helmet and a twisted black amulet.
Carrying: a chicken tail feather, a cured human skin, six cured human hearts, a small wooden shield, four small copper knives and a bone knife.
(under) : an ornate bone corslet.
It takes a bit of time to open the entrance to his chamber, so if it closed while you were inside it takes a while before you can enter again.
He spawns fully equiped with:
And he starts casting Grisald's Reanimated Guardian to get a skeleton warrior right away.
While he doesn't attack when you enter, he does if you consider him and once combat is engaged he likes to cast nasty spells that kill you a lot.
He has been seen casting:
Defensive spells
Offensive spells
Dave returning from the veil:
Dave the Most Horrid and Foul Necromancer appears out of a ball of blackish mist.
Dave the Most Horrid and Foul Necromancer hauls a corpse down from one of the hooks.
Dave the Most Horrid and Foul Necromancer kneels and shudders.
Dave the Most Horrid and Foul Necromancer makes horrid facial expressions.
Dave the Most Horrid and Foul Necromancer groans softly.
Dave the Most Horrid and Foul Necromancer strokes the corpse of an unfortunate adventurer lovingly.
The skeleton groans, stirs and rises.
The skeleton warrior equips a pair of hobnailed boots, a pair of thick woollen socks, a pair of black wool
trousers, a brown linen shirt and a short sword.
The skeleton warrior moves to defend Dave the Most Horrid and Foul Necromancer.
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Skip to main content
Learning SQL
If you aren't aware of it, there's a free online course on databases (and SQL). I took it back when it ran live, but it's just as good self-paced. Jennifer Widom (Stanford) is an outstanding lecturer and the videos and assignments are excellent. SQLite is used to grade the online exercises, so I'd suggesting installing a local copy to experiment with as it's free. I'd also strongly recommend installing either MySQL or PostgreSQL (I recommend PostgreSQL; both are free) so you can learn while using a full-featured database server. BaseX is very helpful for learning XML and mastering XPath and XQuery for web scraping (also free).
https://www.coursera.org/course/db
http://www.postgresql.org/
http://basex.org/
BaseX has a module for handling JSON. I haven't used it personally, but it looks useful for learning about JSON.
http://docs.basex.org/wiki/JSON_Module
A Bayes' Solution to Monty Hall
For any problem involving conditional probabilities one of your greatest allies is Bayes' Theorem. Bayes' Theorem says that for two events A and B, the probability of A given B is related to the probability of B given A in a specific way.
Standard notation:
probability of A given B is written $$\Pr(A \mid B)$$
probability of B is written $$\Pr(B)$$
Bayes' Theorem:
Using the notation above, Bayes' Theorem can be written: $\Pr(A \mid B) = \frac{\Pr(B \mid A)\times \Pr(A)}{\Pr(B)}$Let's apply Bayes' Theorem to the Monty Hall problem. If you recall, we're told that behind three doors there are two goats and one car, all randomly placed. We initially choose a door, and then Monty, who knows what's behind the doors, always shows us a goat behind one of the remaining doors. He can always do this as there are two goats; if we chose the car initially, Monty picks one of the two doors with a goat behind it at random.
Assume we pick Door 1 and then Monty sho…
What's the Value of a Win?
In a previous entry I demonstrated one simple way to estimate an exponent for the Pythagorean win expectation. Another nice consequence of a Pythagorean win expectation formula is that it also makes it simple to estimate the run value of a win in baseball, the point value of a win in basketball, the goal value of a win in hockey etc.
Let our Pythagorean win expectation formula be $w=\frac{P^e}{P^e+1},$ where $$w$$ is the win fraction expectation, $$P$$ is runs/allowed (or similar) and $$e$$ is the Pythagorean exponent. How do we get an estimate for the run value of a win? The expected number of games won in a season with $$g$$ games is $W = g\cdot w = g\cdot \frac{P^e}{P^e+1},$ so for one estimate we only need to compute the value of the partial derivative $$\frac{\partial W}{\partial P}$$ at $$P=1$$. Note that $W = g\left( 1-\frac{1}{P^e+1}\right),$ and so $\frac{\partial W}{\partial P} = g\frac{eP^{e-1}}{(P^e+1)^2}$ and it follows \[ \frac{\partial W}{\partial P}(P=1) = …
Mixed Models in R - Bigger, Faster, Stronger
When you start doing more advanced sports analytics you'll eventually starting working with what are known as hierarchical, nested or mixed effects models. These are models that contain both fixed and random effects. There are multiple ways of defining fixed vs random random effects, but one way I find particularly useful is that random effects are being "predicted" rather than "estimated", and this in turn involves some "shrinkage" towards the mean.
Here's some R code for NCAA ice hockey power rankings using a nested Poisson model (which can be found in my hockey GitHub repository):
model <- gs ~ year+field+d_div+o_div+game_length+(1|offense)+(1|defense)+(1|game_id) fit <- glmer(model, data=g, verbose=TRUE, family=poisson(link=log) ) The fixed effects are year, field (home/away/neutral), d_div (NCAA division of the defense), o_div (NCAA division of the offense) and game_length (number of overtime periods); off…
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# A Geometric Proof of Machin's Formula
by Roger B. Nelsen (Lewis and Clark College)
This article originally appeared in:
Mathematics Magazine
December, 1990
Subject classification(s): Algebra and Number Theory | Number Theory | Famous Problems | Geometry and Topology | Geometric Proof
Applicable Course(s): 3.2 Mainstream Calculus II | 4.1 Introduction to Proofs | 4.8 History of Math
The author presents a geometric proof of Machin's formula, which expresses $\frac {\pi}{4}$ as the difference of two inverse tangent functions.
A pdf copy of the article can be viewed by clicking below. Since the copy is a faithful reproduction of the actual journal pages, the article may not begin at the top of the first page.
To open this file please click here.
These pdf files are furnished by JSTOR.
Classroom Capsules would not be possible without the contribution of JSTOR.
JSTOR provides online access to pdf copies of 512 journals, including all three print journals of the Mathematical Association of America: The American Mathematical Monthly, College Mathematics Journal, and Mathematics Magazine. We are grateful for JSTOR's cooperation in providing the pdf pages that we are using for Classroom Capsules.
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# NAG FL Interfaces30aaf (opt_bsm_price)
## ▸▿ Contents
Settings help
FL Name Style:
FL Specification Language:
## 1Purpose
s30aaf computes the European option price given by the Black–Scholes–Merton formula.
## 2Specification
Fortran Interface
Subroutine s30aaf ( m, n, x, s, t, r, q, p, ldp,
Integer, Intent (In) :: m, n, ldp Integer, Intent (Inout) :: ifail Real (Kind=nag_wp), Intent (In) :: x(m), s, t(n), sigma, r, q Real (Kind=nag_wp), Intent (Inout) :: p(ldp,n) Character (1), Intent (In) :: calput
#include <nag.h>
void s30aaf_ (const char *calput, const Integer *m, const Integer *n, const double x[], const double *s, const double t[], const double *sigma, const double *r, const double *q, double p[], const Integer *ldp, Integer *ifail, const Charlen length_calput)
The routine may be called by the names s30aaf or nagf_specfun_opt_bsm_price.
## 3Description
s30aaf computes the price of a European call (or put) option for constant volatility, $\sigma$, and risk-free interest rate, $r$, with possible dividend yield, $q$, using the Black–Scholes–Merton formula (see Black and Scholes (1973) and Merton (1973)). For a given strike price, $X$, the price of a European call with underlying price, $S$, and time to expiry, $T$, is
$Pcall = Se-qT Φ(d1) - Xe-rT Φ(d2)$
and the corresponding European put price is
$Pput = Xe-rT Φ(-d2) - Se-qT Φ(-d1)$
and where $\Phi$ denotes the cumulative Normal distribution function,
$Φ(x) = 12π ∫ -∞ x exp(-y2/2) dy$
and
$d1 = ln (S/X) + (r-q+σ2/2) T σT , d2 = d1 - σT .$
The option price ${P}_{ij}=P\left(X={X}_{i},T={T}_{j}\right)$ is computed for each strike price in a set ${X}_{i}$, $i=1,2,\dots ,m$, and for each expiry time in a set ${T}_{j}$, $j=1,2,\dots ,n$.
## 4References
Black F and Scholes M (1973) The pricing of options and corporate liabilities Journal of Political Economy 81 637–654
Merton R C (1973) Theory of rational option pricing Bell Journal of Economics and Management Science 4 141–183
## 5Arguments
1: $\mathbf{calput}$Character(1) Input
On entry: determines whether the option is a call or a put.
${\mathbf{calput}}=\text{'C'}$
A call; the holder has a right to buy.
${\mathbf{calput}}=\text{'P'}$
A put; the holder has a right to sell.
Constraint: ${\mathbf{calput}}=\text{'C'}$ or $\text{'P'}$.
2: $\mathbf{m}$Integer Input
On entry: the number of strike prices to be used.
Constraint: ${\mathbf{m}}\ge 1$.
3: $\mathbf{n}$Integer Input
On entry: the number of times to expiry to be used.
Constraint: ${\mathbf{n}}\ge 1$.
4: $\mathbf{x}\left({\mathbf{m}}\right)$Real (Kind=nag_wp) array Input
On entry: ${\mathbf{x}}\left(i\right)$ must contain ${X}_{\mathit{i}}$, the $\mathit{i}$th strike price, for $\mathit{i}=1,2,\dots ,{\mathbf{m}}$.
Constraint: ${\mathbf{x}}\left(\mathit{i}\right)\ge z\text{ and }{\mathbf{x}}\left(\mathit{i}\right)\le 1/z$, where $z={\mathbf{x02amf}}\left(\right)$, the safe range parameter, for $\mathit{i}=1,2,\dots ,{\mathbf{m}}$.
5: $\mathbf{s}$Real (Kind=nag_wp) Input
On entry: $S$, the price of the underlying asset.
Constraint: ${\mathbf{s}}\ge z\text{ and }{\mathbf{s}}\le 1.0/z$, where $z={\mathbf{x02amf}}\left(\right)$, the safe range parameter.
6: $\mathbf{t}\left({\mathbf{n}}\right)$Real (Kind=nag_wp) array Input
On entry: ${\mathbf{t}}\left(i\right)$ must contain ${T}_{\mathit{i}}$, the $\mathit{i}$th time, in years, to expiry, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
Constraint: ${\mathbf{t}}\left(\mathit{i}\right)\ge z$, where $z={\mathbf{x02amf}}\left(\right)$, the safe range parameter, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
7: $\mathbf{sigma}$Real (Kind=nag_wp) Input
On entry: $\sigma$, the volatility of the underlying asset. Note that a rate of 15% should be entered as $0.15$.
Constraint: ${\mathbf{sigma}}>0.0$.
8: $\mathbf{r}$Real (Kind=nag_wp) Input
On entry: $r$, the annual risk-free interest rate, continuously compounded. Note that a rate of 5% should be entered as $0.05$.
Constraint: ${\mathbf{r}}\ge 0.0$.
9: $\mathbf{q}$Real (Kind=nag_wp) Input
On entry: $q$, the annual continuous yield rate. Note that a rate of 8% should be entered as $0.08$.
Constraint: ${\mathbf{q}}\ge 0.0$.
10: $\mathbf{p}\left({\mathbf{ldp}},{\mathbf{n}}\right)$Real (Kind=nag_wp) array Output
On exit: ${\mathbf{p}}\left(i,j\right)$ contains ${P}_{ij}$, the option price evaluated for the strike price ${{\mathbf{x}}}_{i}$ at expiry ${{\mathbf{t}}}_{j}$ for $i=1,2,\dots ,{\mathbf{m}}$ and $j=1,2,\dots ,{\mathbf{n}}$.
11: $\mathbf{ldp}$Integer Input
On entry: the first dimension of the array p as declared in the (sub)program from which s30aaf is called.
Constraint: ${\mathbf{ldp}}\ge {\mathbf{m}}$.
12: $\mathbf{ifail}$Integer Input/Output
On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.
If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ or $\mathbf{1}$ is used it is essential to test the value of ifail on exit.
On exit: ${\mathbf{ifail}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).
## 6Error Indicators and Warnings
If on entry ${\mathbf{ifail}}=0$ or $-1$, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
${\mathbf{ifail}}=1$
On entry, ${\mathbf{calput}}=⟨\mathit{\text{value}}⟩$ was an illegal value.
${\mathbf{ifail}}=2$
On entry, ${\mathbf{m}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{m}}\ge 1$.
${\mathbf{ifail}}=3$
On entry, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{n}}\ge 1$.
${\mathbf{ifail}}=4$
On entry, ${\mathbf{x}}\left(⟨\mathit{\text{value}}⟩\right)=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{x}}\left(i\right)\ge ⟨\mathit{\text{value}}⟩$ and ${\mathbf{x}}\left(i\right)\le ⟨\mathit{\text{value}}⟩$.
${\mathbf{ifail}}=5$
On entry, ${\mathbf{s}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{s}}\ge ⟨\mathit{\text{value}}⟩$ and ${\mathbf{s}}\le ⟨\mathit{\text{value}}⟩$.
${\mathbf{ifail}}=6$
On entry, ${\mathbf{t}}\left(⟨\mathit{\text{value}}⟩\right)=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{t}}\left(i\right)\ge ⟨\mathit{\text{value}}⟩$.
${\mathbf{ifail}}=7$
On entry, ${\mathbf{sigma}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{sigma}}>0.0$.
${\mathbf{ifail}}=8$
On entry, ${\mathbf{r}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{r}}\ge 0.0$.
${\mathbf{ifail}}=9$
On entry, ${\mathbf{q}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{q}}\ge 0.0$.
${\mathbf{ifail}}=11$
On entry, ${\mathbf{ldp}}=⟨\mathit{\text{value}}⟩$ and ${\mathbf{m}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{ldp}}\ge {\mathbf{m}}$.
${\mathbf{ifail}}=-99$
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.
## 7Accuracy
The accuracy of the output is dependent on the accuracy of the cumulative Normal distribution function, $\Phi$. This is evaluated using a rational Chebyshev expansion, chosen so that the maximum relative error in the expansion is of the order of the machine precision (see s15abf and s15adf). An accuracy close to machine precision can generally be expected.
## 8Parallelism and Performance
s30aaf is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.
None.
## 10Example
This example computes the prices for six European call options using two expiry times and three strike prices as input. The times to expiry are taken as $0.7$ and $0.8$ years respectively. The stock price is $55$, with strike prices, $58$, $60$ and $62$. The risk-free interest rate is $10%$ per year and the volatility is $30%$ per year.
### 10.1Program Text
Program Text (s30aafe.f90)
### 10.2Program Data
Program Data (s30aafe.d)
### 10.3Program Results
Program Results (s30aafe.r)
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# SAT Math : Fractions and Percentage
## Example Questions
### Example Question #11 : Fractions
Solve each problem and decide which is the best of the choices given.
There is a bag with green marbles, red marbles, purple marbles, and blue marbles. What is the probability that a red marble is randomly chosen from the bag?
Explanation:
To find the probability of a red marble being randomly chosen, you have to divide the number of red marbles by the total number of marbles.
There are red, and total,
thus, creating the fraction
.
To find the percentage, simply divide by and multiply the result by to get .
### Example Question #11 : Fractions
Determine the approximate percentage given the fraction .
Explanation:
Because a fraction is a part of a whole , set up a proportion.
The fraction is approximately .
### Example Question #1 : Fractions And Percentage
Bob and Jill go eat dinner at a fancy restaurant. Bob gets lobster and Jill gets crab legs. The lobster cost , and the crab legs cost . If they leave tip, how much is the combined bill?
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# Low Dimensional Topology
## March 14, 2014
### Train tracks on a torus
Filed under: Curve complexes,Surfaces — Jesse Johnson @ 11:47 am
A little over a year ago, I started writing a series of posts on train tracks and normal loops, then got distracted by other things. In the mean time, I wrote a paper with Yoav Moriah involving train tracks and curve complex distances, which gave me a whole new perspective on what train tracks really mean, more in line with much of Masur and Minsky’s work [1]. So, I want to resuscitate the series of posts on train tracks, but in a slightly different direction than where I was headed before. I’ll start by looking at a very simple case: train tracks on a torus. If you need a review of what train tracks are (the mathematical object, not the literal ones), you can reread my earlier post.
We can form a train track on a torus by taking two essential loops in the torus that intersect once, then smoothing the intersection, as in the Figure below. (I’m drawing the torus as a square with opposite sides identified.) There are two possible ways to smooth the intersection, and for now we’ll just arbitrarily pick one. (Later on, we’ll come back to look at the difference between the two smoothings.) The resutling graph isn’t a train track, bit we can turn it into a train track by taking a regular neighborhood of it, then giving the neighborhood a foliation by intervals perpendicular to the original graph. The original graph (shown in the middle of the Figure) is called a train track diagram.
The question I want to explore in this post is: What loops in the torus are carried by this train track? The answer will be in terms of the slopes of the carried loops. Recall that the universal cover of the torus is the plane. In every isotopy class of essential loops, there is a representative that lifts to a straight line in the universal cover. In fact, there’s an infinite family of such loops that lift to different lines in the plane, but all these lines have the same slope. This slope is what we call the slope of the (isotopy class of the) loop in the torus. In the Figure above, the blue loop has slope 0 and the red loop has slope 1/0 or $\infty$. Note that both of these loops are carried by the train track. (Or, more precisely, they’re isotopic to loops that are carried by the train track.)
In general, we can calculate the absolute value of the slope of a loop by dividing the number of times it intersects the horizontal boundary of the square by the number of times it intersects the vertical boundary. (You can check that this formula holds for the red and blue loops.) For any slope other than 0 and $\infty$, we can figure out the sign as follows: If an arc has one endpoint on the left side of the square and the other endpoint on the top then the loop has positive slope. If an arc has one endpoint on the left and its other endpoint on the bottom then the loop has negative slope. (It’s not too hard to check that a loop that intersects the sides of the square minimally can’t have both types of arcs.)
There are many other loops in the torus, in addition to the red and blue loops above, that are carried by this particular train track. Examples with slopes $1$, $2$ and $\frac{1}{2}$, respectively, are shown in red in the Figure below.
All these loops have positive slopes, and in fact, you can see that no arc from the left side of the square to the bottom of the square can be carried by this train track. So this means that this train track can only carry positive slopes.
On the other hand, we can put in as many copies of either the vertical or the horizontal arc as we want. We can also put in as many arcs as we want from the left side to the top side, and the same number from the bottom to the right side. By choosing the number of such arcs carefully, we can get the intersections between the resulting loops and the sides of the squares to be whatever we want. (If the number of intersections with the top is greater than the number with the bottom, we’ll only use vertical arcs. Otherwise, we’ll only use horizontal arcs.) So, every loop with positive slope will be carried by this train track.
To make it clear, let me summarize what we’ve learned: The train track that we constructed carries all the loops with positive slopes, as well as the loops with slope 0 and $\infty$. Going back to the beginning of the post, note that if we had chosen to smooth the intersection between the original two loops in the opposite way, the resulting train track would have carried all the negative slope loops, as well as 0 and $\infty$. So, we can think of a train track as a way to separate the loops in a surface into two different classes: the loops that are carried and the loops that aren’t.
One way that this gets really interesting is when consider what these two classes look like in the curve complex for the surface. This approach is one of the main tools used in Masur and Minsky’s work on the curve complex [1], particularly their proof that curve complexes of surfaces are Gromov $\delta$-hyperbolic.
Recall that the curve complex for a surface S is the simplicial complex whose vertices represent isotopy classes of essential, simple closed curves in S and whose faces span sets of isotopy classes with pairwise-disjoint representatives. The curve complex for a torus is pretty boring: Any two disjoint essential loops in a torus are parallel (and thus isotopic) to each other, so there are no edges in this curve complex- It’s just an infinite collection of discrete vertices.
So instead, one generally works with the Farey graph for the torus. Much like the curve complex, the vertices of the Farey graph represent isotopy classes of essential loops in the torus. In particular, each vertex represents a rational number (a slope) including $\infty$, and in fact we can arrange the vertices in order by slope along a circle. Since there are no pairs of disjoint loops, we connect any two vertices representing loops that intersect in a single point.
Similarly, we include in the Farey graph all the triangles bounded by loops of three edges. I’ll leave it as an exercise for the reader to check that for every pair of loops in the torus that intersect in exactly one point, there are exactly two other loops such that each of these loops intersects each of the original two loops in a single point. (The two new loops will intersect each other in two points.) So, in other words, each edge in the Farey graph is in the boundary of exactly two triangles. This tells us that the triangles form a surface. In fact, the surface that they form is the disk bounded by the circle along which we placed the vertices in the previous paragraph.
Six of these triangles are shown in the figure on the right, with the slopes corresponding to their vertices indicated as fractions. For each edge in the Farey graph, we can calculate the third vertex representing one of the adjacent triangles as follows: The numerator of the new slope is the sum of the numerators of the original two, and the denominator is the sum of their denominators. Similarly, to get the vertex defining the other triangle, we subtract the numerators and denominators. (To see why this works, you can think about the normal loops and Haken sums that I mentioned in another post from a while back.)
Notice that the triangles in this picture are different sizes, and in fact they get smaller as the numerators and denominators get bigger. But in reality, the edges of the Farey graph should all be the same length. So, you should think about this circle like the boundary of the hyperbolic plane, and the triangles as being ideal triangles. This isn’t exactly right either, since the edges in the Farey graph have finite length, unlike the edges of ideal triangles. But the Farey graph will have the same symmetry group as a tesselation of the hyperbolic plane by ideal triangles.
The Farey graph is closer in structure to a tree. In fact, we can construct a tree by putting a vertex at the center of each triangle and connecting two vertices whenever the corresponding triangles share an edge. The Farey graph will be quasi-isometric to this tree (though if you don’t know what quasi-isometric means, don’t worry about it.) In the same way that each edge in a tree cuts the tree into two separate trees, each edge in the Farey graph cuts the Farey graph (which is really a cell complex) into two disconnected sets of triangles.
Now, lets go back to the train track from the beginning of this post. Recall that the set of loops carried by the train track consisted of all loops with positive slopes, as well as the loops with slopes 0 and $\infty$. These loops make up the right half-circle of the Farey graph. In particular, the subcomplex of the Farey graph spanned by the loops carried by this train track is exactly one of the two components that we get if we cut along the edge spanned by 0 and $\infty$.
Note that when we constructed this train track, we started with any two loops in the torus that intersect in one point, or equivalently, any edge in the Farey graph. We then had a choice of two different ways to smooth the vertex where they intersect into a pair of switches in the train track. If we had made the other choice with our original two loops, we would have gotten a train track that carried all negative slopes, i.e. the other component defined by the edge between 0 and $\infty$. By symmetry, if we had started with a different pair of loops, the two possible train tracks that we could construct from them would similarly define the two different components that we get by cutting the Farey graph along this new edge. (Note that one can also show that every “reasonable” train track in the torus can be constructed from two loops in this way.)
The point of all this is that the different train tracks on the torus can be thought of as defining all the different ways of cutting the Farey graph along single edges. Train tracks in higher genus surfaces play a very similar role, though it’s more complicated because the curve complexes of these surfaces are much less tree-like (though they’re still delta hyperbolic, which is close.) In particular, you can’t separate these complexes by removing a single edge, or indeed any finite collection of simplices. But train tracks still define subsets of loops that are very nice with respect to the curve complex structure.
The reason this turns out to be useful is that it is often possible to prove things about the types of loops that are carried by a given train track, which can then be translated into the language of the curve complex. This is one of the main techniques in Masur and Minsky’s papers on the curve complex [1], and on disk sets of handlebodies [2]. It also proved very useful in my work with Yoav Moriah [3] and his earlier work with Martin Lustig [4]. But a discussion along those lines will have to wait for a future post.
1. “Recall that the set of loops carried by the train track consisted of all loops with positive slopes, as well as the loops with slopes 0 and ∞”
Isn’t the set of loops limited to slopes m/n; m,n ∈ (0,∞) with at least one of m,n = 1 ? For example, I don’t think that the trefoil (3/2) could be carried by that track.
Comment by Jouni Kosonen — March 15, 2014 @ 8:34 am
• It is possible to have both m and n greater than one. If there are vertical arcs (rather than horizontal arcs) in addition to the diagonals, then m will be equal to the number of diagonals in one of the two classes plus the number of verticals. The value n will be the number of diagonals in one of the two classes. If there are horizontal arcs instead of vertical arcs, then it will be the same with n and m reversed. We’re allowed to have as many of the diagonal arcs as we want, as long as there are the same number of each of the two types of diagonals (though I only drew examples with a single diagonal.)
Comment by Jesse Johnson — March 16, 2014 @ 8:18 pm
• Right, something like ╝│╔ would of course work here for 3/2. Sorry about the noise.
Comment by Jouni Kosonen — March 17, 2014 @ 5:24 am
The Rubric Theme. Create a free website or blog at WordPress.com.
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#### Stochastic Matrices and the Perron-Frobenius Theorem
René Thiemann
Archive of Formal Proofs 2017.
##### Abstract
Stochastic matrices are a convenient way to model discrete-time and finite state Markov chains. The Perron–Frobenius theorem tells us something about the existence and uniqueness of non-negative eigenvectors of a stochastic matrix. In this entry, we formalize stochastic matrices, link the formalization to the existing AFP-entry on Markov chains, and apply the Perron–Frobenius theorem to prove that stationary distributions always exist, and they are unique if the stochastic matrix is irreducible.
``@article{Stochastic_Matrices-AFP, author = {Ren\'e Thiemann}, title = {Stochastic Matrices and the Perron-Frobenius Theorem}, journal = {Archive of Formal Proofs}, month = nov, year = 2017, note = {\url{http://isa-afp.org/entries/Stochastic_Matrices.html}, Formal proof development}, ISSN = {2150-914x},}``
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• Corpus ID: 119235773
# Orientations of Morse flow trees in Legendrian contact homology
@article{Karlsson2015OrientationsOM,
title={Orientations of Morse flow trees in Legendrian contact homology},
author={Cecilia Karlsson},
journal={arXiv: Symplectic Geometry},
year={2015}
}
Let L be a spin Legendrian submanifold of the 1-jet space of a smooth manifold. We prove that the Legendrian contact homology of L with integer coefficients can be computed using Morse flow trees. We also give an algorithm for explicitly computing the sign of a rigid flow tree.
7 Citations
## Figures and Tables from this paper
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### A note on coherent orientations
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### Legendrian contact homology for attaching links in higher dimensional subcritical Weinstein manifolds
Let $\Lambda$ be a link of Legendrian spheres in the boundary of a subcritical Weinstein manifold $X$. We show that the computation of the Legendrian contact homology of $\Lambda$ can be reduced to a
### Koszul duality via suspending Lefschetz fibrations
• Yin Li
• Mathematics
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• 2019
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### A note on coherent orientations for exact Lagrangian cobordisms
Let $L \subset \mathbb R \times J^1(M)$ be a spin, exact Lagrangian cobordism in the symplectization of the 1-jet space of a smooth manifold $M$. Assume that $L$ has cylindrical Legendrian ends
### Braid loops with infinite monodromy on the Legendrian contact DGA
• Mathematics
Journal of Topology
• 2022
We present the first examples of elements in the fundamental group of the space of Legendrian links in (S, ξst) whose action on the Legendrian contact DGA is of infinite order. This allows us to
## References
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### Knot contact homology
• Mathematics
• 2013
The conormal lift of a link K in ℝ3 is a Legendrian submanifold ΛK in the unit cotangent bundle U∗ℝ3 of ℝ3 with contact structure equal to the kernel of the Liouville form. Knot contact homology, a
### Floer homology of Lagrangians in clean intersection
We consider Floer homology associated to a pair of closed Lagrangian submanifolds that satisfy a monotonicty assumption. If the Lagrangians intersect cleanly we decribe two spectral sequences which
### Legendrian Contact Homology
• Mathematics
A rigorous foundation for the contact homology of Legendrian submanifolds in a contact manifold of the form P × R where P is an exact symplectic manifold is established. The class of such contact
### Symplectic homology product via Legendrian surgery
• Mathematics
Proceedings of the National Academy of Sciences
• 2011
The product and Batalin–Vilkovisky operator of symplectic homology is expressed in terms of the Legendrian homology algebra of the attaching spheres of critical handles in that context.
### Knotted Legendrian surfaces with few Reeb chords
For g > 0, we construct g + 1 Legendrian embeddings of a surface of genus g into J(1)(R-2) = R-5 which lie in pairwise distinct Legendrian isotopy classes and which all have g + 1 transverse Ree ...
### Legendrian Contact Homology in P X R
• Mathematics
• 2005
A rigorous foundation for the contact homology of Legendrian submanifolds in a contact manifold of the form $P\times \R$ where $P$ is an exact symplectic manifold is established. The class of such
### Orientations for pseudoholomorphic quilts
• Mathematics
• 2015
We construct coherent orientations on moduli spaces of pseudoholomorphic quilts and determine the effect of various gluing operations on the orientations. We also investigate the behavior of the
### Legendrian contact homology in $P \times \mathbb{R}$
• Mathematics
• 2007
A rigorous foundation for the contact homology of Legendrian submanifolds in a contact manifold of the form P x R, where P is an exact symplectic manifold, is established. The class of such contact
### A complete knot invariant from contact homology
• Mathematics
• 2016
We construct an enhanced version of knot contact homology, and show that we can deduce from it the group ring of the knot group together with the peripheral subgroup. In particular, it completely
### Knot and braid invariants from contact homology II
We present a topological interpretation of knot and braid contact homology in degree zero, in terms of cords and skein relations. This interpretation allows us to extend the knot invariant to
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# Generate a Markdown Template for your Post
Your task is simple: Write a program (or function) that takes no input and outputs something like this:
## *name*, *length* bytes
*code*
Where *name* is the name of the language you are using, *length* is the number of bytes in your code, and *code* is your program's source code. If *code* contains multiple lines, it have four spaces before each line.
Here's a 124-byte example implementation in Python 3:
s = "## Python 3, 124 bytes{2} s = {1}{0}{1}{2}print(s.format(s,chr(34),chr(10)))"
print(s.format(s,chr(34),chr(10)))
The output is:
## Python 3, 124 bytes
s = "## Python 3, 124 bytes{2} s = {1}{0}{1}{2}print(s.format(s,chr(34),chr(10)))"
print(s.format(s,chr(34),chr(10)))
Which in Markdown is:
## Python 3, 124 bytes
s = "## Python 3, 124 bytes{2} s = {1}{0}{1}{2}print(s.format(s,chr(34),chr(10)))"
print(s.format(s,chr(34),chr(10)))
This is , so the shortest answer (in bytes) wins.
• I'm pretty sure this is a dup, but can't find the old one...
Nov 6 '16 at 22:14
• Related Nov 6 '16 at 22:20
• I'd say this is different enough from that one because it's generating one for itself. The idea is similar, but you need to write a quine for this one. Nov 6 '16 at 22:23
• Should we assume standard quine rules (e.g. no opening your own code and reading it)? Nov 6 '16 at 22:32
• @GabrielBenamy Yes. Nov 6 '16 at 22:49
# RProgN 2, 28 Bytes
«" %s"F"#RProgN 2, 28 Bytes"
• As is, this isn't a serious contender and subject to deletion. Please golf your answer. Jul 5 '17 at 17:32
• @Dennis Golfed. Jul 5 '17 at 20:56
• Nice! The dot after the byte count doesn't seem to be required, but there should be four spaces (or a tab) before the code. Jul 5 '17 at 21:09
(#Underload, 48 bytes
)(~:S( ):S*aSaS(:^)S):^
• Post is exactly as produced by the code. The quine is payload-capable (place the payload after the final S), thus making it a true quine by one widely-used definition, but uses a string eval (that said, string eval is the only way to do a loop in Underload; it's fairly fundamental to the language).
– user62131
Nov 12 '16 at 12:35
• After a discussion in Underload quines in chat, we decided this is also a quine by the other widely-used definitions too; the :^ at the end of the program is encoded by the :^ a little earlier, and thus one part of the program encodes a different part.
– user62131
Dec 2 '16 at 23:23
• You can discuss in Underload quines? (Cool!:aSS)Cool!:aSS Jun 21 '17 at 21:23
• @CalculatorFeline Unfortunately, that doesn't work because of the (!). Nov 28 '17 at 3:30
## Python 2, 58 bytes
_='## Python 2, 58 bytes\n _=%r;print _%%_';print _%_
• The contents of this post are exactly as printed by the code. Nov 8 '16 at 13:00
## reticular, 58 bytes
"'34'c: 4*91+c:s:e:t:y:b: 85: :,:r:a:l:u:c:i:t:e:r: :#dqO;
Try it online!
Explanation: :c pushes the single-char string c. This builds the string "## reticular, 58 bytes", backwards character by character, reverses the stack, and Outputs everything, including the string captured by the initial quote.
## CJam, 33 bytes
{"## CJam, 33 bytes"N@S4*\"_~"}_~
Stack trace (N represents \n)
{"## CJam, 33 bytes"N@S4*\"_~"}
{"## CJam, 33 bytes"N@S4*\"_~"} {"## CJam, 33 bytes"N@S4*\"_~"}
{"## CJam, 33 bytes"N@S4*\"_~"} "## CJam, 33 bytes"
{"## CJam, 33 bytes"N@S4*\"_~"} "## CJam, 33 bytes" N
"## CJam, 33 bytes" N {"## CJam, 33 bytes"N@S4*\"_~"}
"## CJam, 33 bytes" N {"## CJam, 33 bytes"N@S4*\"_~"} " "
"## CJam, 33 bytes" N {"## CJam, 33 bytes"N@S4*\"_~"} " " 4
"## CJam, 33 bytes" N {"## CJam, 33 bytes"N@S4*\"_~"} " "
"## CJam, 33 bytes" N " " {"## CJam, 33 bytes"N@S4*\"_~"}
"## CJam, 33 bytes" N " " {"## CJam, 33 bytes"N@S4*\"_~"} "_~"
<implicit output>
# V, 25 bytes
ñi#V, 25 bytes<esc>o´ Ñ<esc>~"qpx
(This is not counted in the generated markdown, because I like providing explanations for my code :P)
Here is a hexdump, since the source code contains unprintable/non-ASCII characters:
00000000: f169 2356 2c20 3235 2062 7974 6573 1b6f .i#V, 25 bytes.o
00000010: b420 d11b 7e22 7170 78 . ..~"qpx
This answer is just a trivial modification of the standard extensible V quine.
Explanation:
ñ " Run the following code one time, storing it in
" register 'q'
i " Enter insert mode
#V, 25 bytes<esc> " And insert the header
o " Open up a newline, and enter insert mode again
´ Ñ " Enter four spaces, then a 'Ñ' character.
" (The reason we insert it uppercase, is because
" lowercase would end the loop now)
~ " Toggle the case of the char under the cursor ('Ñ')
"qp " Paste the contents of register 'q' (this is the
" same as the entire program minus the initial 'ñ',
" followed by a 'ÿ' character because V is weird)
x " Delete the last character (the ÿ)
# JS, 504927 30 bytes
f=_=>#JS, 30 bytes\n f=+f
## Try It
f=_=>#JS, 30 bytes\n f=+f
console.log(f())
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# 0.9 Carrier recovery (Page 5/19)
Page 5 / 19
The squaring nonlinearity is only one possibility in the pllpreprocess.m routine.
1. Try replacing the ${r}^{2}\left(t\right)$ with $|r\left(t\right)|$ . Does this result in a viable method of emphasizing the carrier?
2. Try replacing the ${r}^{2}\left(t\right)$ with ${r}^{3}\left(t\right)$ . Does this result in a viable method of emphasizing the carrier?
3. Can you think of other functions that will result in viable methods of emphasizing the carrier?
4. Will a linear function work? Why or why not?
Determine the phase shift $\psi$ of the BPF when
1. fl=490, 496, 502 .
2. Ts=0.0001, 0.000101 .
3. M=19, 20, 21 . Explain why $\psi$ should depend on fl , Ts , and M .
## Squared difference loop
The problem of phase tracking is to determine the phase $\Phi$ of the carrier and to follow any changes in $\Phi$ using only the received signal. The frequency ${f}_{c}$ of the carrier is assumed known, though ultimately it too must be estimated.The received signal can be preprocessed (as in the previous section) to create a signal that strips away the data, in essence fabricating a sinusoid which has twice the frequency at twice the phase of the unmodulated carrier. This can be idealized to
${r}_{p}\left(t\right)=cos\left(4\pi {f}_{c}t+2\Phi \right),$
which suppresses An example that takes $\psi$ into account is given in Exercise [link] . the dependence on the known phase shift $\psi$ of the BPF and sets the constant $\frac{{s}_{avg}^{2}}{2}$ to unity (compare with [link] ). The form of ${r}_{p}\left(t\right)$ implies that there is an essential ambiguity in the phase since $\Phi$ can be replaced by $\Phi +n\pi$ for any integer $n$ without changing the value of [link] . What can be done to recover $\Phi$ (modulo $\pi$ ) from ${r}_{p}\left(t\right)$ ?
Is there some way to use an adaptive element? [link] suggested that there are three steps to the creation of a good adaptive element: setting a goal,finding a method, and then testing. As a first try, consider the goal of minimizingthe average of the squared difference between ${r}_{p}\left(t\right)$ and a sinusoid generated, using an estimate of the phase; that is, seek to minimize
$\begin{array}{ccc}\hfill {J}_{SD}\left(\theta \right)& =& \text{avg}\left\{{e}^{2}\left(\theta ,k\right)\right\}\hfill \\ & =& \frac{1}{4}\text{avg}\left\{{\left({r}_{p}\left(k{T}_{s}\right)-cos\left(4\pi {f}_{0}k{T}_{s}+2\theta \right)\right)}^{2}\right\}\hfill \end{array}$
by choice of $\theta$ , where ${r}_{p}\left(k{T}_{s}\right)$ is the value of ${r}_{p}\left(t\right)$ sampled at time $k{T}_{s}$ and where ${f}_{0}$ is presumed equal to ${f}_{c}$ . (The subscript SD stands for squared difference, and is used todistinguish this performance function from others that will appear in this and other chapters.)This goal makes sense because, if $\theta$ could be found so that $\theta =\Phi +n\pi$ , then the value of the performance functionwould be zero. When $\theta \ne \Phi +n\pi$ , then ${r}_{p}\left(k{T}_{s}\right)\ne cos\left(4\pi {f}_{0}k{T}_{s}+2\theta \right)$ , $e\left(\theta ,k\right)\ne 0$ , and so ${J}_{SD}\left(\theta \right)>0$ . Hence, [link] is minimized when $\theta$ has correctly identified the phase offset, modulo the inevitable $\pi$ ambiguity.
While there are many methods of minimizing [link] , an adaptive element that descends the gradient of the performance function ${J}_{SD}\left(\theta \right)$ leads to the algorithm Recall the discussion surrounding the AGC elements in Chapter [link] .
$\theta \left[k+1\right]=\theta \left[k\right]-\mu {\left(\frac{d{J}_{SD}\left(\theta \right)}{d\theta }|}_{\theta =\theta \left[k\right]},$
which is the same as [link] with the variable changed from $x$ to $\theta$ . Thus,
$\begin{array}{ccc}\hfill \frac{d{J}_{SD}\left(\theta \right)}{d\theta }& =& \frac{d\text{avg}\left\{{e}^{2}\left(\theta ,k\right)\right\}}{d\theta }\hfill \\ & \approx & \text{avg}\left\{\frac{d{e}^{2}\left(\theta ,k\right)}{d\theta }\right\}\hfill \\ & =& \frac{1}{2}\text{avg}\left\{e,\left(\theta ,k\right),\frac{de\left(\theta ,k\right)}{d\theta }\right\}\hfill \\ & =& \text{avg}\left\{\left({r}_{p},\left(k{T}_{s}\right),-,cos,\left(4\pi {f}_{0}k{T}_{s}+2\theta \right)\right)\hfill \\ & & \phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}sin\left(4\pi {f}_{0}k{T}_{s}+2\theta \right)\right\}.\hfill \end{array}$
Substituting this into [link] and evaluating at $\theta =\theta \left[k\right]$ gives Recall the convention that $\theta \left[k\right]=\theta \left(k{T}_{s}\right)=\theta \left(t\right){|}_{t=k{T}_{s}}$ .
$\begin{array}{cc}\hfill \theta \left[k+1\right]=\theta \left[k\right]-\mu \text{avg}\left\{\left(& {r}_{p}\left(k{T}_{s}\right)-cos\left(4\pi {f}_{0}k{T}_{s}+2\theta \left[k\right]\right)\right)\hfill \\ & sin\left(4\pi {f}_{0}k{T}_{s}+2\theta \left[k\right]\right)\right\}.\hfill \end{array}$
This is implemented in pllsd.m for a phase offset of phoff=-0.8 (i.e., $\Phi$ of [link] is $-0.8$ , though this value is unknown to the algorithm). [link] plots the estimates theta for 50 different initial guesses theta(1) . Observe that many converge to the correct value at $-$ 0.8. Others converge to $-0.8+\pi$ (about $2.3$ ) and to $-0.8-\pi$ (about $-$ 4).
where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
Got questions? Join the online conversation and get instant answers!
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Why is a holomorphic map between compact connected Riemann surfaces a branched covering?
I have seen it claimed that a non-constant holomorphic map $f:X \rightarrow Y$ between compact connected Riemann surfaces is a branched covering i.e. surjective and there is a finite set $\Sigma \subset Y$ and $r \in \mathbb{Z}_+$ such that $|f^{-1}(q)|=r$ for all $q \in Y \setminus \Sigma$. I can see why such a map is surjective, but I don't understand why the rest of the statement is true.
Let $A \subset X$ be the set of all $p \in X$ where $f$ is not locally injective, i.e. let $A$ be the set of $p \in X$ such that there exists no open neighbourhood $U$ of $p$ such that $f$ is injective on $U$. (People usually refer to $A$ as the set of branch points of $f$ in $X$.)
We can show that $A$ is a finite set. To do this, we observe that around any $p \in A$, we can find local coordinates in which $f$ is represented as the mapping $z \mapsto z^k$, with $k \geq 2$. This follows from the open mapping theorem of complex analysis. (Of course, the point $p$ is meant to be the point $z = 0$ in these local coordinates.) But having written $f$ in this way, it's clear that $f$ is not locally injective at any point in this little coordinate patch around $p$, except at $p$ itself. In other words, $p$ is an isolated point in $A$. Since $p$ was chosen arbitrarily, this means that every point in $A$ is isolated. By a compactness argument, it follows that $A$ is a finite set.
Now define your $\Sigma$ to be $f(A)$. So $\Sigma$ is a finite set in $Y$, as required. Moreoever, $f$ is locally injective at any point in $f^{-1}(Y\backslash \Sigma)$, by construction, and therefore, by another application of the open mapping theorem, $f$ is locally a homeomorphism at every point in $f^{-1}(Y\backslash \Sigma)$. And clearly, the preimage of any point in $Y \backslash \Sigma$ is a finite set, by a compactness argument. From these facts, it should be simple to check that the restriction of $f$ to the subset $f^{-1}(Y\backslash \Sigma)$ is a covering map. Finally, $Y \backslash \Sigma$ is connected (because $\Sigma$ is finite), so $|f^{-1}(y)|$ is constant as $y$ varies over $f^{-1}(Y\backslash \Sigma)$: this constant is simply the number of sheets of the covering map.
First of all, your definition of a branched covering (between surfaces) is incomplete. The correct definition is: It is a map $f: X\to Y$ such that there exists a finite subset $W\subset Y$ such that for $Z:=f^{-1}(W)$, the restriction $$f|_{X - Z}: X- Z\to Y- W$$ is a covering map.
To prove that every nonconstant holomorphic map between compact connected Riemann surfaces is a branched covering, let $W\subset Y$ denote the set of critical values of $f$ (i.e. points $w\in Y$ such that there exists $z\in f^{-1}(w)$ so that $f'(z)=0$; such $z$ is called a critical point of $f$). Then observe that since $X$ is compact and $f$ is nonconstant, it has only finitely many critical points (otherwise, the set of critical points has an accumulation point in $X$ which is impossible). Now, the restriction $f|_{X- Z}$ is a local diffeomorphism. It is also a proper map, i.e. preimages of compact subsets in $Y -W$ are compact. (This follows easily from compactness of $X$.) Furthermore, by the maximum principle, nonconstant holomorphic maps are open. Since $X$ is compact, $f(X)$ is closed in $Y$; since $Y$ is connected, it follows that $f(X)=Y$. Thus, by the construction, $f|_{X- Z}: X- Z\to Y- W$ is surjective. Lastly, applying Ehresmann's "Stack of Records" theorem, we conclude that
$f|_{X- Z}: X- Z\to Y- W$ is a covering map.
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# Bootstrapping the Kashiwara crystal
Posted in
Speaker:
Anthony Joseph
Affiliation:
Weizmann Institute
Date:
Sat, 2018-11-24 09:00 - 10:00
Location:
MPIM Lecture Hall
The Kashiwara $B(\infty)$ crystal gives a uniform combinatorial description of each integrable highest weight module $V$ for every Kac-Moody Lie algebra $g$ using only the Cartan matrix as data. More than this it realizes Bott's dream (motivated by the Bott-Samelson resolution of the flag variety) of a multiplicity-free character formula. Just as in the Bott-Samelson resolution, one fixes a (family) of reduced decompositions $J$ and constructs a realization of $B(\infty)$ as a subset $B_J(\infty)$, of integer points in an affine space $B_J$. If the Weyl group $W$ of $g$ is finite, then after Berenstein and Zelevinsky, $B_J(\infty)$ is given by inequalities defined by linear functions constructed from "trails", themselves dependent on $J$, in the fundamental modules (of the Langlands dual). Yet trails are not combinatorially defined and moreover the above result is not yet known to hold in general. A crystal is itself a union of "strings" for each simple root, which are linearly ordered.
Here it is proposed that the set of trails decomposes into $S$-sets for each simple root. This would both give a precise description of the set of all trails and extend the Berenstein-Zelevinsky result to all $g$. $S$-sets are now fully understood but instead of being linearly ordered, are described by the corners of a hypercube. Again the existence of the required simultaneous decomposition into $S$-sets remains elusive.
When $J$ is "bipartite" one can expect that the set of trails identifies with the crystal $B_J(\varpi_t)$ of an appropriate fundamental module.
This is shown when $g$ is classical. Thus $B_J(\infty)$ is described in terms of part of itself. This is the "bootstrapping" referred to in the title.
$S$-sets are now fully understood but instead of being linearly ordered, are described by the corners of a hypercube. Again the existence of the required simultaneous decomposition into $S$-sets remains elusive.
%The relation of $S$-sets to trails comes about through the Chevalley-Serre relations in a Demazure module (as used to describe the global functions on a Schubert variety). In principle this allows one to prove independence of the decomposition on the simple root chosen.
When $J$ is "bipartite'' one can expect that the set of trails identifies with the crystal $B_J(\varpi_t)$ of an appropriate fundamental module.
This is shown when $\eufm g$ is classical. Thus $B_J(\infty)$ is described in terms of part of itself. This is the "bootstrapping'' referred to in the title.
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# Show that the numerator of $\sum_{k=1}^{p^2} \frac1k - \frac1p\sum_{k=1}^p\frac1k$ is divisible by $p^4$
Let $p\ge5$ be a prime. If the following fraction is fully reduced (to an irreducible fraction), prove that the numerator will be divisible by $p^4$.
$$\sum_{k=1}^{p^2} \frac1k - \frac1p\sum_{k=1}^p\frac1k$$
I have a solution to this problem, but I can't understand some parts of it. (Though it is written in Korean, you will have no difficulty in understanding it.)
First of all, I just know about modular arithmetic of integers, but what means that a quotient is congruent to 0 ($\dfrac ab \equiv 0 \mod m$)? (In this problem, $\displaystyle \sum_{i=1,p\nmid i}^{(p^2-1)/2}\frac1{i(p^2-i)} \equiv 0\mod p^2$)
Second, why $\displaystyle \sum_{i=1,p\nmid i}^{p^2}\dfrac1{i^2} \equiv \sum_{i=1,p\nmid i}^{p^2}i^2 \mod p^2$ does hold?
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$a/b\equiv c/d\pmod m$ simply means $ad\equiv bc\pmod m$. In particular, $a/b\equiv0\pmod m$ just means $a$ is a multiple of $m$ (assuming $a/b$ is in lowest terms).
If $p$ doesn't divide $i$ then there is $j$ such that $ij\equiv1\pmod p$ so $1/i^2\equiv j^2$, and as $i$ runs through the residues mod $p^2$, so does $j$.
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# Finding complete sufficient statistic
Let $$X_1 , ....,X_n$$ be iid. $$Uniform[-\theta,\theta]$$. I need to find the complete sufficient statistic for $$\theta$$ or prove there does not exist such.
I know that $$T=(X_{(1)}, X_{(n)} )$$ is a sufficient statistic for $$\theta$$ but it is not a complete sufficient statistic.
I want to prove it. So first I tried to use the Basu's theorem . But in this case $$R = X_{(n)} -X_{(1)},$$ is not a ancillary statistic.
So I tried prove using the definition of the complete sufficient statistic.
Here I have attached my work so far.
But by doing like this , seems like that I am going to prove that $$T$$ is a complete sufficient statistic.
So can someone help to figure it out what I did incorrectly ?
• Since $T$ is a two-dimensional statistic, the expected value will need to be a double integral for arbitrary $g(T)$. – knrumsey May 18 '18 at 0:40
• is it necessary ? because i found the joint distribution of $X_{(1)}$ and $X_{(n)}$. – Sam88 May 18 '18 at 0:42
• Yes it is still necessary. By defintion, $E(g(X,Y)) = \int_x \int_y g(x,y)f(x,y)dx \ dy$ where $f(x,y)$ is the joint distribution. That's where you're going wrong. – knrumsey May 18 '18 at 0:44
• Since $\theta$ is a scale parameter, you need to find a function of $(X_{(1)},X_{(n)})$ that is scale free... – Xi'an Oct 12 '18 at 18:07
• For instance, $X_{(1)}/X_{(n)}$! – Xi'an Oct 12 '18 at 18:08
Recall:
Definition: A statistic $T$ is complete for $\theta$ if $$E(g(T)) = 0, \ \text{ for all \theta} \quad \Rightarrow \quad P(g(T) = 0) = 1, \ \text{ for all \theta}$$
The part about $P(g(T) = 0) = 1$ basically says that the function $g$ is trivially $0$ everywhere (except possibly on a set of measure 0).
So... If you want to prove that $T$ is NOT complete, you can try to find a non-trivial function $g(T)$ for which $E(g(T)) = 0$ for all values of $\theta$.
Hint: Can you find $E(X_{(1)})$ and $E(X_{(n)})$? Start with that, and then try looking at linear combinations of the sufficient order statistics.
• This is what i exactly tried to do. But somehow i am not getting the desired answer. (please check the solution that i attached). So i am trying to figuring out that. – Sam88 May 18 '18 at 0:40
• See my comment above. In this case, you can use $g(T)$ which is just a linear combination of the min and max. This saves you from having to integrate. – knrumsey May 18 '18 at 0:42
• You are suggesting the about finding an ancillary statistic isnt it ? – Sam88 May 18 '18 at 0:48
• @knrumsey $E(X_1)=\frac{\theta}{n+1}$ , $E(X_n)=\frac{n\theta}{n+1}$ now how do I proceed I don't get it you said comput these values but how does that help in $E(g(X,Y)) = \int_x \int_y g(x,y)f(x,y)dx \ dy$ how do I use them here ? – Ronald Oct 12 '18 at 17:09
• @knrumsey $E((-n)g(x)X_1)+E(g(x)X_n)=0$ This makes it valid to say it's not complete isn't it ? – Ronald Oct 12 '18 at 17:22
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# How to use Jenkins Pipeline and choose triggers for email notifications?
Before Pipeline, I used Email-ext plugin to define triggers for sending emails (on first failure, and when back to success).
But in the Pipeline version, I can't control the triggers, I can only "send always", or send based on current build result.
How do I send emails in pipeline based on more general triggers? (first failure, first success, etc)
## 2 Answers
You can use snippet like
post {
changed {
emailext body: '$DEFAULT_CONTENT', recipientProviders: [brokenTestsSuspects(), brokenBuildSuspects(), developers()], subject: '$DEFAULT_SUBJECT'
}
}
in declarative pipelines.
Changed post-condition is called when the build result is changed (i.e. of first failure and back to success). There are post-conditions like "regression" if you want more control.
This seems not to be possible at the moment with pipelines. See this Jira ticket.
• this jira ticket is about changing list of emailed users, not the triggers from question – Andrey Regentov May 3 '18 at 8:48
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# American Institute of Mathematical Sciences
February & March 2007, 18(2&3): 405-428. doi: 10.3934/dcds.2007.18.405
## On the inverse Sturm-Liouville problem
1 Dipartimento di Sistemi e Informatica, Università di Firenze, 50139 Firenze 2 Dipartimento di Matematica U. Dini, Università di Firenze, Italy
Received April 2006 Revised July 2006 Published March 2007
We pose and solve an inverse problem of an algebro-geometric type for the classical Sturm-Liouville operator. We use techniques of nonautonomous dynamical systems together with methods of classical algebraic geometry.
Citation: Russell Johnson, Luca Zampogni. On the inverse Sturm-Liouville problem. Discrete & Continuous Dynamical Systems - A, 2007, 18 (2&3) : 405-428. doi: 10.3934/dcds.2007.18.405
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2019 Impact Factor: 1.338
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Write code to prevent forest fires and discover the basics of artificial intelligence. ,) and can be accessed at its homepage. Greasy Fork is available in English. C-c C-c or C-c C-v e with the point on a 'src' code block 142 calls the org-babel-execute-src-block function, which executes the code in the block, collects the results, and inserts them in the buffer. Download free Adobe Flash Player software for your Windows, Mac OS, and Unix-based devices to enjoy stunning audio/video playback, and exciting gameplay. Configuration properties prefixed by 'hikari' or 'dbcp' will be propagated as is to the connectionpool implementation by Hive. 'markdown-mode' is a major mode for GNU Emacs which provides syntax highlighting and supporting commands for editing Markdown files. This is a hands-on, practical workshop in getting started with literate programming (and beyond) with Emacs + org-mode + org-babel. Currently, these themes can only be used with the C/C++ lexer ! Bright Yellow. 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HTML CSS JS. It is easy for humans to read and write. Language major-mode editing: Exporting code blocks: Export contents and/or results: Extracting source code: Create pure source code files: Evaluating code blocks: Place results of evaluation in the Org mode buffer: Library of Babel: Use and contribute to a library of useful code blocks: Languages: List of supported code block languages: Header. Code organization. you have to into the code block, type C-c ' to get into edit mode, and turn line numbers on. js is single threaded, so concurrency refers to the event loop's capacity to execute JavaScript callback functions after completing other work. Online DGFT India Importer Exporter IEC Code Information with online application procedure to obtain IEC Code Number by Applying Application Aayaat Niryaat Form ANF 2A in Online and Offline in Joint Directorate of Foreign Trade ( JDGFT ). An Emacs feature that defines support for Org-Mode Babel code blocks written in Racket. Espresso Libre. Yet such metadata wouldn’t work if programmers worldwide weren’t using a common, universal metadata language. Org mode requires unique names. For situations where interaction with random peers and blocks is unnecessary or unwanted, Bitcoin Core’s regression test mode (regtest mode) lets you instantly create a brand-new private block chain with the same basic rules as testnet—but one major difference: you choose when to create new blocks, so you have complete control over the environment. Org-mode is great for inserting snippets of code. Posting a dozen lines of code, saying "after line 7 I was expecting to see , but occurred instead" is much more likely to get you a response. Visually Identifying Code Blocks. This site will help to view how much html code is generated for web page. Spam is a fact of life in the digital age. Electronic code book is the easiest block cipher mode of functioning. The thread-loader can be used to offload expensive loaders to a worker pool. Support for the Core Rule Set has moved to a the owasp-modsecurity-core-rule-set mail list. How to use block in a sentence. IE 5 Windows, as well as older browsers like Netscape 4, are permanently locked in quirks mode. Like the Executor, the Reloader also wraps application code. org-mode captions not supported for EXAMPLE blocks? How do I insert code block header :var in exported code block in org-mode. Blocks Programming Reference Manual By Bruce Schafer February 7, 2019. com® is the industry leader in providing REAL IP address information. Inline code in org-mode (2) Markdown allows for embedded code. Code::Blocks is an open source, free, configurable programming environment for C or C++. The OpenWrt Community is proud to present the OpenWrt 18. Online DGFT India Importer Exporter IEC Code Information with online application procedure to obtain IEC Code Number by Applying Application Aayaat Niryaat Form ANF 2A in Online and Offline in Joint Directorate of Foreign Trade ( JDGFT ). Retrieve a file in binary transfer mode. It is fast, it is easy, and it is free!. The trusted source to help you prepare and document dangerous shipments. This can be done with the #+BEGIN_SRC [major-mode-name] [options] #+END_SRC [major-mode-name] adds a lot of extra functionality to these code blocks within your org file. You can execute these blocks and have the output display in your text file. Use C-c ' to edit the current code block. How to Block Porn Sites on all Web browsers & Network Devices. A repository contains one or more modules. wireless communications industry and the companies throughout the mobile ecosystem that enable consumers to lead a 21st Century connected life. Despite all the power of Org it becomes serious advantage in favor of Pelican + Markdown combination for blogging. At any point, you can edit the source code for your entire post by clicking on the three dots in the top-right and selecting Code Editor: Activate full-screen mode, fixed toolbar, etc. Hundreds of thousands of backgrounds, color schemes and more at Userstyles. x kernels, too. Noweb lets you reuse code contained in other org-mode source code blocks through basic syntactic expansion. Currently Emacs gets blocked and you have to wait patiently. On the left is the Star Wars game space where code will run. In addition, a bit in the subsequent block, in the same position as the original mangled bit, will be mangled. Hi, I'm Rachel Rose. Powered by the global Python Community. Cities by ZIP Code™ For more rapid delivery, please use the recommended or recognized city names whenever possible for this ZIP Code ™. Emacs Org mode Babel feature. Classic Tetris : Booster Block Puzzle Pro 2020 cheats tips and tricks added by pro players, testers and other users like you. Unfortunately this code won't work if you want to use multiple roots: if you try to write as \sqrt [b] {a} after you used the code above, you'll just get a wrong output. Note: In plain text mode the symbol for open fold is "{{{ " (that is, with a space at the end). h runs is not available in the library folder of CodeBlocks. In order to use this facility your R installation will need the tikzDevice package. The following 8086/8088 assembler source code is for a subroutine named _memcpy that copies a block of data bytes of a given size from one location to another. It is included from Emacs 22. Project dependencies are a simple way to tell Code::Blocks that a given project "depends" on another (in the same workspace, always). Is there any good plugin to block saved toolbars in creative mode? I have creative server and I am having annoying problem. Note: In plain text mode the symbol for open fold is “{{{ “ (that is, with a space at the end). Always use progn when a code block requires multiple config keywords. HTTP/2 enables a more efficient use of network resources and a reduced perception of latency by introducing header field compression and allowing multiple concurrent exchanges on the same connection. For example, if your op mode includes a block that uses a variable that contains the wrong type of object you should be able to find a line in the log. In my most recent post on org-mode, I talked about using blocks to mark text as being latex, or source code and so on. /isearch On Activate: Copies /isearch to the clipboard whenever an item block is activated. org Unit 5 Lesson q0. Retrieve a file in binary transfer mode. The largest of which are Strict Mode and native JSON support. The instructions for each level are written below the game space. OzoBlockly gives you the power to fully control your Ozobot's movement and behavior. Games for tomorrow's programmers. An open source content management system. When in the JSON with Comments mode, you can use single line (//) as well as block comments (/* */) as used in. Bitcoin Core 0. And if any of the actual argument values are constant, their known values may permit simplifications at compile time so that not all of the inline function’s code needs to be included. Note : This is an example of a publicly-available live Bugzilla site, and not a place to try out Bugzilla. We do this so that more people are able to harness the power of computing and digital technologies for work, to solve problems that matter to them, and to express themselves creatively. # Introduction # To start using Pyew, run it this way: ` \$. Downlink SNR to CQI Mapping for Different Multiple Antenna Techniques in LTE. Source code in org mode is marked up like this:. Writing and running code blocks in org-mode is awesome, when it works. Blocks Programming Reference Manual By Bruce Schafer February 7, 2019. That executes the code block in the other file, and wraps the output in an HTML block in this file! I do not like my code blocks to execute when I export because they are usually expensive calculations, so I have to manually run the line with C-c C-c, but you can override that behavior with a local setting of org-export-babel-evaluate. Note: In plain text mode the symbol for open fold is “{{{ “ (that is, with a space at the end). The Library of Babel is a collection of code blocks accessible to any org-mode file. 11で規定される無線LANのための暗号化 プロトコルである。. h in CodeBlocks ? Please follow below steps in sequence to include "graphics. Sublime Text is a sophisticated text editor for code, markup and prose. Edge 42 on Win10: Can't add a block and the editor is stuck in HTML, no visual mode available (sorry, didn't look at the JS console. Gert van Loo & Dom, have provided some tested code which accesses the GPIO pins through direct GPIO register manipulation in C-code. This operation will block temporarily if another thread is currently either autoloading a constant or unloading/reloading the application. Any of these users can add new usernames to the list. Org Mode supports graphical output for LaTeX documents using the PGF and TikZ graphics system for TeX. Once Block 1 is deployed, OCX will for the first time be able to command and control both Block II and Block III GPS satellites, as well as support the ability to begin broadcasting the civilian L1C signal. Strict Mode is a new feature in ECMAScript 5 that allows you to place a program, or a function, in a “strict” operating context. We do this so that more people are able to harness the power of computing and digital technologies for work, to solve problems that matter to them, and to express themselves creatively. Table of Contents 1. Before you start configuring. The support comes from the knitr package, which has provided a large number of language engines. The way to do that is with a little Emacs Lisp code block that you just need to place somewhere in your file, like: With this code block named, nova-conv, I can use it to post-process the results, as in: In my particular case, I also want to get rid of that first line of dashes to make it more org-mode like:. An example - Folding Mode for C Code. A single source file is of little uses in programs of any useful complexity. GNOME is part of the GNU project. Safe mode is a Namenode state in which it 1. AT&T home telephones are among the world's best-selling cordless systems and come packed with all the latest features for your home or small office. The development of TrueCrypt was ended in 5/2014 after Microsoft terminated support of Windows XP. Players are able to save. All gists Back to GitHub. Like the Gem resources for Ruby, you specify the files containing named blocks that should be accessible. let and const are two relatively new types of variable declarations in JavaScript. Emacs org-mode is a markup language, similar to Markdown, but with far more features. 1 onward as default. What we'd really like to do is allow the teachers to customize what goes into the block. How to create a 3D Terrain with Google Maps and height maps in Photoshop - 3D Map Generator Terrain - Duration: 20:32. SpeedView uses the phone's built-in GPS system to show your current speed. EXPLORE AI IN NEW MINECRAFT HOUR OF CODE Anyone can learn to code in the new Hour of Code lesson, available as a free demo in Minecraft: Education Edition! Write code to prevent forest fires and discover the basics of artificial intelligence. Firefox is created by a global non-profit dedicated to putting individuals in control online. Provides articles, whitepapers, interviews, and sample code for software developers using Microsoft products. Online DGFT India Importer Exporter IEC Code Information with online application procedure to obtain IEC Code Number by Applying Application Aayaat Niryaat Form ANF 2A in Online and Offline in Joint Directorate of Foreign Trade ( JDGFT ). Nmap users are encouraged to subscribe to the Nmap-hackers mailing list. Gert van Loo & Dom, have provided some tested code which accesses the GPIO pins through direct GPIO register manipulation in C-code. For "=10920.
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### Home > CCA > Chapter 9 > Lesson 9.3.2 > Problem9-86
9-86.
1. Solve the following equations and inequalities for x. Check your solution(s), if possible. Homework Help ✎
1. = 9
2. = 4
3. x2 = 25
4. 2(x − 3) > 4
$\frac{1}{3}=\textit{x}$
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# Human insulin is being commercially produced from a transgenic species of :
$\begin {array} {1 1} (1)\;Saccharomyces & \quad (2)\;Escherichia \\ (3)\;Mycobacterium & \quad (4)\;Rhizobium \end {array}$
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### Dimensions of Objects
Here’s an interesting question: what is a dimension? Dimensions can often seem like life. We know it when we see it, but defining it can be kind of tricky. As such, a good heuristic can be useful in thinking about dimensions, and, in particular, the number of dimensions a particular mathematical object has.
If I give you a point $(x,y)$ in the plane, what would you say is the dimension of that point?
It’s tempting - so tempting - to say that the answer is two. That’s almost my initial reaction just looking at the question. In fact, if I gave you the point within the plane, I think it’s fair to say that your reaction would be to say that the its two-dimensional.
You might say, “But I need to give you two coordinates to specify that point! As such, it has to be two-dimensional, or else I wouldn’t need those coordinates.” However, this is a mistake. Or, more precisely, a mix up.
The issue lies with how we are viewing the objects. When I gave you the point, I placed it in the two-dimensional plane. This is important. The plane itself is two-dimensional. However, the objects that go inside of it don’t have to be two-dimensional. In fact, they can be two-dimensional, one-dimensional, or zero-dimensional. A two-dimensional object could be a disk (which is a filled-in circle), a one dimensional object could be a function, and a zero-dimensional object would be a point.
The confusion lies in the fact that we have two things in play here. First, we have some sort of space, which is where we say our mathematical objects “live”. In our example, this is the plane, which is two dimensional. However, we can then place (or embed) various objects into that space, and these objects can have dimensions that are equal to or less than the dimension of the space. This is exactly the situation we find ourselves in when we talk about a point in the plane.
The lesson we learn is that the number of dimensions a mathematical object has isn’t necessarily the same as the dimension of the space it lives in. So how do we think about the dimension of a point? Well, you have to try and do the difficult task of thinking about it without any associated space around it. This isn’t easy, but the following question makes things clearer. How many ways can you “move around” on a point? The answer is zero, since you can’t move anywhere else! There’s only one point, so you have to stay there at that single point. As such, the dimension of a point is zero. It doesn’t matter if it lives in a three-dimensional space or a two-dimensional one. The dimension of the point will still be zero.
Note that there are objects which can superficially seem like points (called vectors), but they aren’t points and so they aren’t zero-dimensional.
A good heuristic to get a sense of the dimension of an object is to imagine yourself as a tiny creature living on the object. Which ways can you move? If you’re on a line or some sort of curve, you can only move forward and backward along that curve. As such, you can only move within one dimension and so the object is one-dimensional. If you were on a surface (say, of a sphere), you could move left and right, and forward and backward. Therefore, the surface would be considered two-dimensional. We still think of the sphere as something that lives in three dimensions, but as its own entity, it’s two-dimensional. In other words, when you are on the surface, you only need two coordinates to specify your location. It doesn’t matter if your surface is also within a seventy-four-dimensional space. The surface itself is the same, and it’s still two-dimensional.
Like I said above, the heuristic of imagining what it would be like to move around on the object itself is a useful strategy to think about the number of dimensions a mathematical object has. As long as you keep in mind the fact that objects can be embedded within higher-dimensional spaces, there won’t be any more confusion as to what the object’s dimension is. Remember, the object can exist independently from the space it lives in, and that is the dimension of the object.
### No Magic
As a tutor at the secondary level, I get an inside look at the various issues that students face within mathematics. While the specific issues are different from person to person, I’ve come to see a pattern emerging. Anecdotally, I think that most of the issues students face could be summarized with one sentence.
Students aren’t sure what formula to use for a given situation.
This is a simple, yet profound issue. On the one hand, you can say that the issue can be easily remedied by telling the students to do a better job committing to memory the various equations that are of use. I don’t think this is really a good suggestion, since the secondary schools allow memory-aids (sheets with notes and equations on them) for many of the tests. As such, the student should have the equations themselves. This still leaves the problem of knowing when to use the equations, but a simple note on their memory-aid should suffice for this.
On the other hand, this issue is profound, since it indicates a lack of familiarity with the equations themselves. For example, if a student is trying to calculate the area of a square with length $s$, and they aren’t sure where to use $4s$ or $s^2$ to do this, I think there’s a fair chance that the student isn’t familiar enough with the concepts and equations for the perimeter and area of a square.
For the above situation, what’s the best way to tackle the uncertainty? Is it to tell them that $s^2$ is the right one to use since you’re multiplying? What about the fact that $4s$ is technically multiplication as well, even though we know that $4s$ represents a series of addition. This could be confusing to the student as well. Suddenly, a simple little problem might be pointing to a larger issue.
The approach that I use is something that I partially learned from one of my professors while taking a class in probability. When introducing a new concept and seeing that we are having a bit of difficulty answering his conceptual questions, his go-to strategy is to bring it back to the basics. He tells us to think about how this new concept boils back down to things we have seen before. By going back to the original definitions, it is easier to build back up and get to the new concepts with a solid foundation.
This philosophy for learning is something I now tell all of the students I work with. I condense it into two words: no magic. My goal as a tutor isn’t only to help a student solve their homework problems and prepare for a test. It’s to give them a sense of confidence in what they are doing. My goal is to move them away from asking, “Which of these two formulas do I use?” to “I know I have to use this specific formula, since we are talking about that concept.”
Related to this idea of making mathematics less magical and more grounded in logic is the issue of knowing where a formula comes from. Recently, I was working with a student on the concept of area for various shapes. In secondary school, the classic shapes that are introduced include a square/rectangle, a triangle, a parallelogram, a circle, and a trapezoid. The student learns about the area of all of these shapes. But really, what they learn are the formulas for the areas. Any time I ask students if they learn why these formulas are used, they just look at me as if I asked something strange of them. It’s as if the thought of why a certain formula corresponds to the area of a shape never occured to them.
To be clear, this isn’t their fault. It’s the fault of the objectives in mathematics classes. The objective is to have the technical skills within a given subject, not necessarily an overall awareness as to the purpose of the mathematics. However, in my experience, being adept at the technical side of doing mathematics is definitely helped by understanding why I need to use certain rules and techniques. Without that knowledge, it’s difficult to ground myself when looking at a problem and trying to think of a possible solution.
This precise scenario came up when I was working with a student on finding the area of a trapezoid. They told me something along the lines of, “I know it has a $b$, $B$, and an $h$ in it, but I can’t remember how it’s done.”
Instead of telling them that the area was $A = \frac{1}{2}h(B+b)$, I told them that we should work at finding out exactly what the area was, using only the tools we knew. I knew that the student understood how to calculate the area of a rectangle, so we should have been capable of finding the area of a trapezoid. I didn’t know the exact steps needed to get to it, but I did know that cutting the shape up into smaller pieces was probably the correct strategy.
This is exactly what I told the student. I didn’t want them to think that this area for a trapezoid was some mix of strange symbols arranged in just the right way to produce the correct area. I wanted to show them that this process jumps right out from the fact that we know how to calculate the area of a rectangle, which is a simple enough fact to get the student on board with. From there, it’s mostly about skillfully rearranging the shape to get new ones that are easier to calculate.
Once again, my mantra was no magic. I firmly believe that the student needs to see this process of obtaining certain results if they want to be more comfortable with using them. At the moment, I shake my head in disbelief every time a student tells me that their teacher gave them a formula, but didn’t explain where it came from. That’s doing the students a disservice, and frankly I wouldn’t be surprised if it resulted in lower performance.
At the same time, I realize that there is a fair amount of material in a given year for secondary mathematics. It’s not easy to go through it all and give derivations for each and every single fact. I can definitely sympathize with that. A rushed derivation is about as good as no derivation at all. However, I would recommend that teachers do their best to include more derivation during class, if they can. While it might be seen as boring (and yes, it sometimes can be!), it helps ground a student in their concepts, so that they are less likely to be unsure of what formula to use during homework and exams.
Remember, no magic. Mathematics can (and should) be explained along almost every step (as much as reasonably is needed). At the moment, students learn a lot of techniques, but they don’t have the experience of learning why a fact is true. In my humble opinion, this is where change needs to begin.
### Going to the Extreme
Last summer, the site Brilliant ran a program where participants tried to answer one new problem every day, within varying topics and of different difficulty. One in particular was interesting. Unfortunately, I can’t seem to find it on the site, but this is roughly how it goes:
Imagine you are on a boat in the middle of a lake, and there is a stone on board. You pick up the stone, and then toss it into the lake, where it sinks to the bottom (which means the density of the rock is greater than the density of water). What happens to the lake and the ship?
On the site, the question isn’t open-ended, but instead is one of four possible answers. These include things such as: the boat rises, the water level rises, or either of the two sink. Here though, I want to discuss the answer, and how one comes about it. In particular, I want to talk about how taking an extreme perspective can help one come up with the correct answer, no fancy physics involved.
I remember when I first read the problem, I asked myself, “Well’s what’s the radius of the rock? How massive is it? What kind of shape does it have?”
These are all questions that I thought were needed to address the problem, but it turns out that they aren’t. If you want to try your hand at answering the question, now is the time to do so.
To answer the question, let me give you a clear example that I think will make the answer more or less obvious in general. Imagine that you have a rock that is about the size of a pebble, yet has the same mass as a car. If that pebble is on your boat, what happens?
Evidently, your boat should pushed downward, before the buoyant force counteracts the force of gravity. At this point, the boat will be lower than without the pebble, so that water level in the lake should increase, since the boat displaces the amount of water equal to the submerged part of the ship. You end up getting the following situation.
This is the situation that the problem begins with. The pebble is on your boat. Then, you find some inner strength and toss that pebble over the ship. What happens now? Well, the boat suddenly has a lot less weight forcing it down, which means the boat will rise. This happens because the buoyant force is now greater than the gravitational force at the moment the pebble is thrown overboard, which means the boat should have a net upwards acceleration.
At the same time, what happens to the water level in the lake? Well, remember that the water level was originally high since the volume of the submerged part of the boat was taking up place. However, with the boat floating upwards due to the removal of the pebble, the result is that less of the boat is submerged. This means less water gets displaced, and so the water level should go down. We can’t forget the pebble though. It has a certain volume too, which will increase the water level of the lake. However, the volume of the pebble is certainly less than the change in the volume of the submerged part of the boat, so the net result is the water level falling. As long as the rock doesn’t contribute to a larger volume change than the submerged part of the boat, this will be the end result. The boat will rise, and the water level will descend.
So there you go! By looking at an extreme example (a rock with a small volume, but a very large mass), the answer made itself clear. Instead of working with intermediate cases where the rock is sort of large and sort of massive, we examine the extreme cases (here, in opposite directions from what we would expect), and the answer is more apparent. The way I think about the above puzzle is in the following way. The rock’s mass on the boat translates to having the boat sink lower. This means the boat’s submerged volume will increase, and that increase in volume tends to be more than the volume of the rock itself, so throwing the rock into the lake means that less water is displaced overall. In a sense, the mass of the rock on the boat “contributes” to the displacement of the water more than simply its volume would.
Like I said, I love these kinds of problems because they showcase the power of thinking in the extremes. As one does more and more theoretical work in the sciences and mathematics, answers to questions usually come through using specific equations and some sort of mathematical argument. While that can be done here, I like the simplicity of the answer as well. It shows how one can answer questions in different manners and still arrive at the same answer. Yes, the quantitative analysis may be more precise and encompassing of the situation, but this skill of teasing out the extreme scenarios can also prove to be fruitful.
### Overhang
Physical balance has always fascinated me. We do it unconsciously, and yet it is an essential part of movement. Balance is what keeps us from wiping out, or from getting our legs tangled in a mess of movement. Balance let’s us reach on one leg for an item that’s just out of reach, and it also lets us do complex movements when playing sports.
However, what I described above is what you could call dynamic balance. It’s balance that’s achieved through the act of moving. Think of riding a bicycle. You’re able to balance on a bicycle because you’re pedalling the bicycle. Unless you’re really talented, you don’t find yourself balancing on a bicycle while it’s not moving.
But balance can also be static. This is the kind of balance you get when trying to perform a particular yoga pose. It’s also the type of balance that you can probably see around you right now. Just look at the objects near you. Chances are, they aren’t moving. My pencil, eraser, and paper are beside me right now, and they are completely still. That’s not an accident. It’s due to the fact that the forces acting on them cancel each other out exactly (in the classical sense). As such, there’s a balance between the force of gravity acting on my pencil and the equal-and-opposite normal force that is exerted on the pencil by the table.
Here’s another example of balancing that you may have done before. Have you ever taken an object (like a book), and slowly slid it across a table until it reaches the end and begins to create a bit of an overhang? I’ve tried many times to see just how far I could push the book before gravity took over and pulled it down. It’s an interesting experiment to run. You’re pushing the book just a little bit further each time, and then suddenly it tips and falls over. There’s a very sharp divide between the book staying on the table and the book falling. But where is it exactly? Let’s find out.
## A little bit of geometry
If you do some experiments with a book that roughly resembles a block with constant density (and so there’s no bias of matter to one side of the book or the other), you could probably come up with the answer to the above question pretty quickly. You might even know the answer intuitively without doing any calculations.
However, let’s do a small analysis to show where this point is. Imagine we have a block of constant density of mass $M$ amd length $1$ (these don’t really matter, but it just simplifies things). We know that its centre of mass is the geometric centre of the block. The question we want to know is: at what point will the overhang on the block force the block to fall over?
Essentially, we want to know what the $x$-coordinate of the block will be at the divide between falling over and staying balanced.
Well, first we need to decide on how to locate the block of wood. Where’s the most natural place to stick our coordinate point? In my eyes, it would be the centre of mass, since we know that we can approximate a mass as being a point mass at the centre of mass. As such, we want to look at the horizontal location of the centre of mass. If we make a sketch of the situation with the appropriate forces, we get the following diagram:
From the above paragraphs, I mentioned that the two forces at play here (gravity and the normal force) exactly balance each other now. However, we know that this cannot be true forever, since the block does indeed fall as we push it further and further. So when does this occur?
Remember that the force of gravity and the normal force act on the block at its centre of mass. Consequently, there’s a very clear point at which the block will fall: when the block’s centre of mass no longer is under the table. At that moment, the block’s centre of mass will not be held up by the table, and so gravity will pull it down. Therefore, the answer to our question is that the block will be perfectly balanced up to the point where the block is halfway off the table.
So that’s great, but now the logical extension to this question comes up. If I place a book underneath my first one, such that I now have two books, what kind of overhang can I get? Furthermore, can I keep on adding books to make the “path” longer and longer, and when will it fall?
It turns out that this is a problem that many people have thought about before. In fact, there are a number of varieties to this problem, usually dependent on how one goes about adding the books. In this case, let’s focus on the simplest case. We will continually add books of the same size and mass, one by one. We want to see when the whole structure will fall.
## In Rhythm
We have a lot of choice with two blocks now. We can slip the second one under our original so most of it is still under the table. However, like we did for the case with one block, we may as well find the furthest point that will keep the structure stable (we want to be efficient with our block stacking).
From our analysis with only block, we know that the structure will fall once the centre of mass passes the edge of the table. Therefore, we don’t want that to happen. We will keep our initial block with an overhang of $1/2$ (since that’s the maximum it can be at before the block falls), and will decide how to place the second block on the table. First, we should note that both block have their centre of mass in their geometric centres, represented by the black dots on the diagrams. Additionally, we now care about their combined or common centre of mass, since if that is further out than the edge of the table, the blocks will fall.
To find this centre of mass, consider the fact that the top block has an overhang of $1/2$, and so the two blocks look like this:
From the diagram, we can see that the common centre of mass of both blocks will be somewhere in between the centre of masses of each respective block. This corresponds to somewhere within the overlapping sections of the blocks. However, since the overlapping section is exactly half of each block, and the density of each block is constant, we can use an argument by symmetry to say that the common centre of mass is directly in the middle of the centre of masses of each block. This is because the rest of the mass is distributed exactly evenly to the left and the right of that point. Note that I’m only talking about the $x$-coordinate of the centre of mass, which is all we care about in this problem. As such, the centre of mass for our new structure is given by placing the bottom block such that it has an overhang of $1/4$. As shown below.
We then want to repeat the procedure with a third block, and see if we can notice a pattern. Three blocks is slightly more tricky, but not too bad. Once again, we place the third block underneath the previous two such that the overhang of the top two blocks begins at their centre of mass. This is much easier seen in a sketch.
We can now consider the two blocks that we have analyzed previously to have a “total” mass of $2M$ and a common centre of mass located at 1 unit from the diagram above. The bottom block has a centre of mass located at $1/2$ a unit from the zero point, which begins at the left end of the bottom block. Therefore, the common centre of mass for the three blocks is given as: $$$x_{cm} = \frac{(2M)(1)+(\frac{1}{2})M}{2M + M} = \frac{5}{6}.$$$ As such, if we want to place the common centre of mass on the edge of the table, we need to make the third block have an overhang of $1-5/6 =1/6$.
Now that we’ve looked at the three first steps, let’s see how much overhang we get for each new block added. With one block, the overhang is $1/2$. For two blocks, we get an extra $1/4$, which makes for a total of $\frac{1}{2} + \frac{1}{4} = \frac{3}{4}$. For three blocks, we get another $1/6$, which makes for a total of $\frac{1}{2} + \frac{1}{4} + \frac{1}{6} = \frac{11}{12}$.
Do you notice a pattern? If we factor out a half from each term, we get the fractions $1/1$, $1/2$, and $1/3$ for each new block added. As such, if we generalize this progression for when we have $n$ blocks, we should expect something like this for the amount of overhang $d_n$: $$$d_n = \frac{1}{2} \left[ \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{n} \right].$$$ Note that this can be proved by induction. We will prove this in terms of how much overhang the $n^{th}$ block will have, which is given by $D_n = \frac{1}{2n}$. For the first case with $n=1$, we see that $D_1 = 1/2$, which is exactly what we expect. For the induction hypothesis, we say that the overhang for block $k$ will be $D_k = \frac{1}{2k}$. Now, let’s consider the structure with $k+1$ blocks. From above, we’ve seen that our strategy is to align the edge of the new block with the combined centre of mass of the structure above it. A sketch helps to see this.
You can see that the amount of overhang that the structure with $k$ blocks has compared to the $k+1$ block is given by $D_k$, our induction hypothesis. If we then take the zero point to be at the left end of the $k+1$ block, geometry tells us the the centre of mass of the structure of $k$ blocks is exactly $1$ unit away. Additionally, the combined mass of that structure is $kM$, since there are $k$ blocks. Finally, the last block has a mass of $M$ and a centre of mass of $1/2$, like usual. Therefore, we can calculate the centre of mass for the $k+1$ blocks to be: $$$x_{cm} = \frac{(kM)(1) + \left( \frac{1}{2} \right) (M)}{kM + M} = \frac{k + \left( \frac{1}{2} \right)}{(k+1)} = \frac{2k + 1}{2k+2}.$$$ To find out how much overhang there is, we simply align the centre of mass to the edge of the table. Since the total length of the bottom block is one, the overhang for the $k+1$ block is given by: $$$D_{k+1} = 1 - \frac{2k + 1}{2k+2} = \frac{1}{2(k+1)}.$$$ And, this completes the induction. Therefore, the $n^{th}$ block will have an overhang of $1/2n$. Furthermore, the total overhang si given by simply adding up the overhang of each individual block, which gives us our sum up above.
At first glance, this sum looks like it will plateau quickly. As $n$ gets larger, each successive term gets smaller and smaller. For $n=100$, the extra distance on the overhang is only an extra $0.01$. This only gets smaller for larger $n$, so it makes sense to think this sum will reach a certain point in which nothing really gets added to the total. But how can we show this?
In mathematics, the above expression for $d_n$ is called a partial sum. It’s called a partial sum because “real” sums are infinite series, the result of adding terms as $n$ approaches infinity. We have tools to deal with what happens when $n$ gets closer to infinity, and it allows us to deal with our expression here. If we can actually take this limit and get a finite answer (one that isn’t infinity), then we will have found the maximum overhang possible.
Before we tackle this question, let’s go through a quick example of infinite series and how they can indeed give a non-infinite answer, even after adding infinitely many terms. Imagine you have to cross a room, and you say that the length of the room is one unit long. Then, in order to get to the other side of the room, you first have to cross half of the room. You then have to cross a half of that remaining distance, which is a quarter of the whole distance. You then have to cross half of that remaining distance, which corresponds to an eighth, and so on. If we keep doing this for an infinite number of times, what should be the total distance traveled?
To answer this, remember that the total distance of the room is one unit. Therefore, if you do an infinite number of those small steps as you go across the room, it stands to reason that by the end of it all, you will have crossed the room! Putting this into mathematics, it means that we get the following: $$$\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \ldots = 1.$$$ Here, the ellipsis signifies that we are adding up all the terms, every single one. Historically, this is known as Zeno’s paradox. The idea was that, if you always had to cover another half of whatever remaining distance there was, you’d never quite get to the end, since you’re always just a smaller and smaller distance away from your end goal. However, if you try to cross a room, you know that you will get there in the end. So the paradox is resolved by the fact that if you do an infinite number of steps (and not just a lot), you do indeed get to the other side. As such, the infinite series that is shown above does indeed go to one.
But what about ours? We have $\frac{1}{2} \left[ \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{n} \right]$, which is a bit of a different series. This one is not quite the same flavour as the previous one. In fact, the series which is within the brackets is actually known as the harmonic series, and is well known in mathematics. To figure out if the series adds up to a finite number (we say that the series “converges”) or goes to infinity (we say that the series “diverges”), we can compare it to another series, in which every denominator gets changed to the next largest power of two. We will only compare the series (which is the terms in the brackets). As such, we get our original series, and the new one, which looks like: $$$\left[ \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{7} + \frac{1}{8} + \ldots \right],$$$
If you look closely, the first series should clearly be larger than the second one, since the denominators are smaller than or equal to the corresponding terms in the second series. But if we group the terms in the second series, we get something interesting: $$$\left[ \frac{1}{1} + \frac{1}{2} + \left( \frac{1}{4} + \frac{1}{4} \right) + \left( \frac{1}{8} + \frac{1}{8} + \frac{1}{8} + \frac{1}{8} \right) + \ldots \right].$$$ Simplifying this is nice, since all of the terms in the parentheses are $1/2$. Furthermore, since this trend continues, the sum is simply the result of adding a bunch of halves together. If we keep on adding the same number to itself for an infinite number of times, the series will diverge. The only exception to this is zero, which will converge to zero. But the number here is $1/2$, so the series will diverge and grow indefinitely. Consequently, since we said that the series we are interested in is bigger than this series that diverges, our series has to also diverge! Think about it: the only way to be larger than infinity is if it’s also a series that diverges. Therefore, we can conclude that our series $d_n$ (which is just the series we were talking about above, scaled by $1/2$) diverges.
This is not something you would expect. Think about the consequence of this result. If $d_n$ grows indefinitely, then one can keep on stacking books in just the right way such that the overhang is infinite! We can reach from your table to your neighbouring town, without it the stack ever falling.
Physically, this means that, despite having the books reaching as far away from your table as you would like, the centre of mass of the whole structure still won’t pass the edge of the table. In my eyes, this is pretty incredible. We just came up with a structure that can hold itself over an edge for an infinite distance. That’s not something you’d exactly expect when asked.
## Wait a second
“But this is ridiculous,” you might say. “We can’t actually do this. I can’t even get a structure going for one metre of overhang! What’s the catch?”
Of course there’s a catch.
First, we need to remember our assumptions. We started with the fact that the only forces acting on the books are gravity and the normal force. However, this obviously neglects the fact that air is present in the room, that there are other disturbances which could ruin this stacking. Additionally, one has to be exact in the placement, since having any block being a bit too far will cause the whole structure to collapse. As such, this is far worse than trying to create a long line of dominoes.
We also assumed that every block has exactly the same mass, is rigid, and has exactly the same dimensions, which isn’t exactly a reasonable assumption for something in real life. Still, it makes the mathematics of the problem easier, so we go with it.
The other big issue with this stacking is that it grows very slowly. In fact, the harmonic series is distinct in its slow growth. It turns out that the harmonic lies right on the border between series of the form $\frac{1}{n^a}$ which will diverge (when $a \lt 1$), and those that will converge ($a \gt 1$). To give you an idea of how slow this series grows, if we stack thirty identical books with this method, the resulting overhang is $d_{30} \approx 1.99749$. Therefore, thirty books doesn’t even net you two book lengths of overhang. But it gets worse, since the numbers only grow more slowly as $n$ gets large. If you take a thousand books, you get an overhang of $d_{1000} \approx 3.74274$. You can see that this isn’t exactly a fast process. By adding $970$ books, we still can’t even double the length we had for $30$ books.
So the stacking process is extremely slow. And that’s kind of the amazing part. Even though the process is so slow (and gets to be essentially as slow as you want), the structure can get as large as you’d like. I like to think of it as an “unstoppable force meets an immovable object” scenario. In this case though, the structure can grow forever, and so the slowness of the building process does not stop it.
Want to know what this structure looks like as the number of books gets large? Well, here you go1.
You can see that the structure grows vertically quite quickly, while it’s horizontal movement is relatively slow. This means that getting any meaningfull amount of overhang in real life will be tedious. Still, if done the right way, and with the right materials, it should be possible. I won’t be trying it anytime soon, but if you want to take a crack at it, by all means go for it and share the results.
## Smarter stacking
Throughout all of this, you might have been wondering something along the lines of, “This is a stupid way to stack the blocks. I want to stack them such that I can get a counterweight to balance the whole structure.”
And, you’re absolutely right. There are plenty of other ways to stack the blocks, depending on the rules you want to follow. Above, we followed the implicit rule that each block had to be on its own “level”. In other words, there can be only one block directly on top of the first block. As such, you can’t build an inverted pyramid type of structure, since that requires having more than one block per level. If we relax our rules though, we can then easily look at these more complicated situations. It’s all a matter of what we want our rules to be. The Wikipedia page has some details on variations of book stacking, and you can see what the other strategies look like. But that’s enough for now. You’re armed with a strategy to stack blocks and create an overhang to infinity and beyond without ever making the stack fall.
1. This image is from Wolfram MathWorld
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Find Paper, Faster
Example：10.1021/acsami.1c06204 or Chem. Rev., 2007, 107, 2411-2502
Comparative compositional analysis of cassava brown streak disease resistant 4046 cassava and its non-transgenic parental cultivar
GM Crops & Food (IF3.074), Pub Date : 2020-11-04, DOI: 10.1080/21645698.2020.1836924
H. Wagaba, P. Kuria, P. Wangari, J. Aleu, H. Obiero, G. Beyene, T. Alicai, A. Bua, W. Esuma, E. Nuwamanya, S. Gichuki, D. Miano, P. Raymond, A. Kiggundu, N. Taylor, B.M. Zawedde, C. Taracha, D.J. MacKenzie
ABSTRACT
Compositional analysis is an important component of an integrated comparative approach to assessing the food and feed safety of new crops developed using biotechnology. As part of the safety assessment of cassava brown streak disease resistant 4046 cassava, a comprehensive assessment of proximates, minerals, amino acids, fatty acids, vitamins, anti-nutrients, and secondary metabolites was performed on leaf and storage root samples of 4046 cassava and its non-transgenic parental control, TME 204, collected from confined field trials in Kenya and Uganda over two successive cropping cycles. Among the 100 compositional components that were assessed in samples of 4046 and control TME 204 cassava roots (47 components) and leaves (53 components), there were no nutritionally relevant differences noted. Although there were statistically significant differences between the transgenic and control samples for some parameters, in most cases the magnitudes of these differences were small ($<$20%), and in every case where comparative literature data were available, the mean values for 4046 and control cassava samples were within the range of normal variation reported for the compositional component in question. Overall, no consistent patterns emerged to suggest that biologically meaningful adverse changes in the composition or nutritive value of the leaves or storage roots occurred as an unintended or unexpected consequence of the genetic modification resulting in 4046 cassava. The data presented here provide convincing evidence of the safety of 4046 cassava with respect to its biochemical composition for food and feed, and it could be considered as safe as its non-transgenic control.
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##### Child pages
• Astro&Theory Seminar
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# Astro&Theory Seminar
The seminar of the Astro & Theory Section takes place Thursdays (alternating with the Journal Club) in E3-128 and on zoom, starting normally at 14.15. If you would like to suggest a seminar speaker or want to be added to the email list, please contact the organizer (Michael.Kachelriess@ntnu.no).
A list of seminars in the previous and the current years can be accessed in the sidebar; the (planned) seminars in 2022 are
• 17.02., Marco Turchetta (IFY, NTNU): Searches and characterisation of optical and X-ray pulsations from candidate millisecond pulsars
Abstract: In recent years three transitional millisecond pulsars (tMSPs) have been identified, showing transitions between rotation and accretion-powered pulsar state. In 2016 the SiFAP2/TNG (INAF) optical photometer unveiled for the first time optical pulsations from one of these systems, PSR J1023 + 0038 (J1023). The issues in explaining this phenomenon in terms of emission fed by either rotation or accretion power have fostered the formulation of new models, in which both the two mechanisms conspire to yield the emission of optical pulsations. During this talk I will present the results obtained in my master thesis work, which was aimed to gain insight into the nature of these optical pulsations. At this purpose, I have performed periodicity searches in optical and X-ray band from five candidate tMSPs, all showing the same multi-wavelength emission features observed in both the two states of J1023.
• 21.02., Patrick Reichherzer (RUB Bochum): !postponed!
• 10.03., Petter Taule (TU Munich): Non-linear structure formation in cosmologies with non-trivial time- and scale-dependence
Abstract: Mapping out the large-scale structure (LSS) of the Universe is one of the key advances driving precision cosmology. Current and near-future large-scale surveys offers the prospect of testing deviations of the LambdaCDM model, such as measuring the absolute neutrino mass scale or probing properties of dark energy or dark matter. Major efforts have been devoted to describing non-linear scales perturbatively, and in this talk I discuss a framework for computing loop corrections in cosmological perturbation theory for cosmologies with non-trivial time- and scale-dependence. I apply this framework to cosmologies with massive neutrinos taking neutrino perturbations beyond the linear level into account. Finally, I discuss the bispectrum in the context of the effective field theory of LSS, going to next-to-next-to-leading order in perturbation theory.
slides
• 17.03., Robert Plantey (NTNU): Renormalization group evolution analysis of the gauged Froggatt-Nielsen mechanism in 2HDMs
Abstract: There are many free parameters in the flavour sector of the Standard Model which exhibit hierarchies. From a theoretical point of view this situation, known as the flavour puzzle, is not satisfying and the Froggatt-Nielsen mechanism aims to partially address it. In this model, hierarchies in the flavour parameters can be removed at the cost of introducing a new scalar field and heavy vector-like fermions. In this talk, I will present my master thesis which focused on building a realistic, theoretically consistent 2-Higgs-doublet model equipped with the Froggatt-Nielsen mechanism.
• 23.03., Gabriela Barcenas Enrique (Universidad de Guanajuato; NTNU): Self-gravitating Scalar Field Dark Matter
Abstract: Diverse evidence has proved the existence of dark matter in the universe, with the arrival of accurate cosmological and astrophysical observations, some as part of the scientific community consider it the most interesting problem in modern physics. We are no able to discard the existence of new particles with properties that may look exotic in comparison with the particles that constitute all that we know as ordinary matter. The scalar field dark matter is a model that considers the existence of a scalar field, in which the principal parameter is a very small mass. This model has displayed consequences in the formation of cosmological structure. Furthermore, scalar field dark matter presents a solution to galactic scales. We review a particular configuration of self-gravitating scalar field dark matter with the aim of presenting a viable candidate to describe the behaviour of the galactic centre. We present an approach to test this configuration with recent observations from the closest stellar cluster to Sgr A*, moreover, we expect to find new constrictions for the exact quantity for the mass of the scalar field.
slides
• 30.03. Yan-Chuan Cai (University of Edinburgh, NTNU): Astrophysics and Cosmology with the Cosmic Web
Abstract: On large scales of our observable Universe, the distribution of matter follows a web-like pattern, consisting of knots, filaments, sheets and voids. The cosmic-web is non-Gaussian, containing valuable information about astrophysics and cosmology. I will summarise recent research activities in trying to extract some of this information, and how we can use observations of the cosmic-web to tackle some of the major problems in cosmology.
• 07.04. Inga Strumke (AI Lab, NTNU): Introduction to machine learning - a guided tour with examples from particle physics
Abstract: Inga will give us a crash course in machine learning, how it's done and which forms exist. She will take us through a a few examples from HEPP, demonstrating current applications and their challenges. Finally, the million dollar question of how to explain machine learning models - also referred to as the "black box problem" - is disseminated and an overview of the status of explainable AI (XAI) is given. The talk is open for everybody, and intellectually available to anyone comfortable with arithmetic and the existence of the Higgs boson :-)
• 12.05., Patrick Reichherzer (RUB Bochum): Influence of diffusive cosmic-ray transport on multimessenger observables
Abstract: Cosmic-ray transport in astrophysical environments is often dominated by diffusion in a magnetic field with a turbulent component. The diffusion properties of charged particles directly influence observable properties, such as the spectrum of cosmic rays and their secondaries produced in interactions. In many diffusion scenarios, the simplified assumption of fully resonant Kolmogorov diffusion in the quasi-linear limit results in a parallel diffusion coefficient D ~ E^(1/3). A quantitative investigation of the scattering regimes, however, shows that the diffusion coefficient tensor can deviate significantly from this behaviour. In this talk, the complex dependencies of charged particle diffusion on the turbulence level of the magnetic field are presented. Examples of how this affects observational signatures will be shown in the context of galaxies or the transient sky, i.e., flaring Blazars.
• 4.5. Karri Koljonen (IFY): Shocking news - a polarizing study of a tidal disruption event
Abstract: Supermassive black holes have been known to disrupt passing stars producing outbursts called tidal disruption events (TDEs) offering a unique view on the early stages of the accretion disk and jet formation. The advent of large-scale optical time-domain surveys has significantly increased the number of known events and challenged our understanding of their dynamics and emission processes. Especially, the so-called optical TDEs have shown late-time X-ray and radio emission years after the optical peak emission indicating delayed accretion disk formation and long timescales for the circularization process. In this seminar, I will present our study on the most polarized TDE up-to-date without any indication of contribution from a jet to the emission. Our observations demonstrate that optical TDE emission can be powered by tidal stream shocks.
• 19.5. Sven Heinemeyer (IFT (CSIC), Madrid): New Physics around the corner?!
Abstract: Three recent experimental results will be reviewed that deviate from the Standard Model (SM) prediction by $\sim 4 \sigma$. These are the anomalous magnetic moment of the muon, excesses in the searches for light Higgs bosons at the LHC and the measurement of the W-boson mass by CDF. The implications for new physics beyond the SM as well as corresponding
prospects for future experiments will be discussed.
• 25.05. Inga Strumke (AI Lab, NTNU): Introduction to machine learning - a guided tour with examples from particle physics -- PART II
• 8.9. Tim Ruhe (TU Dortmund):
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# How to flip normals of Graphics3d faces?
Is there an easy way to flip the normals for all the faces of a sage.plot.plot3d.base.Graphics3d or sage.plot.plot3d.base.Graphics3dGroup object?
I checked the source of https://github.com/sagemath/sage/blob... but couldn't find any answers there.
### Background:
I am generating a 3-dimensional surface on the YZ plane via sage.plot.plot.parametric_plot using long-running functions and want to mirror this surface by the XY plane to produce a final mesh which includes both the original and mirrored surfaces.
mySurface = parametric_plot(
[
0,
lambda u, v: longRunningYFunction(u, v),
lambda u, v: longRunningZFunction(u, v)
],
...
)
The reason I want to mirror the original surface instead of regenerating it is because the long-running functions take a very long time to complete, so doing it this way effectively cuts down the processing time in half.
I tried a few ways to mirror the surface:
• Rotating by 180° around the Y axis
mirroredSurface = mySurface.rotateY(pi)
• Scaling by -1 in the Z direction:
mirroredSurface = mySurface.scale([1, 1, -1])
and when I display or write both surfaces it looks ok:
show(mySurface + mirroredSurface)
but when inspected more closely, the normals of mirroredSurface are in the opposite direction of mySurface. This requires me to manually flip the surfaces with Blender.
### Question:
Is there any extension or function I can apply on the Graphics3d object mirroredSurface that would flip all the surface normals?
Something like the following?
mirroredSurface.flip_normals()
# or
flip_normals(mirroredSurface)
edit retag close merge delete
This could be considered as a bug in TransformGroup. You are welcome to help fix the bug by diving into sage code.
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# Convection diffusion reaction equation (stiffness, solver)
I am trying to solve the CDR-Equation in 2D:
$$\frac{\partial c(x,y)}{\partial t} + \nabla \cdot ( -d\nabla c(x,y) + \vec{v}(x,y) c(x,y))+ a c(x,y)=0\,,$$ with Boundary Conditions (length of square is $L$): $$c(0,y)=0$$ $$-d\nabla c(L,y) + v(L,y) (c(L,y))=0\,.$$. $$c(x,y=0)=0$$ $$c(x,y=L)=0$$
1.) Why exactly is this equation stiff? Does it depend on the reaction term $ac(x,y)$?
2.) Can I solve the equation with the Crank-Nicholson method? Is the error huge? If yes, what is the best method?
• Please correct the second boundary condition and add some boundary condition on the other two sides of the square domain. Crank-Nicolson with a correct treatment of reaction term and advection term (the last one maybe with an upwind method) shall give an accurate scheme. For too large time steps you can have some unphysical oscillations in numerical solution, but if you would like to have an accurate numerical solution, you should avoid such large time steps. – Peter Frolkovič Jan 11 '16 at 20:03
• Stiffness is generally regarded as a property of the ODEs you get by semi-discretizing, not of the PDEs. Do you have a semi-discretization in mind? – David Ketcheson Jan 12 '16 at 6:36
• I am asking for stiffness, because the CDR equation is often given as an example for a stiff equations. And there are multiple papers discussing different solvers because of the difficulties in handling it. – Paulinchen2 Jan 12 '16 at 13:01
1. Mathematically speaking, stiffness is meaningless for a single differential equation, and is rather attributed to a set of differential equations that have different time-scales (e.g. when trying to solve two coupled equations with time-scales of 1 second and 1 day, respectively). However, a single equation can also be referred to as stiff if certain numerical integration methods are numerically unstable. Source/sink terms can give rise to stiffness, for instance: $$\frac{dy}{dt}=-1000y$$ is a good example where sink term has given rise to stiffness. That being said, $ac(x,y)$ might be causing the stiffness in your PDE.
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# a big hand for rfe
Here are some tools that I’ve put together that make a huge difference to a clunky rfe workflow. Bored already? Don’t worry, I’ve written the script already: tl;dr
Imagine power cycling a DICE server with redundant PSUs, using our lovely power bar control files. You don’t know where it’s installed, so you have to search for it. Continue reading
# alpine, nagios and display filters
I’ve been aware of alpine’s “display filter” feature for some time, used as it is for on-the-fly GPG interpretation amongst other things. But I’d never really examined the feature before now. The manual says:
The [filter] command is executed and the message is piped into its standard input. The standard output of the command is read back by Alpine.
This says it all: display filters turn out to be an extremely powerful generic mechanism for reformatting and enhancing text; it works particularly well when applied to machine generated messages. Maybe its power is best explained by the example which caused me to investigate in in the first place:
### An example (the nagios bit):
A longstanding irritant to me has been a my difficulty in shutting nagios up. For a long time I’ve been relying on a filter to parse nagios’ incoming emails and generate a URL. The display filter closes the loop, automatically injecting that magic URL at the end of the message.
Here’s a simplified version of the filter, reminiscent of the one in the previous post:
#!/usr/bin/gawk -f
# Crude detection of problem type for acknowledgement link
# Don't forget to validate these inputs...
/Notification Type: / { TYPE=$3; } /Service:/ { SERVICE=substr($0,length($1)+1,length($0)); }
/Host:/ { HOST=$2; } # Important: this is a filter, so don't forget to print input lines back out! // {print;} # Now add the acknowledgement link below: END { if (HOST && TYPE == "PROBLEM") { # this is the script which generates the URL. # ideally this should be replaced with some awk to do the same thing cmd="~/bin/nagack "HOST" "SERVICE cmd | getline url close(cmd) # now add the link to the email. print "[Acknowledgement link: "url" ]" } Now, to alpine’s Display Filters setting, add: Display Filters = _LEADING("***** Nagios")_ /path/to/nagios-filter-script that’s it! My emails from nagios now look like: ***** Nagios ***** Notification Type: PROBLEM Service: ssh Host: myhost Address: 192.168.12.34 State: CRITICAL ... [Acknowledgement link: https://nagiosserver/nagios/cgi-bin/cmd.cgi?cmd_typ=3... ] ### Important caveats: • If you’re not careful, by adding these filters you will have introduced a trivial local shell injection attack to your mail client. Validate your inputs — just like I didn’t above! • The developers have this to note about running filters on every message: Testing for the trigger and invoking the filter doesn’t come for free. There is overhead associated with searching for the trigger string, testing for the filter’s existence and actually piping the text through the filter. The impact can be reduced if the Trigger Modifying Tokens […] are employed. I’ve certainly noticed a small (immeasurable, but noticeable) delay in opening messages with triggers. Large enough to be annoying if I’d planned to filter every message, even using a trivial bash filter which itself is quick to complete. • One additional caveat on DICE: if your alpine session outlives your AFS credentials, and you’ve stored your display filters in your home directory, you will find that the display filters simply disappear. As good a reminder as any to renew, and thankfully a “renc” is all that’s required to restore your filters to former glory. That’s it! Surprisingly trivial, and with a handful of these triggers, the benefits are huge. I’m using five so far, mostly generating clickable links to some of our automated systems, but I’d be pleased to hear what other people are doing with these filters. # Editing component files with vim Editing LCFG component source files using Vim is of course The Right Thing to do, but due to the way these source files are named (typically filename.ext.cin) vim doesn’t necessarily pick up on the filetype, and goodies such as syntax highlighting are lost. This is easy to fix using vim’s ftdetect system. Some examples for simple types: " These files are always POD in disguise au BufRead,BufNewFile *.pod.cin : set filetype=pod " Slightly contentious: a new filetype is needed, really, but this is a decent match. au BufRead,BufNewFile *.def.cin : set filetype=cpp " For other, unknown types, detect from the as-yet undefined shebang: au BufRead,BufNewFile *.cin : if getline(1) =~ '^#!@SHELL@' | set filetype=sh | endif au BufRead,BufNewFile *.cin : if getline(1) =~ '^#!@PERL@' | set filetype=perl | endif (note the latter two lines are specified separately, rather than elseifed, purely for readability). It’s fairly obvious that this can be extended to any file type, and there’s also scope for adding an automatic mapping to allow all files of form file.typ.cin to be mapped automatically to their default .typ. “sub-extension” file type. Anyway, the above has already improved my productivity no end so I’ll leave the latter exercise to the reader. Comments and contributions are welcome, as always — so long as they’re not suggestions to use Emacs(!) # get on the rpm bus This is a quickie script which streamlines my RPM building and submission to a single command. Note that this is entirely dependent on our shiny new Package Forge system, which feeds RPMs to multiple platforms for building and eventual submission into our RPM buckets. All it does is chain up “rpmbuild -bs [spec]; pkgforge submit [srpm]” but it’s a nice timesaver nonetheless. Side-benefits include the automatic generation of a readable ID and provision of a tracking link for pkgforge so that you can anxiously refresh the page to watch the build progress (or you could just wait for the report email…). So, here is is; my very simple and stupid RPM automation. Suggested name: ‘rpmbus’. #!/bin/bash if [[ -z$2 ]]; then
echo "RPMbus: build -> submit assist"
echo "Usage: basename $0 [pkgforge args]" exit 1 fi bucket=$1; shift
spec=$1; shift args=$*
output=rpmbuild -bs ${spec} | tail -n 1 pkg=echo${output} | sed -e 's_^Wrote: __'
if [[ ! -e ${pkg} ]]; then echo "Package wasn't built:${output}"
exit 1
fi
id=basename ${spec} | sed -e 's_\.spec__' -e 's_\.__g'-date +"%s" echo -e "Found source package:\n${pkg}"
echo " Extra args: ${args:-none}" read -p "Submit to '${bucket}'?" foo
if [[ ${foo} != 'y' ]]; then echo "Cancelled" exit 1 fi echo "Submitting to${bucket}..."
pkgforge submit --id ${id} -B${bucket} ${args}${pkg} && \
echo " https://pkgforge.inf.ed.ac.uk/job/view?id=${id}" Caveats: well, they’re numerous and they’re pretty apparent. But it took five minutes to write and it WFM :) # losing locate As much as MacOS’ Spotlight is an integral and indispensable part of my interaction with my laptop, a part of me still begrudges the “gratuitous” CPU and disk utilisation which is of course a necessary part of its operation. However as a hardened Linux user unprepared to do without the luxury of the locate database, my inner resource miser was further upset on discovering that these databases were not shared, and with even more irritation enabled the periodic updatedb cron job, as was suggested by locate itself. Whether it was SSD envy, a nagging sense of a job half-done or sheer procrastination I’m not sure, but last week I felt compelled to do away with the needless platter-spinning and found the answer far too quickly, in the form of the Spotlight shell utility mdfind. One alias later: alias locate="mdfind -name" and I was able to destroy the locate database, and discontinue its indexing: launchctl stop /System/Library/LaunchDaemons/com.apple.locate.plist launchctl unload -w /System/Library/LaunchDaemons/com.apple.locate.plist whew! #### Some obligatory qualifications… This applies largely to OS X 10.6, Snow Leopard. Leopard’s arrangement is slightly different, and I know nothing about earlier versions… And no, it doesn’t support all of locate’s arguments, but I rarely used them (apart from -i) anyway (and don’t have any case-sensitive, indexed filesystems on the mac right now). man mdfind provides workarounds for many of the more unusual uses of locate, and grep provides the rest… # Chrome and SPNEGO Update, Aug 2015: The landscape on OS X has changed several times since this post was written. Chrome on the Mac now fully supports the “defaults” mechanism to set policy defaults. Chrome on Linux gained a proper managed configuration, which we use locally (I produced the lcfg-chrome component for this purpose). Quick guide to configuring SPNEGO on the Mac: $ defaults write com.google.Chrome AuthServerWhitelist <cosign.server.tld> \$ defaults write com.google.Chrome AuthNegotiateDelegateWhitelist <cosign.server.tld>
Restart Chrome and rejoice. What follows is probably only of historical interest…
I was most impressed by the efficient conclusion to the enhancement request for SPNEGO on Chrome, but having read that the request had been met, I struggled for far too long to discover how to activate it.
Irritated by Firefox 4 beta 7’s breakage of SPNEGO on the Mac*, but reluctant to revert 3.6, I felt it was time to reinvestigate the alleged Chrome support Continue reading
# Nag nag nag nag nagios
Nagios is an extremely useful tool, until it isn’t. Which is to say, it’s nothing but a hindrance to have nagios continue to bombard you with IMs and emails when you’re already working on the problem.
### Surely you can just acknowledge the fault and shut it up…?
Well, sometimes, but it is hardly convenient to break out a Firefox session when you’re attached to a serial console with your lovely secure-shell-enabled phone. And even if you are on a DICE machine it’s a bit of a pain to have to navigate the slightly clunky Nagios UI to find the host and service you wish to silence.
I started with a dumb bash script. Continue reading
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# Different Euclidean metrics on a vector bundle
Suppose I have two Euclidean metrics $\mu_1, \mu_2$ on a given vector bundle $\xi$. Does anyone know of necessary and/or sufficient conditions to ensure that there is a homeomorphism $\phi: E(\xi) \to E(\xi)$ between fibers such that $\mu_1 \circ \phi = \mu_2$?
I vaguely recall results relating to this question, but it's been a while since I studied algebraic topology.
-
## 1 Answer
It turns out that there is no additional requirement: a Euclidean structure on a vector bundle $\xi$ is unique up to isometric isomorphism of Euclidean vector bundles. This is Exercise 2-E of Milnor and Stasheff's Characteristic Classes.
In fact, we can say more.
Theorem. Let $\xi_1 = (E_1, p_1, B)$ and $\xi_2 = (E_2, p_2, B)$ be two vector bundles over a common base space $B$, and let $\mu_1$ be a Euclidean metric on $\xi_1$ and $\mu_2$ a Euclidean metric on $\xi_2$. If $\phi: \xi_1 \longrightarrow \xi_2$ is a vector bundle isomorphism, then $\phi$ is homotopic through vector bundle isomorphisms to an isometric isomorphism $\tilde{\phi}: (\xi_1,\mu_1) \longrightarrow (\xi_2,\mu_2)$.
Proof. First, suppose $\xi_1$ and $\xi_2$ are trivial bundles, so that the isomorphism $$\phi: B \times \mathbb{R}^n \longrightarrow B \times \mathbb{R}^n$$ is given by $$\phi(x,v) = (x,g(x)v)$$ for some map $$g: B \longrightarrow \mathrm{GL}(n).$$ Now $\mathrm{O}(n)$ is a deformation retract of $\mathrm{GL}(n)$, so $g$ is homotopic to some map $$h: B \longrightarrow \mathrm{O}(n).$$ Write $g_t$ for this homotopy, so that $g_0 = g$ and $g_1 = h$. Define $$\phi_t: B \times \mathbb{R}^n \longrightarrow B \times \mathbb{R}^n$$ by $$\phi_t(x,v) = (x,g_t(x)v).$$ Then $\phi_t$ is a homotopy of vector bundle isomorphisms from $\phi$ to $\tilde{\phi} = \phi_1$, and clearly $\tilde{\phi}$ is an isometric isomorphism of vector bundles.
For the general case where $\xi_1$ and $\xi_2$ are not trivial bundles, apply the above to a locally finite cover of $B$ that simultaneously trivializes $\xi_1$ and $\xi_2$. $~\Box$
-
I don't see the last part of your argument. If you choose a locally finite cover $\{U_\alpha\}$ and apply the above you get that every $\phi_\alpha:=\phi|_{U_\alpha}$ is homotopic through isomorphisms to an isometry $\tilde \phi_\alpha$ on $U_\alpha$. But for $U_\alpha \cap U_\beta \neq \emptyset$ why would the isometries $\tilde \phi_\alpha$ and $\tilde \phi_\beta$ agree on the overlap? Of course you could paste the various $\tilde \phi_\alpha$ together with a partition of unity. This would yield a well-defined map, but one might lose the isometry property on the overlaps. – Meneldur May 6 '12 at 10:36
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# SSAT Upper Level Math : Rational Numbers
## Example Questions
### Example Question #1 : How To Add Complex Fractions
Simplify.
Explanation:
Don't try to find the least common denominator as it will take a lot of time and a definite mistake in arithmetic. Instead try to see if these quadratics can simplify.
Upon inspection, we get
.
Remember, to break down the quadratic equation by finding the binomials, two numbers that are factors of c must add up to make b.
With the cancellations, we should get
.
The common denominator will be
Remember when foiling, you multiply the numbers/variables that first appear in each binomial, followed by multiplying the outer most numbers/variables, then multiplying the inner most numbers/variables and finally multiplying the last numbers/variables. The left fraction numerator is multiplied by and the right fraction numerator is multiplied by .
Overall, the new fraction should read
.
After simplification, answer should be .
### Example Question #2 : How To Add Complex Fractions
Simplify.
None of the above are correct.
Explanation:
Try to simplify the fraction rather than finding the least common denominator. By breaking the quadratic equation into its factors, it becomes:
.
Remember, to break down the quadratic equation by finding the binomials, two numbers that are factors of c must add up to make b. Also, if the values of a, b, and c in the quadratic equation can be reduced, then factor out that divisor to make the quadratic easier to factor.
Upon cancelling, we should get
.
The common denominator is or or Remember when foiling, you multiply the numbers/variables that first appear in each binomial, followed by multiplying the outer most numbers/variables, then multiplying the inner most numbers/variables and finally multiplying the last numbers/variables. Then multiply the numerator of left fraction by and the numerator of right fraction by and the new fraction should look like,
.
Upon distributing the four and simplifying the fraction, answer is shown.
### Example Question #1201 : Ssat Upper Level Quantitative (Math)
Simplify.
Explanation:
Least common denominator is . Just multiply the left fraction numerator by and solve.
### Example Question #1202 : Ssat Upper Level Quantitative (Math)
Simplify.
Explanation:
Try to simplify the fractions rather than trying to find the least common denominator. It should look like this:
.
Remember, to break down the quadratic equation by finding the binomials, two numbers that are factors of c must add up to make b. The may not be easy to factor but when put into the quadratic formula
, we get roots of and . Then set equations equal to so that when solving for , the answer is the root.
Now after cancellations, we get .
The common denominator is or or .
Remember when foiling, you multiply the numbers/variables that first appear in each binomial, followed by multiplying the outer most numbers/variables, then multiplying the inner most numbers/variables and finally multiplying the last numbers/variables. For the left fraction numerator you multiply by what it's lacking and same with the right fraction numerator.
The overall fraction should look like
Once simplified, the answer will be shown.
### Example Question #1203 : Ssat Upper Level Quantitative (Math)
Explanation:
Rewrite the fractions using a division sign.
To change the division sign to a multiplication sign, take the reciprocal of the second terms.
Simplify.
Find the LCD, and rewrite the fractions to add the numerators.
### Example Question #1 : How To Find A Complex Fraction
Simplify:
Explanation:
Add the fractions in the numerator, then divide the sum by the denominator:
### Example Question #2 : How To Find A Complex Fraction
Simplify:
Explanation:
Simplify the sum in the numerator, then divide by the denominator:
### Example Question #3 : How To Find A Complex Fraction
Simplify:
Explanation:
Rewrite this as a division problem, then solve:
### Example Question #4 : How To Find A Complex Fraction
Simplify:
Explanation:
Rewrite this as a division problem, then solve:
Simplify:
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Article Contents
Article Contents
# Characteristic analysis of carrier based on the filtering and a multi-wavelet method for the information hiding
• The characteristic consistency between the original and the stego carriers is an important indicator to evaluate an information hiding algorithm. Different from the traditional carrier pre-processing methods which are based on the operation domains, we propose a characteristics analysis-based preprocessing scheme. We use the Gaussian pyramid filtering and CARDBAL2 multi-wavelet transform to analyze the energy characteristics of the carrier, so the original carrier can be decomposed into several sub-regions with different energy level. And at the same time, the processed carrier shows us the redundancy space structurally through the combination bit plane method, which can provide some invisible hiding positions. Obviously, the energy and structure characteristics are at least related with the robustness and invisibility of the hiding result respectively. So we can improve these performances compared with the traditional methods. At the same time, some optimization theories like the Chebyshev map are used to improve other performances. At last, the experimental shows the achievements of this scheme in the form of data.
Mathematics Subject Classification: Primary: 94A62, 68Q30; Secondary: 94A08.
Citation:
• [1] A. Basu, A. Saha, J. Das, S. Roy, S. Mitra and I. Mal, On the implementation of a digital watermarking based on phase congruency, Advances in Intelligent Systems & Computing, 328 (2014), 113-120.doi: 10.1007/978-3-319-12012-6_13. [2] L. Cui and W. Li, Adaptive multiwavelet-based watermarking through JPW masking, IEEE Transactions on Image Processing, 20 (2011), 1047-1060.doi: 10.1109/TIP.2010.2079551. [3] A. Durdek, S. R. Jensen and J. Juselius, et al., Adaptive order polynomial algorithm in a multiwavelet representation scheme, Applied Numerical Mathematics, 92 (2015), 40-53.doi: 10.1016/j.apnum.2014.12.006. [4] K. Jafari-Khouzani, Multiwavelet grading of pathological images of prostate, IEEE Trans. Biomed. Eng., 50 (2003), 697-704.doi: 10.1109/TBME.2003.812194. [5] J. Kim, M. Yi and M. S. Obaidat, Advanced computer mathematics based cryptography and security technologies, International Journal of Computer Mathematics, 90 (2013), 2512-2514.doi: 10.1080/00207160.2013.868728. [6] Y. Kutlu, Feature extraction for ECG heartbeats using higher order statistics of WPD coefficients, Comput. Methods Programs Biomed., 105 (2012), 257-267.doi: 10.1016/j.cmpb.2011.10.002. [7] Y. Li, H. L. Wei and S. A. Billings, Identification of time-varying systems using multi-wavelet basis functions, Control Systems Technology IEEE Transactions on, 19 (2011), 656-663.doi: 10.1109/TCST.2010.2052257. [8] X. B. Ren, An optimal image thresholding using genetic algorithm, Proceedings of the 2009 International Forum on Computer Science-Technology and Applications, 1 (2009), 169-172.doi: 10.1109/IFCSTA.2009.48. [9] B. Stoyanov and K. Kordov, Novel image encryption scheme based on chebyshev polynomial and duffing map, The Scientific World Journal, 2014 (2014), Article ID 283639, 11 pages.doi: 10.1155/2014/283639. [10] M. Saini and R. Chhikara, Performance evaluation of DCT and DWT features for blind image steganalysis using neural networks, International Journal of Computer Applications, 114 (2015), 20-23.doi: 10.5120/19974-1868. [11] A. R. Tate, N. Beloff and A. R. Balques, et al., Exploiting the potential of large databases of electronic health records for research using rapid search algorithms and an intuitive query interface, Applied Numerical Mathematics, 21 (2014), 292-298.doi: 10.1136/amiajnl-2013-001847. [12] L. Yang, J. Lv and Y. Xiang, Underdetermined blind source separation by parallel factor analysis in time-frequency domain, Cognitive Computation, 5 (2013), 207-214.doi: 10.1007/s12559-012-9177-9. [13] T. Zhang, D. J. Mu and S. Ren, A confidential communication-oriented information hiding algorithm based on GHM multi-wavelet and DCT, Applied Mathematics & Information Sciences, 7 (2013), 1803-1807.doi: 10.12785/amis/070518.
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# Linear Algebra - Can vector $v$ be expressed as a linear combination of $u_1$ and $u_2$
I have a question: Can the vector $v = (1,2)$ be expressed as a linear combination of $u_1 = (1,3)$ and $u_2 = (4,1)$?
What I have tried:
$a + 4b = 1$
$3a + b = 2$
$a = 1 - 4b$
$3(1 - 4b) +b = 2$
$3 - 12b + b = 2$
$3 -11b=2$
$3 -2 = 11b$
$1 = 11b$
$b = 1/11$
$a + 4(1/11) = 1$
$a =1 - 4/11$
$a = 7/11$
Therefore, $v = 7/11x + 1/11y$
That's what I got but I know it's wrong because it doesn't seem right! Any help about how to go about doing this will be much appreciated!
-
You know it's wrong because "it doesn't seem right"? Well, that's not a very mathematical argument, is it? And BTW: it is correct. – DonAntonio Feb 11 '14 at 16:45
$$\frac{7}{11}(1,3) + \frac{1}{11}(4,1) = (\frac{7}{11},\frac{21}{11})+(\frac{4}{11},\frac{1}{11}) = (\frac{11}{11},\frac{22}{11}) = (1,2)$$
It's generally true that as long as $u_2$ isn't a scalar multiple of $u_1$, you can find a unique linear combination of $u_1$ and $u_2$ to give any desired $v$. That's because the condition is exactly what it takes for $\{u_1,u_2\}$ to be a basis for $\mathbb{R}^2$.
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# A change of variables in the euler equation
If someone could help me with the proposed change of variables, it would be greatly appreciated. Consider Euler's equation:
$$z^2w'' + \alpha zw' + \beta w = 0$$
where $w$ is a function of $z$ and $\alpha, \beta$ are constants. How would the change of variables $t =\ln(z)$ transform this equation?
-
This is calculus, so we calculate. Note that $$\frac{dw}{dz}=\frac{dw}{dt}\frac{dt}{dz}=\frac{dw}{dt}\frac{1}{z}.\tag{1}$$
For the second derivative, we need to differentiate $\frac{dw}{dt}\frac{1}{z}$ with respect to $z$. Use the Product Rule. We get $$\frac{dw}{dt}\left(-\frac{1}{z^2}\right) +\frac{1}{z}\frac{d}{dz}\left(\frac{dw}{dt}\right).$$
For the unfinished second part, we get $$\frac{1}{z}\frac{d^2w}{dt^2}\frac{1}{z},$$ by the same sort of Chain Rule calculation that we used for $(1)$.
Put things together. We get $$\frac{d^2 w}{dz^2}=\frac{1}{z^2}\left(-\frac{dw}{dt}+\frac{d^2w}{dt^2}\right).\tag{2}$$
Now substitute for $\frac{d^2w}{dz^2}$ and $\frac{dw}{dz}$ in the original DE. The $z^2$'s cancel in the first term, and the $z$'s cancel in the second term. We end up with a very tractable DE. This was the whole purpose for the change of variable.
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Let $\displaystyle f \subseteq \mathbb{R}^2$ $\displaystyle \to \mathbb{R}^2$. Show that if the determinant of the Jacobian Matrix of $\displaystyle f$ is not equal to zero at $\displaystyle (x_o,y_o)\in D$, then $\displaystyle f$ is injective in some neighborhood of $\displaystyle (x_o,y_o)$.
2. First, the Jacobian is continuous in (x, y) (you may need to show that) so if it is not 0 at $\displaystyle (x_0, y_0)$ it is not 0 in some neighborhood of that point. Now use the "mean value theorem". If $\displaystyle f(x_1, y_1)= f(x_2, y_2)$ then $\displaystyle f(x_1, y_1)- f(x_2, y_2)= J(x, y)\begin{bmatrix}x \\ y\end{bmatrix}= 0$ for some point (x, y) on the line between $\displaystyle (x_1, y_1)$ and $\displaystyle (x_2, y_2)$
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Builder pattern
This pattern is a common way of creating instances in Rust. It will help you write cleaner and more readable code that'll be easy to expand later.
Let's dive straight into everyones favorite toy example, the car:
#![allow(unused_variables)]
fn main() {
#[derive(Debug)]
struct Car {
number_of_doors: usize,
color: String,
}
}
Cars have a number of defining properties, let's pretend there's only two for now. (This struct is very simple, so we could of course create an impl with a new() in it in this case, but bear with me.)
In Rust, the builder pattern consists of a struct with multiple functions that consume self mutably and returns it again. It is commonly given the name of the type it builds, followed by the word Builder. In our case, it would be a CarBuilder.
#![allow(unused_variables)]
fn main() {
struct CarBuilder {
number_of_doors: usize,
color: Option<String>,
}
}
This CarBuilder contains data that will later be used to construct the Car. Note that the signature for color differs from the one in Car.
Let's start by giving the CarBuilder a new() and initialize the values.
#![allow(unused_variables)]
fn main() {
impl CarBuilder {
pub fn new() -> Self {
Self {
number_of_doors: 5,
color: None,
}
}
}
}
Here we set the number of doors to 5, as that's a very common number to have. Four actual doors plus one trunk. The color is set to None, because there's no "normal" color for a car to have.
Let's add another function to build a Car. We'll set a rule here that only builds one if we've set a color.
#![allow(unused_variables)]
fn main() {
impl CarBuilder {
pub fn build(self) -> Result<Car, CarBuilderError> {
let color = match self.color {
Some(color) => color,
None => return Err(CarBuilderError::NoColor),
};
Ok(Car {
number_of_doors: self.number_of_doors,
color,
})
}
}
}
You'll notice that build() returns Result<Car, CarBuilderError>. We'll get to CarBuilderError in a bit.
Next we'll add a function that can set the amount of doors. number_of_doors is a usize, and we don't judge here, so users can have millions of doors if they want. That means that we'll only have one rule; don't set the number to 0.
#![allow(unused_variables)]
fn main() {
impl CarBuilder {
pub fn number_of_doors(mut self, number_of_doors: usize) -> Result<Self, CarBuilderError> {
if number_of_doors == 0 {
Err(CarBuilderError::WrongNumberOfDoors)
} else {
self.number_of_doors = number_of_doors;
Ok(self)
}
}
}
}
The rule about the number of doors is enforced by returning an error if the number is wrong.
We will also add a function that lets us set the color. If you look back at the build function, you'll notice that it will fail to build if you don't pick a color.
#![allow(unused_variables)]
fn main() {
impl CarBuilder {
pub fn color(mut self, color: Color) -> Self {
self.color = Some(color);
self
}
}
}
(As we all know, cars can only be one of two colors).
#![allow(unused_variables)]
fn main() {
#[derive(Debug)]
enum Color {
Red,
Green,
}
}
Now all we have left to do is to define those errors we mentioned before.
#![allow(unused_variables)]
fn main() {
#[derive(Debug)]
enum CarBuilderError {
WrongNumberOfDoors,
NoColor,
}
impl Error for CarBuilderError {
fn description(&self) -> &str {
match self {
CarBuilderError::WrongNumberOfDoors => "The car must have at least one door.",
CarBuilderError::NoColor => "The car must have a color.",
}
}
}
impl fmt::Display for CarBuilderError {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
write!(f, "{}", self.description())
}
}
}
That's it. Try it out like this:
fn main() -> Result<(), Box<dyn Error>> {
let car = CarBuilder::new()
.number_of_doors(3)?
.color(Color::Red)
.build()?;
println!("car = {:?}", car);
Ok(())
}
`
If you've discovered a new feature a car might have, like horsepower or a chromed exhaust pipe tip, you can easily add it now.
Good luck.
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# YX8018 solar led light - adaptable to li-ion?
#### Grum
Joined Apr 30, 2018
41
Hi all - I have a row of these cheap solar garden led light alongside a path that is mostly in the shade, so the batteries very seldom charge sufficiently to give more than about 30 minutes of light at dusk, and are completely exhausted by the time it really gets dark and we could actually benefit from them!
I am thinking about attempting to wire them all to a common 1S3P 18650 li-lion power pack in my shed, which would in turn be charged from a much better placed solar panel via a ‘proper’ charge controller.
So I am guessing the easy part is simply removing the batteries from the lights, and wiring them to the li-ion pack instead. My question is whether I should be leaving the remainder of the circuit as is, but regulating the input voltage down to 1.5v at each light, or can the YX8018 operate from a 3-4.2v supply without releasing the magic smoke, and if so, should I replace the inductor (between Vcc and LX pins) with a current limiting resistor instead?
Any thoughts, or alternative solutions with the emphasis on cheap (I.e. as close to free as is practical), and minimally invasive. Given that the lights were only $2 each, spending$\$ on a solution kind of defeats the object of the exercise really.
TIA
Grum
#### MisterBill2
Joined Jan 23, 2018
11,900
The simple work-around will be to put two of the garden lights in series so that the required voltage is twice as much. Then it will be pairs pf the lights, a bit more complex in wiring but not requiring any extra regulation. It may also be that the lights can keep their internal batteries and simply those batteries be charged in series from the higher voltage solar panel. It will require more complex wiring but no extra electronics, although still a charge controller from the solar cell array.
#### Alec_t
Joined Sep 17, 2013
12,817
The simple work-around will be to put two of the garden lights in series
I doubt it would be that simple. Those garden lights typically have an internal blob which both detects the light/dark threshold and controls a boost converter for raising the cell voltage to ~3V for the LED. Or did you mean connect directly to the LEDs and cut out the detector/converter?
#### Grum
Joined Apr 30, 2018
41
Those garden lights typically have an internal blob…
No blob in this case Alec_t, it is wired exactly as per the (corrected) example diagram in the data sheet - see attached. So, maybe it is as ‘simple’ as stringing two together - not that I pretend to quite understand how that could work…
#### Alec_t
Joined Sep 17, 2013
12,817
No blob in this case Alec_t
That YX chip is the 'blob' I was referring to. Some lamps have a circuit-on-board blob instead of a pinned rectangular chip.
#### Grum
Joined Apr 30, 2018
41
The simple work-around will be to put two of the garden lights in series…
LOL - MisterBill2, you credit me with a lot more than I have in the knowledge area…. I’ve attached a circuit diagram that shows one lamp… can you explain how connecting two of them in series might look? Connecting them in parallel I can visualise, but in series has got me stumped.
#### Grum
Joined Apr 30, 2018
41
That YX chip is the 'blob' I was referring to. Some lamps have a circuit-on-board blob instead of a pinned rectangular chip.
Aha - now I understand… I guess that just because it has a device number on it, unless you can actually get a schematic of the device operation, then it might just as well be an anonymous blob…
#### MisterBill2
Joined Jan 23, 2018
11,900
OK, I should have been much more specific. I meant to put the battery connections in series, possibly even with the original battery still in place. An external power source will then not only be stabilized by the internal battery, it will also charge that battery. So adding external power by that means can be safe and effective, in addition to costing much less.
To answer the question in post #6, about the series connection, first visualize a second copy of the circuit shown.
Then, from the positive terminal of the solar cell package, a wire to the positive terminal of the first circuit, leaving all internal connections unchanged. Next, another wire connected to the negative terminal of that battery in the first circuit to the positive terminal of the battery in the second circuit. Finally, a wire from the negative terminal of the battery in the second circuit to the negative terminal of the solar cell package. This is a series connection. The voltage from the solar cell array will be divided between the two batteries, hopefully fairly equally.
If it happens that the rated output of the array is six volts, then there will need to be four light devices in the series string instead of two.
Last edited:
#### Ya’akov
Joined Jan 27, 2019
5,666
No blob in this case Alec_t, it is wired exactly as per the (corrected) example diagram in the data sheet - see attached. So, maybe it is as ‘simple’ as stringing two together - not that I pretend to quite understand how that could work…
View attachment 267378
The way that IC works is to use the solar cell both to charge the battery and sense darkness. The output of the solar cell is on the CE (Chip Enable) pin which must be pulled low to turn on the chip. As long as there is enough light to keep the pin at logical high, the solar cell is connected to ground and has a path to charge the battery.
Once it gets dark enough for the voltage from the solar cell to be low, the IC disconnects the solar cell from ground and the battery starts to discharge into the VDD pin. The inductor is the only external part of a simple boost converter than brings the 1.2V from the NiMH battery up to the ~3V the LED needs.
You could probably just insert a diode into the input from the larger battery so the solar cell wouldn’t try to charge the LiIon battery. But you also need to replicate the action of not discharging the LiIon battery into the lights until it is dark.
#### Ya’akov
Joined Jan 27, 2019
5,666
Alternatively, you could just bypass the IC altogether and supply 3V centrally using a buck converter. You would just replicate the charge until dark, power until light part of the circuit back at the main supply and the buck converter would turn on a 3V feed to the LEDs when it became dark, and off while the sun charged the battery.
You would just need a current limiting resistor for each LED and feed them directly through that.
#### Grum
Joined Apr 30, 2018
41
... I meant to put the battery connections in series …
Ok - so you mean to basically wire the whole lamp circuit in series with the next one..? 8-o
That’s actually considerably simpler than I imagined. If I am understanding correctly, you mean something like this?
You really think that would work? I think I would remove the little Nicads altogether, and put a diode in each one so as to make the charge part of each lamp redundant, but leave everything else to run as normal at night, using a proportion of the Li-ion cell’s voltage.
#### Grum
Joined Apr 30, 2018
41
Alternatively…
Many thanks for your previous explanation Ya’akov, and this alternative solution. I must confess, I like this idea and had thought of something similar myself, but at the moment, I have no way to use the solar panel for charging the 18650, to also act as a signal for the daytime charging to switch over to night time loading (and it would also make the entire innards of the lamp redundant, except for the LED itself, and I hate to see waste). I do have a 12v time clock switch that I was wondering if I could utilise somehow, but 12v… that’s a whole new different kettle of fish! LOL
#### Ya’akov
Joined Jan 27, 2019
5,666
Many thanks for your previous explanation Ya’akov, and this alternative solution. I must confess, I like this idea and had thought of something similar myself, but at the moment, I have no way to use the solar panel for charging the 18650, to also act as a signal for the daytime charging to switch over to night time loading (and it would also make the entire innards of the lamp redundant, except for the LED itself, and I hate to see waste). I do have a 12v time clock switch that I was wondering if I could utilise somehow, but 12v… that’s a whole new different kettle of fish! LOL
You don’t need to use the solar panel, you can use a photosensitive switch of various kinds.The simplest ones require only a few components. Or you could make a high impedance connection to the solar cell output and switch with that. I am sure many members here would enjoy working out possible circuits.
#### MisterBill2
Joined Jan 23, 2018
11,900
Ok - so you mean to basically wire the whole lamp circuit in series with the next one..? 8-o
That’s actually considerably simpler than I imagined. If I am understanding correctly, you mean something like this?
View attachment 267383You really think that would work? I think I would remove the little Nicads altogether, and put a diode in each one so as to make the charge part of each lamp redundant, but leave everything else to run as normal at night, using a proportion of the Li-ion cell’s voltage.
That is indeed exactly what I meant, except that the added diodes provide no benefit. One diode in the string will prevent any chaarge from running back thru the solar cell array, while if it has any external circuit to deliver a battery charging current it will all ready have a reverse current prevention arrangement.
#### Grum
Joined Apr 30, 2018
41
That is indeed exactly what I meant, except…
Thanks MisterBill2. Point taken about the diodes. I guess I’ll grab a couple of the lights and test this theory out on my workbench. At just a couple of bucks, I can always grab a couple from Bunnings for the test…
#### MisterBill2
Joined Jan 23, 2018
11,900
The big part will be keeping the polarity correct. The individual battery at each position will tend to hold the voltage constant, and the external power will supplement the internal power so that they should stay lit longer. And if you have a storage battery in addition to the solar array the lights may stay on all night.
#### Grum
Joined Apr 30, 2018
41
…the lights may stay on all night.
LOL - I just checked and found that each light draws less than 10mA, so even a single 18650 with a marginal efficiency that can store 2000mAh could presumably power all 6 of my lights (3 pairs in parallel) all night for 3 nights without ANY recharging.
#### MisterBill2
Joined Jan 23, 2018
11,900
LOL - I just checked and found that each light draws less than 10mA, so even a single 18650 with a marginal efficiency that can store 2000mAh could presumably power all 6 of my lights (3 pairs in parallel) all night for 3 nights without ANY recharging.
OK, that is educational indeed. While the numbers say that it could do that, those numbers are based on the cell actually having the ability to deliver that much energy and having been fully charged. Rechargable batteries do lose capacity with cycling and depending on both the depth of discharge and the recharging cycle.
#### Grum
Joined Apr 30, 2018
41
OK - I bought a couple of new lights this morning - same manufacturer, but a slightly different model, and of course, it uses a different flamin’ chip
This new chip is a YX8050, which appears to be just another version of the same thing, but with the boost circuit running at a different frequency. So I’ve connected the two new lights in series to a freshly charged 18650 (4.15v) without their internal batteries, and without any diodes (not connected to solar charging yet anyway), and I can confirm that the concept works as predicted by MisterBill2.
I initially observed that the first lamp in the string was brighter than the second, but swapping the two units around brought the dimness to the front of the line, so I conclude that this is simply due to quality or accuracy variations in the individual components of the two lamps. One of them is simply dimmer than the other.
The individual lamps all have on/off switches, and these will obviously all need to be in the ON position, as any one of them being off will break the circuit for all the lamps in that loop.
The individual solar panels no longer act as switches for their own lamp, but appear to work in tandem, in a similar fashion to the on/off switches - if both are in the dark, the lights come on. If light then falls on one solar panel, both lights stay on, but if light affects BOTH panels, then both lights turn off. Going the opposite way, as soon as one panel senses darkness, then both lights come on.
One other observation - while my previous test on a single YX8018 based lamp drew just under 10mA from its 100mAh Nicad battery, testing BOTH of the new lamps in series (i note that these come with 200mAh Nicads), the pair are only drawing 6.5mA total from the 18650, while a single one is drawing about 12.5 from its Nicad… I guess that the increased voltage from the fully charged 18650 (2.1v per circuit) requires less current than the 1.2v from the Nicad, to achieve the same power output..? A quick check with calculator shows that 2.1v x 6.5mA is almost the same Wattage as 1.2v x 12.5mA.
BTW - while switching from two lamps in series, to a single lamp to check the current, I inadvertently left it connected to the 18650 with the perhaps unsurprising consequence of the lamp being incredibly bright, strangely drawing nearly 180mA, but most rewardingly, without the release of any magic smoke. So it could be possible to simply run all the lamps in parallel, if I reduce voltage and find the sweet spot maybe around that 2.1v area.
Phase II of experimentation commencing. If only I had a variable bench power supply :-(
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# to tilde or not to tilde
Schneider, Thomas (NIH/NCI) [E] schneidt at mail.nih.gov
Mon Oct 7 00:29:14 CEST 2019
Paulo:
> NO centered mathematical formula should contain any punctuation at
> the end of the line -- even if it is to terminate a sentence.
>
> Punctuation have a role in typography -- to introduce a pause at
> reading -- and with a centered formula that pause already EXIST. The
> correct is:
>
>
> A = \pi r ^2
>
>
> even if it is ending a sentence or a paragraph.
I think we will just have to agree to disagree. I find the comma
useful for pausing while the period ends a sentence and otherwise I
feel I'm hanging. In any case, the journal accepts them.
Tom
Thomas D. Schneider, Ph.D.
Senior Investigator
National Institutes of Health
National Cancer Institute
Center for Cancer Research
RNA Biology Laboratory
Biological Information Theory Group
Frederick, Maryland 21702-1201
schneidt at mail.nih.gov
https://alum.mit.edu/www/toms
More information about the texhax mailing list
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# 8. Permutations and the Determinant
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
There are many operations that can be applied to a square matrix. This chapter is devoted to one particularly important operation called the determinant. In effect, the determinant can be thought of as a single number that is used to check for many of the different properties that a matrix might possess. In order to define the determinant operation, we will first need to define permutations.
### Contributors
Both hardbound and softbound versions of this textbook are available online at WorldScientific.com.
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Now use the chart wizard ***EXCEL NOTE *** to draw graphs of x vs t and y vs t on the same axes and a separate graph of y vs x. Magic of SOLIDWORKS Equation Driven Curves. For example, the curtate cycloid is a curve traced out by a (red) point Pon the interior of a given (blue) circle, rolling along the (black) straight line (/axis):. I really do think the one thing you should take away from curvature is the idea that it's the derivative of the unit-tangent vector with respect to arc length and if you need to, you can just look up a formula like this but it's worth pointing out that it makes some things easier to compute because finding the tangent vector and everything can. Graphs of these functions are straight lines. A cycloid is a specific form of trochoid and is an example of a roulette, a curve generated by a curve rolling on another curve. This will give you y=c for some constant “c. It apears from the graph that there are vertical tangents at these points. The graph of this equation is: Figure 13. To Do and Notice. Define cycloids. Therefore, parametric equations of the cycloid are: x = r (θ- sin θ) y = r (1 - cos θ) θ R. Plug x=-sqrt(3) and x=sqrt(3) back into the function y=x^3 - 9x to get y= 10. (101b)) becomes ρ˙ +3 ρ + 1 3 ρ a˙ a. Would really like to be able to use variables to define t. Graph function y(x)=1. txt) or view presentation slides online. quadratic equations. The cycloid catacaustic when the rays are parallel to the y-axis is a cycloid with twice as many arches. Description. Visualization: [Press here to see animation again!]. How does the graph differ from those in parts (b) and (c)?. (View topic) • Apache OpenOffice Community Forum. A Cartesian graph or curve represented by two parametric equations. 4) Parametrize the graph y = f(x), a x b, and show that its arclength is given by the standard formula length = Z b a p 1+(f0(x))2 dx 4. Find the length of one \arch" of this cycloid, that is, nd the distance traveled by a small stone stuck in the tread of a tire of radius R during one revolution of the rolling tire. Keep in mind there are many different versions of Excel, so what you see in the video above might not always match up exactly with what you'll see in your version. This is a work which has never been translated into English, apart from a few sections ; it forms a bridge between Newton's Principia and Euler's Mechanics; indeed Euler and Hermann, distantly related, worked together at St. Create the top plot by passing ax1 to the plot function. you can generate a graph of x vs y for a range of time points timeRange the following way using the SPLINE command:. Finally, assuming dθ dx >0, we can solve for xas a function of θand obtain a parametric curve x(θ) = r(θ− sinθ) y(θ) = −r(1− cosθ). This is equivalent, I believe, to Swiss standard NHS 26702. Polyhedra formula investigation Cycloid activity and Pick’s Theorem activity – workbook activities (cannot post) GSP work-graph. Power transmission and sizing While the previous chapters have considered the analysis of a proposed motor-drive system and obtaining the application requirements, it must be recognised that the system comprises a large number of mechanical component. The equation of the cycloid can be written easily if expressed in terms of parameter θ. cycloid top: surface view of cycloid. A point on the circle traces a curve called a cycloid. Hello, You can create an new GDL object and use the parametric equation of a. Parametric Equation of a Cycloid. 1+cos angle area bounded asymptotes axis cardioid circle coefficient constant cos2 cosec cosh cot jc curve is symmetrical cycloid differential equation dx dx dx dy dy dx eigen ellipse Evaluate f/ie Find the area Find the volume function given equation Hence homogeneous function ILLUSTRATIVE EXAMPLES Ex initial line intersection intrinsic. This ratio determines the number of cusps. Answer to: Find all the points of a cycloid described by x=a(t-\sin t) \ and \ y=a (1-\cos t) where the tangent line is horizontal and a\neq 0 is a for Teachers for Schools for Working Scholars. Betreff: Draw Cycloidal gears with the Equation Editor zip and attach the sldprt file here. However, the two solutions of an equation in two variables that are generally easiest to find are those in which either the first or second component is 0. A moving point on the cycloid with a cusp at the origin, created by a circle of radius a centimetres, has the vector equation: r t a t t i a t j( ) ( sin ) (1 cos ) , where t is a real parameter. Note: A cardioid is a special case of the limaçon family of curves. 2 of Rogawski's Calculus [1] for a detailed discussion of the material presented in this section. Create the top plot by passing ax1 to the plot function. I really do think the one thing you should take away from curvature is the idea that it's the derivative of the unit-tangent vector with respect to arc length and if you need to, you can just look up a formula like this but it's worth pointing out that it makes some things easier to compute because finding the tangent vector and everything can. A cycloid is the curve traced by a point on the rim of a circular wheel e of radius a rolling along a straight line. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. thatthe cycloid is the curve of quickest descent because research on cycloids has been devel-oping for a considerable length of time. well as the architect, Christopher Wren, all wrote on various aspects of the cycloid. Xuan Luo's answer makes a clear case as to why the linear path is not the brachistochrone using the short-vs-steep quantitative argument. When theta = 2 pi n, both dx/d theta and dy/d theta are 0. How does the graph differ from those in parts (b) and (c)?. general category of cycloid are several more specific terms, of which the one I will be discussing is known to the mathematician as a curtate cycloid. More than one solution may exist, which is fine. View Notes - Cusp on the cycloid review from MATH 6435 at Georgia State University. You can use the auto mode or the step mode. Solution The equation r 2 = 4 cos u requires cos u Ú 0 , so we get the entire graph byrunning u from -p>2 to p>2. Create the top plot by passing ax1 to the plot function. math dictionary to view the specific definition for each math term. The curve traced out by a point P on the circumference of a circle as the circle rolls along a straignt line is called a cycloid. The calculator will find the unit tangent vector of a vector-valued function at the given point, with steps shown. Find the equation traced by a point on the circumference of the circle. The applet below shows two complete turns of such a wheel of variable radius. The standard equations of the cycloid are x = r[t sin(t) ] and y = r[1 cos(t) ], where r is the radius of the rolling circle and t goes through the numbers from 0 to 2Pi for one period. A cycloid is paraetrized by the equations x = r( t - sint) y = r(1 - cost)? a) find an equation of the tangent to the cycloid at point where t = b)at what point is the tangent horizontal?at what points is it vertical?. (c) The ant travels along a prolate cycloid. And the area dxdy in this case is given by r * rdɵ. The basic Cycloid Drawing Machine package consists of: the base; 2 geared turntables (120 and 150 teeth) 12 wooden gears (32, 34, 40, 50, 58, 60, 72, 74, 90, 94, 98, and 100 teeth) 3 connecting rods; 2 extender rods to lengthen gear diameter; newly designed maple penholder; 50 sheets of round 9-inch diameter heavy paper; 100 sheets of hexagonal test paper. A brief intro: The linear trendline equation is made of two excel functions, linked to your dataset. Since the cam's movement is usually constant then equal time intervals can be represented by equal distances along the horizontal axis and the resulting follower movement (or ‘displacement’) along the vertical axis. He then solved the differential equation to show that the desired curve is a cycloid. This article presents the design and experimental testing of CBR reducer. well as the architect, Christopher Wren, all wrote on various aspects of the cycloid. Imagine a metal bead with a wire threaded through a hole in it, so that the bead can slide with no friction along the wire. The motion executed by the follower here, is similar to that of the projection of a point moving along a cyloidal curve on a vertical line as shown in figure 7. Get more help from Chegg. The calculator will find the unit tangent vector of a vector-valued function at the given point, with steps shown. When point P is located at distance c along a radial line coming from the center of the rolling circle but different from its radius, then the path generated is referred to as an EPITROCHOID. Motion of a bead on a cycloid 35 [2] M. Pressure Angle (∞): If you can draw a common normal line to the meshing teeth surfaces at the contact point between the meshed teeth and a tangent plane common to the pitch circles of both the gear then angle between the common normal line and the tangent plane is called pressure angle. And what I wanna do is find the arc length of this curve, from when x equals zero to when x is equal to-- and I'm gonna pick a strange number here, and I picked this strange number 'cause it makes. As is readily apparent, this equation is unwieldy and not amenable for searching for primes. Find an equation describing the cycloid, where the circle has radius 1. b) drag the “dist” slider to travel the path of the graph. The equation $$x^2+y^2=1$$ defines a curve that is the unit circle. Pol, Dec 18 2013. Now, we could graph this to verify that the curve is traced out exactly once for the given range if we wanted to. Formula one race strategy. The general equation of a straight-line graph is y= mx+c. If the cycloid has a cusp at the origin and its humps are oriented upward, its parametric equation is. Explore thousands of free applications and open-source resources. The radial curve of a cycloid is a circle. Monkey Tree - calculating length, area and volume of fractals. If you specify one that is too small, it may take longer for your equation to graph. Graph the cycloid defined by the given equations for t in the specified interval. A tautochrone or isochrone curve is the curve for which the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point on the curve. We are going to be looking at this curve in more detail after this example so we won't sketch its graph here. Many thanks. Cycloid % Approximate times of descent for a cycloid from (0,c) to (d,0), corresponding to theta=0, theta=theta1 respectively and the value r for the radius of the rolling circle. Using a graphing calculator to graph a system of parametric equations: TI-86 Graphing Calculator [Using Flash] TI-85 Graphing Calculator. A particle with positive charge$q$ and mass$m$ is released from the origin, and initially at rest. general category of cycloid are several more specific terms, of which the one I will be discussing is known to the mathematician as a curtate cycloid. A; B ; C ; x; y; t 0 are the in tegration parameters deter-mined b y the initial conditions. A moving point on the cycloid with a cusp at the origin, created by a circle of radius a centimetres, has the vector equation: r t a t t i a t j( ) ( sin ) (1 cos ) , where t is a real parameter. How do you find the length of the curve #x=3t-t^3#, #y=3t^2#, where #0<=t<=sqrt(3)# ? Calculus Parametric Functions Determining the Length of a Parametric Curve (Parametric Form) 1 Answer. Figure $$\PageIndex{14}$$: (a) The ant is hanging onto the flange of the train wheel. 6) Tauto = equal, chronos = time: the curve to be followed in equal time. The curve traced out by a point on the rim of a circle rolling along a straight line is called a cycloid. ppt), PDF File (. Most SOLIDWORKS users are comfortable creating models with the familiar sketch commands (lines, rectangles, splines, arcs, etc. Calculate the length of a line segment. However, the two solutions of an equation in two variables that are generally easiest to find are those in which either the first or second component is 0. If you've ever seen a reflector on the wheel of a bicycle at night, you've probably seen a cycloid. math dictionary to view the specific definition for each math term. We take the line to be the x-axis and think of it as an oriented curve by setting =. O' is the origin (point of mass), A' point on the circle and phi the angle between O'A' and the y-axis. This equation works well:. "Folium of Descartes, with its asymptote. The Apache OpenOffice User Forum is an user to user help and discussion forum for exchanging information and tips with other users of Apache OpenOffice, the open source office suite. So for example, if x = 2, the y-value will be `y = 2 sin. Euler introduced a condition on the path in the form of differential equations, which we later introduce as Euler’s Equation. Calculus (11 ed. The calculator generates a list of points for a half curtate cycloid curve with either a fixed x interval or a fixed y interval. 【送料無料】 dunlop ダンロップ ウィンターmaxx 01 wm01 215/45r17 17インチ スタッドレスタイヤ ホイール4本セット lehrmeister レアマイスター ヴァッサーノ(ブラックポリッシュ) 7j 7. Finally, the first object is the one we will animate using the parameter a. Get more help from Chegg. If I have two points on a Cartesian plane, and I know that they are connected by a cycloid, then how do I find the equation for that cycloid? For background information, I have been playing around. We are going to be looking at this curve in more detail after this example so we won’t sketch its graph here. Math Videos are also included. Parametric Equations are a little weird, since they take a perfectly fine, easy equation and make it more complicated. 38m Definition : The radius of curvature between tooth surface and the tooth root. Informations d'achats et de prix Boutique en ligne Maplesoft Demande de devis. The second Friedmann equation (eq. If you see signs of a severe allergic reaction (hives, swelling of the face and throat, difficulty breathing, a fast heartbeat, dizziness, or weakness), call 9-1-1 and get the person to the nearest hospital. Scilab Textbook Companion for Higher Engineering Mathematics by B. A tautochrone or isochrone curve is the curve for which the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point on the curve. 5, a = 1 (the true cycloid), and a = 2. Extension ideas. math dictionary to view the specific definition for each math term. Solution: The velocity vector is h−2costsint,3 − 3t 2 ,1i at time t,. Equation Graphic; The cycloid was first studied by Cusa when he was attempting to find the area of a circle by integration. More specifically, the brachistochrone can use up to a complete rotation of the cycloid (at the limit when A and B are at the same level), but always starts at a cusp. As you do this, what happens to your POIs? Pretty cool, right?!. The functionality of the brake is guaranteed for a max value of the air-gap of 0,7 mm (wear 0,5 mm). A; B ; C ; x; y; t 0 are the in tegration parameters deter-mined b y the initial conditions. Function Graphing Software GRAPES 6. V arious cycloidal writing curv es The angular v elo cities! x and y are determined b y the ratios b et w een spring constan ts and masses. The classical cycloid is elements of this set. Many thanks. To make it look like an ellipse you will need to drag the axes until they are the same size. The arc length Integral_{theta=0. Plot a parametric equation in Matlab. cycloid - Free download as Powerpoint Presentation (. Lu, "Transmission Efficiency Analysis of pin-Cycloid Planetary Gearing Reducer Applying Two-Stage Speed Reduction Used in Propeller Pitch Variator", Advanced Materials Research, Vols. Graph the cycloid defined by the given equations for t in the specified interval. The classical cycloid is elements of this set. Let L be the line through P and Q. You can use the auto mode or the step mode. Particles drift parallel to the magnetic field with constant speeds, and gyrate at the cyclotron frequency in the plane. Consider two springs with different spring constants$k_1$ and$k_2$. Plane Curves and Parametric Equations. The cycloid is represented by the parametric equations x = rt − rsin(t), y = r − rcos(t) Two related curves are generated if the point P is not on the circle. Find an equation describing the cycloid, where the circle has radius 1. BU113: Critical Thinking and Communication in Business Creating an Index and graph to compare Company Stock Price Performance with the market (S&P 500) I. 2 is extracted from JIS B 1701-2: 1999 which defines the tooth profile and dimensions of involute spur gears and helical gears. ] Which polar function corresponds to each of the graphs below? [For each polar function, write the letter corresponding to the graph in the box. Visualizing parametric curves in the plane. Indicate with arrows the direction in which the curve is traced as t increases. Connect with Google Algebra Slope, Equation of Lines Template. Grewal1 Created by Karan Arora and Kush Garg B. More specifically, the brachistochrone can use up to a complete rotation of the cycloid (at the limit when A and B are at the same level), but always starts at a cusp. 59 KB) back to top. txt) or view presentation slides online. represent graphs that are more general than graphs of functions. Chicago, IL, University of Chicago Press, (1984) 129-130. The third equation is: (x,y) = ( (t+sin t) cos (t+sin t), (t+sin t) sin (t+sin t) ) …it was reparametrized with t+sin t First consider the graph when the parameter is t. Many graphing devices won’t plot the inverse of a given function directly, but we can obtain the desired graph by using the parametric graphing capa-bility of such a device. Graph of a cycloid with the arch over highlighted. For any positive value of r the graph gives the corresponding value of k. Keep in mind there are many different versions of Excel, so what you see in the video above might not always match up exactly with what you'll see in your version. Calculus III - Lab 1b: Parametric Equations Parametric graphs Explanation A very well-known parametric curve is the cycloid. Let the radius of the circle be. (c) Use a graphing utility to graph the curve represented by the parametric equations. "Folium of Descartes, with its asymptote. Allowing the tracing point to be either within or without the circle at a distance from the center generates curtate or prolate cycloids respectively. This is the parameter form of a cycloid , the curve that describes how a point of the circumference of a wheel as the wheel rolls along a straight line. CRC Press, 1997. This page is a list of mathematics articles in Mathematics and Multimedia. The amplitude of the step. So (as expected) y(x) is linear, y(x) = (b=a)x. Therefore, parametric equations of the cycloid are: x = r (θ- sin θ) y = r (1 - cos θ) θ R. Home » Mathematics. INTRODUCTION The physics of rolling is thought to be completely understood in terms of classical mechanics. Now, we could graph this to verify that the curve is traced out exactly once for the given range if we wanted to. The brachistochrone is a cycloid, but that cycloid is not the only curve satisfying the equation. We can verify this by using l'Hospital's Rule as follows. An analysis of the motion between two teeth and the calculation of the path of contact. The equation is usually written in polar coordinates. The time (h) for the air-gap adjustment is calculated with the following formula: The preivous formula allows the calculation of a wear equal to 0,1 mm. cycloid top: surface view of cycloid. Cycloid The cycloid is a famous curv e in mathematics obtained b y rolling circle along at surface and follo wing the tra jectory of a particular p oin t on circle. 534 Chapter 10 Parametric, Vector, and Polar Functions EXAMPLE 4 Finding Parametric Equations for a Cycloid Find parametric equations for the path of the point P in Figure 10. To write a piecewise function, use the following syntax: y = {condition: value, condition: value, etc. Theacceleration vectoris simply the derivative of the velocity vector with respect to time, ~a= d~v dt: For the cycloid the acceleration vector is ~a. Explain its shape by graphing its projections onto the three coordinate planes. This can be done using the following simple construction. An allergic reaction could occur after the vaccinated person leaves the clinic. In geometry, an epicycloid is a plane curve produced by tracing the path of a chosen point of a circle — called an epicycle — which rolls without slipping around a fixed circle. Using Parametric Equations to Describe Complex Movements. The calculator generates a list of points for a half curtate cycloid curve with either a fixed x interval or a fixed y interval. In equation 1, below, P identifies the number of the planet gear teeth, S that of the sun gear, and ω2 the angular velocity of the planet gear. Epicycloid and hypocycloid both describe a family of curves. The parametric equations of a cycloid c 𝑃( ) r ( ) r P Figure 8 This is the curve traced out by a point on a circle of radius as it rolls on a straight line without slipping. The curve drawn above has a = h. Technology-enabling science of the computational universe. If you specify one that is too small, it may take longer for your equation to graph. Minimum and maximum speed: For a continuous velocity function, the minimum speed is zero whenever the maximum and minimum velocities are of opposite signs or when one of them is zero. Jim Lambers MAT 169 Fall Semester 2009-10 Lecture 32 Notes These notes correspond to Section 9. The curve is formed by the locus of a point, attached to a circle (cycle -> cycloid), that rolls along a straight line. Magic of SOLIDWORKS Equation Driven Curves. Calculus (11 ed. Call the nexttile function to create an axes object and return the object as ax1. April 14 is Christiaan Huygens' birthday. (d) Eind the rectangular equation by eliminating the parameter. 1, Open GeoGebra and select Algebra and Graphics from the Perspectives menu. The rst step in the solution of the Euler-Lagrange equation for the brachistochrone problem: 2yy00+ 1 + (y0)2 = 0 is to reduce it to a rst-order equation. We are going to be looking at this curve in more detail after this example so we won't sketch its graph here. Be aware that this will affect the fineness of non-parametric graphs as well. For this reason, it plays an important role of first line of defence in a number of ways. education2000. Answer to In Problem 1-3, find the equation of the tangent line to the given curve at the given value of t without eliminating the parameter. x vs t and y vs t graphs for the first 20 values. They are also useful when the curve in question is not the graph of a function. PDF | This article presents the problem of quickest descent, or the Brachistochrone curve, that may be solved by the calculus of variations and the Euler-Lagrange equation. The Cycloid. , it is the curve of fastest descent under gravity) and the related. What you saw in the previous video was an analysis of the behavior of the trajectory near. An analysis of the motion between two teeth and the calculation of the path of contact. In Calculation,. If the circle has radius and rolls along the -axis and if one position of is the origin, find para- metric equations for the cycloid. The Math Forum has a rich history as an online hub for the mathematics education community. The title command allows you to put a title on the. derive the mean and variance of the binomial distribution now to find the variance, we rewrite x^2 as x(x-1) +x before we start out for explanation of mean of poisson distribution try the link mean of poisson distribution. Looking again at the animated graph, we can watch the variation in position and velocity of a point on the rim of the wheel. Hence, in scaling up, Huygens separated the trajectory from the graph of motion, at first drawing the parabola as lying inside the cycloid and intersecting it at what would correspond to K in Fig. This document is offered by KHK. (Shifrin Problem 1. The average velocity you are computing is an average rate. These works will lay the foundation for the cycloid gear's designing and profile modification and NC machining, and so on. It is observed that the bending stress in involute pinion teeth is lower than the cycloidal pinion teeth for the same module. % Uses quad8 for theta=. Such a curve would be generated by the reflector on the spokes of a bicycle wheel as the bicycle moves along a flat road. Linear functions are described in detail here. 7 is a planar view of an oil pump rotor, wherein the outer teeth of the inner rotor are formed along the combined cycloid curve originated within the limits. Formula one race strategy (498. Description. this is a parabola that opens to the right. cycloid definition: Geom. In Chart, allow Show chart names and set Data markers on hover and leave the rest unchecked for now. Involute Tooth Profile is a page to learn gear technical knowledge especially about teeth profile of gears. Starting at different places produces the same pattern just rotated around from the original. Finally, the first object is the one we will animate using the parameter a. cycloid top: surface view of cycloid scales of a bony fish bottom: The parametric equations of this cycloid are x = r , y = r. is If you would like to see a GSP demonstration of the movement traced out, click here. Assume the generating circle of the cycloid has radius 1. This article presents the design and experimental testing of CBR reducer. Extension ideas. - [Voiceover] So, right over here, we have the graph of the function y is equal to x to the 3/2 power. Keep in mind there are many different versions of Excel, so what you see in the video above might not always match up exactly with what you'll see in your version. curiously like a cycloid as drawn by a circle with diameter D! If you take the parametric equations for such a cycloid, you can fit them into the differential equation above, so the cycloid is, indeed, our brachistochrone. cycloid top: surface view of cycloid scales of a bony fish bottom: The parametric equations of this cycloid are x = r , y = r. Here are a few examples: Spiral; Cycloid. Interestingly, the cycloid described above is one of a number of cycloid-type parametric curves which are de ned similarly and which therefore have similar parametric representations. Find an equation describing the cycloid, where the circle has radius 1. A Curtate Cycloid. A graph of a prolate cycloid is shown in the figure. Visualization: [Press here to see animation again!]. The calculator takes the following arguments: Length of half cycloid. Wolfram Science. Find parametric equations to represent a curve. Consider the circle below of radius "r". The equation of motion and kinematic model of the. If the cycloid has a cusp at the origin and its humps are oriented upward, its parametric equation is. If the smaller circle has radius r, and the larger circle has radius R = kr,. The rst step in the solution of the Euler-Lagrange equation for the brachistochrone problem: 2yy00+ 1 + (y0)2 = 0 is to reduce it to a rst-order equation. Plane Curves - Lemniscate, Cycloid, Hypocycloid, Catenary, Trochoid SPECIAL PLANE CURVES. Now use the chart wizard ***EXCEL NOTE *** to draw graphs of x vs t and y vs t on the same axes and a separate graph of y vs x. ) Revise your equation, if necessary. This is the path followed by a point on the rim of a rolling ball. It was studied and named by Galileo in 1599. Tangents and Normal to a Curve A tangent is a line that touches a curve. 6 Graphing in Polar Coordinates 721EXAMPLE 2 Graph the Curve r2 = 4 cos u. O' is the origin (point of mass), A' point on the circle and phi the angle between O'A' and the y-axis. A cycloid is defined by xata t y aa t=− =− −∞∞sin cos for t in ,( ) Homework exercises 33 - 34. When point P is located at distance c along a radial line coming from the center of the rolling circle but different from its radius, then the path generated is referred to as an EPITROCHOID. Answer to In Problem 1-3, find the equation of the tangent line to the given curve at the given value of t without eliminating the parameter. For more information on formatting the data and displaying the text see the previous tutorials. • Lesson 4: Showing that a Pendulum Constrained by two Inverted Cycloids Swings in the Path of a Congruent, Inverted Cycloid. Use 75 or 50 ohm cable to feed the centre of the dipole. Calculus Questions: (a) Find the length of the curve between two points. Later this curve arose in connection with the brachistochrone. And flow chart for parametric design of cycloid curve is done. In case of a sector, it is known that the centroid lies at a distance of 2r/3 from the centre. By the view of expressive modeling approach, giving the task of ^construct the cycloid curve without using its formal equation _ to our students will be more useful than presenting a ready cycloid graph, even if it is also dynamic. Plane Curves and Parametric Equations Definitions If f and g are functions of a variable t on an interval I, then the equations x f(t)= and y g(t)= are called parametric equations and t is called the parameter. For example, the curtate cycloid is a curve traced out by a (red) point Pon the interior of a given (blue) circle, rolling along the (black) straight line (/axis):. The data in table 3. Simplification of Euler's equation. The shortest route between two points isn’t necessarily a straight line. " - Wikipedia In many calculus books I have, the cycloid, in parametric form, is used in examples to find arc length of parametric equations. You'd have to numerically subject the cycloid to Fourier analysis. Here are the simple steps you need to build a chart or graph in Excel. [size=150] I would thank a step-by-step information about how to draw a cycloid by locus with GeoGebra. It was studied and named by Galileo in 1599. The curve traced out by a point on the rim of a circle rolling along a straight line is called a cycloid. In this example, we are multiplying the sine of each x-value by the x-value. For example, the simplest way to express a spiral similarity in algebraic terms is by means of multiplication by a complex number. Graph function y(x)=1. The parameter θ varies from 0 at P1= (0,0) to θ2 at P2= (x2,y2) which may be found numerically as the solution to y2 x2=1−cosθ2 θ2−sinθ2 Substitution back into the second parametric equation then gives R=y2 1−cosθ2. A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slippage. "Folium of Descartes, with its asymptote. It issufficientto understand thatthis curve was taken as a hypothesis and the solution was obtained using the calculus of variations. Assume the generating circle of the cycloid has radius 1. 1-understand what is a cycloid. Cycloid, the curve generated by a point on the circumference of a circle that rolls along a straight line. ” This is the equation of the horizontal tangent line. Polyhedra formula investigation Cycloid activity and Pick’s Theorem activity – workbook activities (cannot post) GSP work-graph. t = ½ (y+1) into x to give: x = ¼ y2 + y + ¾. Loading Unsubscribe from GGBin7? Cancel Unsubscribe. In Calculation,. It maintains the high standards and careful development that have been the hallmark of the Thomas’ Calculus series, but this text follows a bee line to the essential elements of calculus. Managed to paint only half of the period, I do not understand what it is. Consider the parametric equations and (a) Create a table of - and -values using 0, and (b) Plot the points generated in part (a), and sketch a graph of the parametric equations. We take the line to be the x-axis and think of it as an oriented curve by setting =. This page is a list of mathematics articles in Mathematics and Multimedia. And flow chart for parametric design of cycloid curve is done. Find out what he did and what else occurred April 14 in science history. Equation curves are used to model complex geometry, such as gear tooth profiles, or sweep paths for hydraulic pumps. This can be done using the following simple construction. Now, we could graph this to verify that the curve is traced out exactly once for the given range if we wanted to. A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slipping. In the film clip, a piece of white tape on the rear tire labels such a point. Initial Point The initial point of a parametric curve is the point which represents the x and y values when the parameter takes on the lowest value in its domain. (a) y = x 3 In standard form, the equation is x y = 3, so a = 1, b = 1, and c = 3. Cycloid Curve Written by Paul Bourke June 1997 Everyone has witnessed a rolling wheel or tyre, have you ever stopped to wonder what curve is traced out by a point on the rim of the wheel? Such a curve is called a cycloid. The point-roulettes for which a circle rolls on a line or on another circle, are known as cycloidal curves.
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