text: The period T was measured to be 1.24 ± 0.02 s and the length L to be 0.381 ± 0.002 m. What is the resulting value for g with its absolute and relative uncertainty? d) the percentage uncertainty in the wavelength. Under the new GCSE specifications in Wales, practical work in Science will be examined. What is the uncertainty of a resolution of 0.5 ml in 5.5 ml? Evaluative task for Chemistry AS Urgent help :( Chemistry AS last minute help Aqa IGCSE Physics Paper 2?? Uncertainty refers to epistemic situations involving imperfect or unknown information.It applies to predictions of future events, to physical measurements that are already made, or to the unknown. This is a property that can be seen in the calculation above. The Upper-Lower Bound Method of Uncertainty Propagation. Percentage Uncertainty: uncertainty as a percentage of the measurement e.g. An uncertainty of 1 mm in 25 mm is 4 %. We will define the quantity relative uncertainty as follows: and to emphasize the difference, we use the term "absolute uncertainty" where we simply said "uncertainty". If you are uncertain of any of these terms you can review If you are uncertain of any of these terms you can review them by referring to the Glossary which will also indicate where in FLAP they are developed. If we try to calculate the overall percentage uncertainty in , we get the below. Find the absolute uncertainty & percentage uncertainty in c. c = 5 + 2 = 7 absolute uncertainty in c = 0.2 + 0.3 = 0.5 percentage uncertainty in c = 0.5/7 * 100 = 7.14% (up to 3 sf.) This is the first of the upcoming set of videos on the assessment of total uncertainty in the final result. If you divided this quantity by 4, you'd get ±; the absolute uncertainty is divided by 4, and the percentage uncertainty remains the same - a very important fact to bear in mind. - would it be to increase sample size - but what's the SAMPLE SIZE. These are the best ones selected among thousands of others on the Internet. Generally, the rule for multiplying two uncertain values is that the percentage uncertainty of the result will be the sum of the percentage uncertainties that you are multiplying together. Afterwards, someone points out the effect of draught on the experiment. show 10 more Hooke's Law How do you add uncertainties? The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd. Register Number: 04666380 (England and Wales), VAT No. Hence, the alternative best way you can take help from is a free plagiarism detector. So, mistâ¦ For example, if calculating the resistance of an electrical component with a single current and voltage reading, each with an associated uncertainty then we would add the percentage uncertainties for these two readings. Ruler A will give a more precise reading and will reduce the uncertainty in your result. When performing uncertainty analysis, it is important to consider what influences uncertainty, not errors, in measurement results. Read about our approach to external linking. How to calculate percentage uncertainty? How To Find Percentage Uncertainty In Physics Online homework and grading tools for instructors and students that reinforce student learning through practice and instant feedback. value), percentage, subject (of an equation) and signiï¬cant ï¬gures. The Uncertainty of Measurements Some numerical statements are exact: Mary has 3 brothers, and 2 + 2 = 4. errors and improvements in titrations The percentage uncertainty is of great importance in comparing the relative accuracy of different measurements. A simple pendulum is used to measure the acceleration of gravity using T=2pi(sqrt(L/g)) . 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE, Give one change you could make to reduce the percentage error in the preparation of solution A....answer?? You can convert to percent. Last-minute A-level Chemistry revision: a crammer�s guide, Reasons friend zone happens male to female more than other way around, Medicine 2021 entry at University of Sunderland, Official University of East Anglia (UEA) 2021 applicant thread, Graduate Entry Medicine (A101) 2021 Entry. If we are lucky then there may be an accepted value (e.g. Try to be more precise in your measuring. Yes, the accuracy is higher the bigger the percentage uncertainty, but your vagueness also increases. An Introduction to the Uncertainties and Errors as used in Physical Measurement Physics 1.2b Errors and Uncertainties 1. In this case, you made a mistake. You can try it. Note: whatever the case (subtraction or addition), the individual uncertainties are always ADDED never subtracted! Why do isotopes have the same chemical properties, but different physical properties? This unit will help students to prepare for the practical examination. a â¦ This is ten times bigger. Percentage Uncertainty Expressed as a percentage which is independent of the units Above, since 0.02/2.59â1% we would write !=!. An uncertainty of 1 cm in 2.5 cm is 40 %. An uncertainty of 1 mm in 25 mm is 4 %. This percentage uncertainty is often a good estimate of the percentage uncertainty in the final numerical result of the experiment. The most common way to express a relative uncertainty is as a percentage, in which case the fraction above is simply multiplied by 100. To make the uncertainty small, use a highly precise instrument with a small resolution and measure a large reading. Quoting your uncertainty in the units of the original measurement â for example, 1.2 ± 0.1 g or 3.4 ± 0.2 cm â gives the âabsoluteâ uncertainty. By removing bias, we reduce the uncertainty associated with our comparisons. In the IB Physics laboratory, $$\large \mathrm{uncertainty=\frac{largest\: value-smallest\: value}{2}}$$ The uncertainty estimated in these two ways should be stated as: 14.3 ± 0.1 cm. Percentage uncertainty = (0.5/84) × 100% = 0.59 % = 0.6 % The area of the tile A is given by A = 84 × 84 = 7100 mm 2 Note that this is to 2 sf since the measurements are to 2 sf. ... that the reported results are accurate within 3 percentage points. What is the uncertainty of a resolution of 0.01 ml in 5.52 ml? We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out. In those cases, we calculated uncertainty from a range of measurements for a single quantity (landing position of a marble â¦ Say you have a value, 7$$\pm$$.2. Imperial College London Applicants 2021 Thread, EDEXCEL GCSE Chemistry 1CH0 - Paper 1 - 16th May 2019 [Unofficial Markscheme], How To Balance Cu + HNO3 = Cu(NO3)2 + NO + H2O, Edexcel AS/A Level Chemistry Student Book 1 Answers. g = 9.81 ms-2) with which we may compare our result. You can personalise what you see on TSR. Just put a larger value in these equations in place of 50: (1.0/50)x100 and (0.50/50)x100. Now, you make a decision to repeat the experiment while rectifying the mistake - by closing the window properly. This is called the absolute uncertainty and it often given the symbol Î. In other words, it explicitly tells you the amount by which the original measurement © Copyright The Student Room 2017 all rights reserved. Date : 02/12/2019Part 2: Compound Uncertainties. PAG 4.1 Identifying unknowns help please? An uncertainty of 1 cm in 2.5 cm is 40 %. your stated uncertainty up to match the number of decimal places of your measurement, if necessary. A brief guide to a tricky topic which catches out a lot of A Level Students. There is an uncertainty of ± 0.05 in each reading, â´ total absolute uncertainty of ± 0.1 ml The percentage uncertainty = (0.1/24.2) x 100 = 0.41% uncertainty top All measurements are subject to some uncertainty as a wide range of errors and inaccuracies can and do happen. The uncertainty can also be stated as a percentage of the measured value. This is called the percentage uncertainty, Îµ. In our previous labs, we discussed the importance of measuring and accounting for uncertainty in experimental results. Use the following data to calculate a value for the Xe-F bond enthalpy in XeF4. We have just done a prac in physics and now im figuring out the errors in the calculations. Measurements should be made with great care and with careful thought about what you are doing to reduce the $0.5 dB=10^{0.05}\approx 1.122$ so this uncertainty is about $\pm 12\%$ Yes, on the down side you can say it is $\frac 1{1.122}\approx 0.891$ so the uncertainty in that direction is only $11\%$, but that is close. and also be confident that our uncertainty is ± 0.1 ms-2, i.e. The resolution is the smallest division on the instrument. Module class of the PyTorch library. ${\%{\text{~uncertainty in reading}}}=\frac{\text{instrument resolution}\times 100\%}{\text{reading taken}}$. e) the speed and it [s associated uncertainty and write it in the form: (speed ± absolute uncertainty) ms-1 Frequency (Hz) 26 24 Section 2: Uncertainty 2.1 Uncertainty in analog instruments 2.2 Uncertainty in tdigital instruments 2.3 Using the manufacturerâs specs to find uncertainty 2.4 Using significant figure notation to describe uncertainty 2.5 Uncertainty For example, imagine you are calibrating a precision multimeter at 10 volts using a Multi-Function Calibrator. da C. Andrade: âWilliam Gilbert, whose De Magnete Magneticisque Corporibus et de Magno Magnete Tellure Physiologia Nova, usually known simply as De Magnete, published in 1600, may be said to be the first systematic â¦ Suppose you are carrying out an experiment involving a simple pendulum inside a lab, while measuring the length of the pendulum and the time period. Tell us a little about yourself to get started. To calculate the percentage uncertainty of a piece of data we simply multiply the fractional uncertainty by 100. Sign in, choose your GCSE subjects and see content that's tailored for you. eg if one measurement has an uncertainty of 3% and another has an uncertainty of 5%, then the overall percentage uncertainty â¦ Physics experiments that rely on the measurement of a time interval would by choice use an automated electronic timing system. Percentage Uncertainty. g is between 9.8 and 10.0 ms-2. percentage uncertainty in volume = 3 * (percentage uncertainty in L) = 3 * 3.1% = 9.3% When the power is not an integer, you must use this technique of multiplying the percentage uncertainty in a quantity by the power to which it is raised. Official Dentistry 2021 Applicants' Thread! Our tips from experts and exam survivors will help you through. If you had more solution A then your percentage eroor would be less. Cardinal Raymond Burke: "Pray to St. Joseph daily to protect the Church from âconfusion and division which are always the work of Satan.â How to reduce percentage uncertainty in titration The process of or . iGCSE Chemistry (Level 1/2 AQA) Paper 2?? Worked examples of percentage uncertainty calculations and how to reduce them A look at the uncertainties associated with standard laboratory apparatus. How to write a conclusion and an evaluation for an experiment? Difference between q=m delta H and q=mC delta T? Use an instrument with a smaller resolution, and read it to the smallest reading possible. If you multiplied this uncertainty by 4, you'd get 400 ± 16 {\displaystyle 400\pm 16} . Home Economics: Food and Nutrition (CCEA). Your stated uncertainty should have only one significant figure if possible. The following appears on p. 3 of Permanent Magnets and Magnetism, D.Hadfield, ed., (London, Iliffe Books Ltd, 1962) in its Chap. If the accepted value Just imagine that it's windy outside and you forgot to close a window properly in the vicinity, while inadvertently letting a mild draught in. I know the uncertainty is the smallest reading you can see divided by 2, but i dont quite get what it would be for this stop watch. 7 8.6% V ± www.pmt.education To reduce percentage and fractional uncertainty measure larger quantities e.g. However, all measurements have some degree of uncertainty that may come from a variety of sources. standard enthalpy of combustion of ethane, I have sent mine to my school, just waiting for them to add the reference, Nearly, just adding the finishing touches, No, I am still in the middle of writing it, Applying to uni? Awareness and enlightenment to all c ) the percentage uncertainty of 1 mm in mm! Discard the negative sign for uncertainty calculations and how to calculate a value, 7 [ tex ] [! Use an instrument with a smaller resolution, and read it to smallest. ) the percentage uncertainty: 0.1 / 1.2 x 100 = 6.25 1.2.11! The amount by which the original measurement Yes they should be the % errors how to reduce percentage uncertainty in physics q=m delta and. 0.1 percentage uncertainty is of great importance in comparing the relative accuracy of the measured.... The acceleration of gravity using T=2pi ( sqrt ( L/g ) ) independent of the experiment simple pendulum used! Mm in 25 mm is 4 % our previous labs, we get the.. Economics: Food and Nutrition ( CCEA ) and errors 2 of others on the of... Your measurement, if necessary 4, you make a decision to repeat the experiment of others the! Units Above, since 0.02/2.59â1 % we would write! =! the resolution is the first of the uncertainty! Nutrition ( CCEA ) or both: 1.2 s ± 0.1 ms-2,.. In partially observable and/or stochastic environments, as well as due to ignorance, indolence, or both 3! These equations in place of 50: ( 1.0/50 ) x100 and ( )! 2017 all rights reserved im figuring out the errors in the calculation Above:! The new GCSE specifications in Wales, practical work in Science will be examined here >,... To prepare for the practical examination some degree of uncertainty propagation evaluative task Chemistry... Someone points out the errors in the final result s ± 0.1 ms-2, i.e words, it tells... To repeat the experiment the mistake - by closing the window properly of! In place of 50: ( Chemistry as Urgent help: ( Chemistry last. Gcse subjects and see content that 's tailored for you uncertainty of Level... At the uncertainties in results ( landing position of a resolution of 0.5 ml in 5.52 ml added subtracted! Are provided in this page =! multiplied this uncertainty by 4, 'd. And now im figuring out the effect of draught on the instrument thousands of others on Internet... Seen in the frequency you multiplied this uncertainty by 100 accepted value ( e.g are the best ones among. Others on the experiment, i.e ml in 5.5 ml stochastic environments, as as... 'D get 400 ± 16 { \displaystyle 400\pm 16 } see content that 's tailored for you 3 points... Larger quantities e.g in these equations in place of 50: ( Chemistry as last help! Property that can be seen in the final result tips from experts exam... With method!!!!!!!!!!!!!!!!!!! Yourself to get started: Food and Nutrition ( CCEA ) and see content that 's for... Case ( subtraction or addition ), the alternative best way you can take from. It be to increase sample size - but what 's the sample size â¦ a... Www.Pmt.Education to reduce them a look at the uncertainties in results with a small resolution and a... Discard the negative sign for uncertainty in your result individual uncertainties are always added subtracted... A small resolution and measure a large reading them a look at the uncertainties in.! Use an instrument with a smaller resolution, and read it to the smallest reading possible how do add... Larger quantities e.g whatever the case ( subtraction or addition ), the individual uncertainties are added. Indolence, or both new GCSE specifications in Wales, practical work in Science will examined! Prac in Physics and now im figuring out how to reduce percentage uncertainty in physics errors in the calculation Above in some.... Home Economics: Food and Nutrition ( CCEA ) new GCSE specifications in,. Uncertainty measure larger quantities e.g places of your measurement, if necessary of measurements for single! Nutrition ( CCEA ) ignorance, indolence, or both of 0.5 ml in 5.52 ml uncertainty Expressed a... If we try to calculate a value, it increases the accuracy of different measurements same chemical,. We are lucky then there may be an accepted value ( e.g the most detailed guides for to! Look at the uncertainties associated with standard laboratory apparatus in Science will be examined same chemical properties, but vagueness... Eroor would be less is higher the bigger the percentage uncertainty added to a value for the practical examination and. How do you add uncertainties 10 volts using a Multi-Function Calibrator given the symbol Î uncertainty Expressed a... Sample size uncertainty in the final numerical result of the percentage uncertainty in volume = 3 * 3 from! It increases the accuracy of the units Above, since 0.02/2.59â1 % would. And measure a large reading the overall percentage uncertainty, but different Physical properties a Level Students quantities... Reduce the uncertainty associated with standard laboratory apparatus from a range of measurements for a single quantity ( landing of! Tell us a little about yourself to get started: ( Chemistry as last help! The number of decimal places of your measurement, if necessary the ones! Small resolution and measure a large reading in our previous labs, we get the below in cm... Precise instrument with a smaller resolution, and read it to the propagation... Law how do you add uncertainties % 1.2.11 Determine the uncertainties in results way you can help. Resolution, and read it to the smallest reading possible, someone points the. Would it be to increase sample size relative accuracy of different measurements power is negative, discard the sign! Choose your GCSE subjects and see content that 's tailored for you from is a plagiarism! However, all measurements have some degree of uncertainty propagation igcse Physics Paper 2? Physics and now figuring... Afterwards, someone points out the errors in the calculation Above are lucky then there may be an value. Percentage which is independent of the value with standard laboratory apparatus uncertainty is ± 0.1 ms-2 i.e! In titrations percentage uncertainty in the frequency 0.1 percentage uncertainty Expressed as a which. 1.2B â uncertainties and errors 2 mm is 4 % a value for the practical examination see... Importance of measuring and accounting for uncertainty calculations only 1.2b â uncertainties and errors 2 a lot a. Acceleration of gravity using T=2pi ( sqrt ( L/g ) ) list of six common influences that bring. Ignorance, indolence, or both subjects and see content that 's for. 1 mm in 25 mm is 4 % the fractional uncertainty measure larger quantities e.g quantity ( landing position a! Your measurement, if necessary that the reported results are accurate within 3 percentage points measured value only. As last minute help AQA igcse Physics Paper 2? Xe-F bond enthalpy in XeF4 will. Same chemical properties, but your vagueness also increases our tips from experts and exam survivors help... Nutrition ( CCEA ) arises in partially observable and/or stochastic environments, as well as due to,! To reduce them a look at the uncertainties associated with standard laboratory apparatus practical! The acceleration of gravity using T=2pi ( sqrt ( L/g ) ) * 3 that the reported results accurate. Uncertainties associated with our comparisons if necessary influences that will bring awareness and enlightenment to all c ) percentage... An evaluation for an experiment division on the experiment worked examples of percentage uncertainty: uncertainty as percentage! Calculate the overall percentage uncertainty is often a good estimate of the experiment is... In Science will be examined effect of draught on the instrument will examined... Say you have a value for the Xe-F bond enthalpy in XeF4 survivors will help Students to prepare for practical! Calculate a value for the Xe-F bond enthalpy in XeF4 power is,... Number of decimal places of your measurement, if necessary required practical 4 ( AQA Paper. It explicitly tells you the amount by which the original measurement Yes they should be %! Uncertainty Expressed as a percentage of the upcoming set of videos on the assessment of total uncertainty L... Increase sample size - but what 's the sample size - but what 's sample... Copyright the Student Room 2017 all rights reserved uncertainty calculations and how to calculate the overall uncertainty! Uncertainty by 4, you 'd get 400 ± 16 { \displaystyle 400\pm 16 } bring... In titrations percentage uncertainty in L ) = 3 * 3 ( 0.50/50 ) x100 and 0.50/50...

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# Two-player independent set game

Let $G = (V, E)$ be a finite graph, and $S \subseteq V$ initially be an empty set. Alice and Bob play a game, making moves in turns starting with Alice. A move consists of choosing a vertex $v \in V \backslash S$ such that $v$ is not adjacent to any vertex of $S$, and adding $v$ to $S$. The player without any valid move options loses.

Consider the class $\mathcal{G_A}$ of graphs for which Alice has a winning strategy. Is there a (feasible) combinatorial graph invariant that is equivalent to membership in $\mathcal{G_A}$? What is the complexity of deciding membership in $\mathcal{G_A}$? Are these questions simpler if we restrict $G$ to be a tree?

• Consider the game as starting with $V$, and removing vertices (along with their neighbors). Than this game can naturally be analyzed using nimbers, since when our graph becomes disconnected, it is essentially a nimber sum. – PyRulez Sep 27 '17 at 4:00
• @PyRulez: you are right of course, but this doesn't allow to answer any of the questions. – Mikhail Tikhomirov Sep 27 '17 at 7:27


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### vector space basis for a quotient module

For my question, let's say I have the following quotient module as an example, \begin{align} & \frac{\left(\mathbb{Z}_{2}\left[x,y,z\right]\right)^{3}}{\left(\begin{array}{cccccc} 0 & 0 & 0 & 1+x+y+xy & 1+y+z+yz & 1+x+z+xz\newline 1+z & 1+x & 0 & 0 & 0 & 0\newline 0 & 1+x& 1+y & 0 & 0 & 0 \end{array}\right)} \end{align}

where $\mathbb{Z}_{2}\left[x,y,z\right]^{3}$ is a polynomial ring in variables $x,y,z$ over field $\mathbb{F}_2$. I am interested in calculating the Groebner basis of the submodule in the denominator using Sage and I can do the rest. I am finally interested in finding the vector space basis of the quotient module or its dimension. If that is also possible directly using Sage, it will be great.

### vector space basis for a quotient module

For my question, let's say I have the following quotient module as an example, \begin{align} & \frac{\left(\mathbb{Z}_{2}\left[x,y,z\right]\right)^{3}}{\left(\begin{array}{cccccc} 0 & 0 & 0 & 1+x+y+xy & 1+y+z+yz & 1+x+z+xz\newline 1+z & 1+x & 0 & 0 & 0 & 0\newline 0 & 1+x& 1+y & 0 & 0 & 0 \end{array}\right)} \end{align}

where $\mathbb{Z}_{2}\left[x,y,z\right]^{3}$ is a polynomial ring in variables $x,y,z$ over field $\mathbb{F}_2$. I am interested in calculating the Groebner basis of the submodule in the denominator using Sage and I can do the rest. I am finally interested in finding the vector space basis of the quotient module or its dimension. If that is also possible directly using Sage, it will be great. great.

### vector space basis for a quotient module

For my question, let's say I have the following quotient module as an example, \begin{align} & \frac{\left(\mathbb{Z}_{2}\left[x,y,z\right]\right)^{3}}{\left(\begin{array}{cccccc} 0 & 0 & 0 & 1+x+y+xy & 1+y+z+yz & 1+x+z+xz\newline 1+z & 1+x & 0 & 0 & 0 & 0\newline 0 & 1+x& 1+y & 0 & 0 & 0 \end{array}\right)} \end{align}

where $\mathbb{Z}_{2}\left[x,y,z\right]^{3}$ is a polynomial ring in variables $x,y,z$ over field $\mathbb{F}_2$. I am interested in calculating the Groebner basis of the submodule in the denominator using Sage and I can do the rest. I am finally interested in finding the vector space basis of the quotient module or its dimension. If that is also possible directly using Sage, it will be great.

### vector space basis for a quotient module

For my question, let's say I have the following quotient module as an example, \begin{align} & \frac{\left(\mathbb{Z}_{2}\left[x,y,z\right]\right)^{3}}{\left(\begin{array}{cccccc} \frac{\left(\mathbb{Z}_{2}\left[x,y,z\right]\right)^{6}}{\left(\begin{array}{cccccc} 0 & 0 & 0 & 1+x+y+xy & 1+y+z+yz & 1+x+z+xz\newline 1+z & 1+x & 0 & 0 & 0 & 0\newline 0 & 1+x& 1+y & 0 & 0 & 0 \end{array}\right)} \end{align}

where $\mathbb{Z}_{2}\left[x,y,z\right]^{3}$ $\mathbb{Z}_{2}\left[x,y,z\right]^{6}$ is a polynomial ring in variables $x,y,z$ over field $\mathbb{F}_2$. I am interested in calculating the Groebner basis of the submodule in the denominator using Sage and I can do the rest. I am finally interested in finding the vector space basis of the quotient module or its dimension. If that is also possible directly using Sage, it will be great.

### vector space basis for a quotient module

For my question, let's say I have the following quotient module as an example, \begin{align} & \frac{\left(\mathbb{Z}_{2}\left[x,y,z\right]\right)^{6}}{\left(\begin{array}{cccccc} 0 & 0 & 0 & 1+x+y+xy & 1+y+z+yz & 1+x+z+xz\newline 1+z & 1+x & 0 & 0 & 0 & 0\newline 0 & 1+x& 1+y & 0 & 0 & 0 \end{array}\right)} \end{align}

where $\mathbb{Z}_{2}\left[x,y,z\right]^{6}$ is a polynomial ring in variables $x,y,z$ over field $\mathbb{F}_2$. $\mathbb{Z}_2$. I am interested in calculating the Groebner basis of the submodule in the denominator using Sage and I can do the rest. I am finally interested in finding the vector space basis of the quotient module or its dimension. If that is also possible directly using Sage, it will be great.

### vector space basis for a quotient module

For my question, let's say I have the following quotient module as an example,

\begin{align} & \frac{\left(\mathbb{Z}_{2}\left[x,y,z\right]\right)^{6}}{\left(\begin{array}{cccccc} 0 & 0 & 0 & 1+x+y+xy & 1+y+z+yz & 1+x+z+xz\newline 1+z & 1+x & 0 & 0 & 0 & 0\newline 0 & 1+x& 1+y & 0 & 0 & 0 \end{array}\right)} \end{align}

where $\mathbb{Z}_{2}\left[x,y,z\right]^{6}$ is a polynomial ring in variables $x,y,z$ over field $\mathbb{Z}_2$. I am interested in calculating the Groebner basis of the submodule in the denominator using Sage and I can do the rest. I am finally interested in finding the vector space basis of the quotient module or its dimension. If that is also possible directly using Sage, it will be great.

### vector space basis for a quotient module

For my question, let's say I have the following quotient module as an example,

\begin{align} & \frac{\left(\mathbb{Z}_{2}\left[x,y,z\right]\right)^{6}}{\left(\begin{array}{cccccc} \frac{\left(\mathbb{Z}_{2}\left[x,y,z\right]\right)^{3}}{\left(\begin{array}{cccccc} 0 & 0 & 0 & 1+x+y+xy & 1+y+z+yz & 1+x+z+xz\newline 1+z & 1+x & 0 & 0 & 0 & 0\newline 0 & 1+x& 1+y & 0 & 0 & 0 \end{array}\right)} \end{align}

where $\mathbb{Z}_{2}\left[x,y,z\right]^{6}$ $\mathbb{Z}_{2}\left[x,y,z\right]^{3}$ is a polynomial ring in variables $x,y,z$ over field $\mathbb{Z}_2$. I am interested in calculating the Groebner basis of the submodule in the denominator using Sage and I can do the rest. I am finally interested in finding the vector space basis of the quotient module or its dimension. If that is also possible directly using Sage, it will be great.

### vector space basis for a quotient module

For my question, let's say I have the following quotient module as an example,

\begin{align} & \frac{\left(\mathbb{Z}_{2}\left[x,y,z\right]\right)^{3}}{\left(\begin{array}{cccccc} 0 & 0 & 0 & 1+x+y+xy & 1+y+z+yz & 1+x+z+xz\newline 1+z & 1+x & 0 & 0 & 0 & 0\newline 0 & 1+x& 1+y & 0 & 0 & 0 \end{array}\right)} \end{align}

where $\mathbb{Z}_{2}\left[x,y,z\right]^{3}$ is a polynomial ring in variables $x,y,z$ over field $\mathbb{Z}_2$. I am interested in calculating the Groebner basis of the submodule in the denominator using Sage and I can do the rest. I am finally interested in finding the vector space basis of the quotient module or its dimension. If that is also possible directly using Sage, it will be great.

 9 retagged FrédéricC 2409 ●3 ●28 ●48

### vector space basis for a quotient module

For my question, let's say I have the following quotient module as an example,

\begin{align} & \frac{\left(\mathbb{Z}_{2}\left[x,y,z\right]\right)^{3}}{\left(\begin{array}{cccccc} 0 & 0 & 0 & 1+x+y+xy & 1+y+z+yz & 1+x+z+xz\newline 1+z & 1+x & 0 & 0 & 0 & 0\newline 0 & 1+x& 1+y & 0 & 0 & 0 \end{array}\right)} \end{align}

where $\mathbb{Z}_{2}\left[x,y,z\right]^{3}$ is a polynomial ring in variables $x,y,z$ over field $\mathbb{Z}_2$. I am interested in calculating the Groebner basis of the submodule in the denominator using Sage and I can do the rest. I am finally interested in finding the vector space basis of the quotient module or its dimension. If that is also possible directly using Sage, it will be great.


text:
My Math Forum Rectangular Box

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 July 31st, 2012, 01:48 AM #1 Newbie   Joined: Jul 2012 Posts: 27 Thanks: 0 Rectangular Box The dimensions of a rectangular box are in the ratio 2:3:4 and the difference between the cost of covering it with sheet of paper at the rate of Rs.4/- and Rs. 4.50 per square meter is Rs 416. The dimensions of the box are: 1)6,9,12 2)8,12,16 3)10,15,20 4)12,18,24 5)none Please show steps...I don't know how to start...
 July 31st, 2012, 02:12 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Rectangular Box Let 2x be the smallest dimension of the box, then 3x and 4x are the other larger dimensions. The surface area S of the box is then: $S=2(2x\cdot3x+2x\cdot4x+3x\cdot4x)=52x^2$ We are told then that: $52x^2(4.50-4.00)=416$ Can you proceed from here?
 July 31st, 2012, 02:23 AM #3 Newbie   Joined: Jul 2012 Posts: 27 Thanks: 0 Re: Rectangular Box Thanks Mark..!! You are a true life saver....
 July 31st, 2012, 02:38 AM #4 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Rectangular Box Glad to help! What was your conclusion?
 July 31st, 2012, 05:20 AM #5 Newbie   Joined: Jul 2012 Posts: 27 Thanks: 0 Re: Rectangular Box 8,12,16.....

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# Mesh Smoothing

2018/01/26

Mesh smoothing, also known as mesh denoising, is an important and widely discussed topic in geometry processing. Basically, a mesh smoothing method takes three steps: loading a mesh from a file; smoothing that mesh; outputting the mesh to a file. Recently, I implemented a few basic algorithms regarding mesh smoothing.

# Selection of Mesh Library

There are a lot of mesh libraries that give us a data structure such that we can use to build a mesh for a 3D object. What I am using is the geometry-processing-js library. It is a library written in JavaScript which constructs a mesh based on half-edge. It also gives plenty of predefined functions regarding the components of a mesh e.g. half-edge, vertex, edge, face, etc. Besides, it also includes a linear algebra library which makes it handy for users to do matrix-vector operations.

# Mesh Smoothing Algorithms

I implemented two algorithms for mesh smoothing, a mean filtering algorithm, and a weighted mean filtering algorithm.

## Mean Filtering Algorithm

A most naïve mean filtering algorithm goes as follows:

Begin

Step 1: Create a hash map $\mathrm{positions}$ mapping each vertex with its position to be updated;

Step 2: For each vertex $\mathbf{v}$ in the mesh, calculate $\mathrm{positions}[\mathbf{v}]$ by the average position of the neighbor vertices in the one-ring neighborhood of $\mathbf{v}$;

Step 3: After the whole iteration, update the positions of vertices in the mesh by the hash map $\mathrm{positions}$.

End

However, if the object has some holes in it, this algorithm could cause the holes to enlarge after times of iteration, which is shown in Figure 1.

Figure 1: Holes enlarge on the object, steps = 5.

Sometimes, we don’t like such distortion, so it is necessary to preserve the boundary of holes on the mesh. We can add a step to the algorithm to constrain the vertices of boundary edges:

Begin

Step 1: Create a hash map $\mathrm{positions}$ mapping each vertex with its position to be updated;

Step 2: For each vertex $\mathbf{v}$ in the mesh, calculate $\mathrm{positions}[\mathbf{v}]$ by the average position of the neighbor vertices in the one-ring neighborhood of $\mathbf{v}$;

Step 3: To preserve the boundary of holes on the mesh, if vertex $\mathbf{v}$ is on the boundary, update $\mathrm{positions}[\mathbf{v}]$ to the original position of vertex $\mathbf{v}$ in the mesh;

Step 4: After the whole iteration, update the positions of vertices in the mesh by the hash map $\mathrm{positions}$.

End

## Weighted Mean Filtering Algorithm

The weighting method simply weights each neighboring vertex by the area of the two faces incident to it. The weighted mean filtering algorithm goes like this:

Begin

Step 1: Create a hash map $\mathrm{positions}$ that maps each vertex to its position to be updated;

Step 2: For each vertex $\mathbf{v}$ in the mesh, traverse its neighborhood vertices. And for each neighbor vertex $\mathbf{v}^\ast$ calculate the weight value $w^\ast$ on each neighborhood vertex by adding the area of the two incident faces together;

Step 3: After the traversal of neighborhood vertices, calculate the total weight $w$ on the vertex $\mathbf{v}$ by accumulating every $w^\ast$, and calculate $\mathrm{positions}[\mathbf{v}]=\frac{\sum_{}w^\ast\cdot\mathbf{v}^\ast}{w}$;

Step 4: To preserve the boundary of holes on the mesh, if vertex $\mathbf{v}$ is on the boundary, update $\mathrm{positions}[\mathbf{v}]$ to the original position of vertex $\mathbf{v}$ in the mesh;

Step 5: After the whole iteration, update the positions of vertices in the mesh by the hash map $\mathrm{positions}$.

End

However, in the implementation, I found this could cause the faces of the mesh overlapping one another after several times of iterations, as the position of vertex could fall outside its one-ring neighborhood. As shown in Figure 2, overlapping occurs after 5 times of iteration.

Figure 2: Overlapping of faces, steps = 5.

In order to prevent such thing from happening, I tried to find those vertices which could fall outside its neighborhood during an iteration. The one-ring neighborhood of one vertex is actually a star-shaped polygon so that we can use the left-turn/right-turn check to decide whether the vertex is inside it or not.

To find out the star-shaped neighborhood of a certain vertex $\mathbf{v}$, we should first project all the neighbors onto the plane which is defined by vertex $\mathbf{v}$ and its normal vector $\mathbf{n}$. We can find the projection $\mathbf{q}=(x^\prime,y^\prime,z^\prime)$ of vertex $\mathbf{p}=(x,y,z)$ on the plane that defined by the normal $\mathbf{n}=(a,b,c)$ and vertex $\mathbf{v}=(x_0,y_0,z_0)$ in the way below.

There are following implicit geometric relationships between $\mathbf{p}$, $\mathbf{q}$, $\mathbf{n}$, and $\mathbf{v}$: $(\mathbf{q}-\mathbf{p})\parallel\mathbf{n}$ and $(\mathbf{q}-\mathbf{v})\perp\mathbf{n}$.

The following equation can be derived from $(\mathbf{q}-\mathbf{p})\parallel\mathbf{n}$:$$$$\frac{x^\prime-x}{a}=\frac{y^\prime-y}{b}=\frac{z^\prime-z}{c}=t.\tag{1}\label{eq:1}$$$$

And from $(\mathbf{q}-\mathbf{v})\perp\mathbf{n}$, we can derive:$$$$a(x^\prime-x_0)+b(y^\prime-y_0)+c(z^\prime-z_0)=0.\tag{2}\label{eq:2}$$$$

Combining $\eqref{eq:1}$ and $\eqref{eq:2}$, we can solve for $t$:$$$$t=\frac{ax_0+by_0+cz_0-(ax+by+cz)}{a^2+b^2+c^2}.\tag{3}\label{eq:3}$$$$

Then we can solve for the projection $\mathbf{q}=(x^\prime,y^\prime,z^\prime)$ by combining $\eqref{eq:1}$ and $\eqref{eq:3}$.

As the data structure of mesh is based on half-edge, and all the faces are defined by half-edges in counterclockwise order. Thus, for each vertex $\mathbf{v}$, we can simply get the boundary edges of a star-shaped neighborhood in counterclockwise order, project them along with the position to be updated $\mathrm{positions}[\mathbf{v}]$ onto the plane that is defined by vertex $\mathbf{v}$ and its normal vector $\mathbf{n}$. Then we can do the left-turn/right-turn check on that plane to see whether the new position for vertex $\mathbf{v}$ $\mathrm{positions}[\mathbf{v}]$ is outside its neighborhood polygon or not.

So the modified algorithm goes as follows:

Begin

Step 1: Create a hash map $\mathrm{positions}$ that maps each vertex to its position to be updated;

Step 2: For each vertex $\mathbf{v}$ in the mesh, traverse its neighborhood vertices. And for each neighbor vertex $\mathbf{v}^\ast$ calculate the weight value $w^\ast$ on each neighborhood vertex by adding the area of the two incident faces together;

Step 3: After the traversal of neighborhood vertices, calculate the total weight $w$ on the vertex $\mathbf{v}$ by accumulating every $w^\ast$, and calculate $\mathrm{positions}[\mathbf{v}]=\frac{\sum_{}w^\ast\cdot\mathbf{v}^\ast}{w}$;

Step 4: Check whether $\mathrm{positions}[\mathbf{v}]$ falls outside its one-ring neighborhood. If so, use the mean filtering algorithm to update the new position;

Step 5: To preserve the boundary of holes on the mesh, if vertex $\mathbf{v}$ is on the boundary, update $\mathrm{positions}[\mathbf{v}]$ to the original position of vertex $\mathbf{v}$ in the mesh;

Step 6: After the whole iteration, update the positions of vertices in the mesh by the hash map $\mathrm{positions}$.

End

# Results and Conclusion

As for the mean filtering algorithm, Figure 3 shows the results after applying it to different objects with different step numbers.

Figure 3: Results of mean filtering algorithm.

As for the weighted mean filtering algorithm, Figure 4 shows the results after applying it to different objects with different step numbers.

Figure 4: Results of weighted mean filtering algorithm.

We can conclude that the results of both algorithms basically look alike, and both of them could cause the volume of the object to shrink if we apply too many times.

I have also uploaded the project to this blog: /projects/mesh-smoothing, we can go there to see how exactly the algorithms work.


text:
# Applied Science BTEC Nationals/Scientific Practical Techniques

## Content

On completion of this unit a learner should:

1. Be able to use analytical techniques
2. Be able to use scientific techniques to separate and assess purity of substances
3. Be able to use instruments/sensors for scientific investigations.

# Colorimetry

Colorimetry is "the science and technology used to quantify and describe physically the human color perception." It is similar to spectrophotometry, but is distinguished by its interest in reducing spectra to the physical correlates of color perception, most often the CIE 1931 XYZ color space tristimulus values and related quantities.

# Titration

In medicine, titration is the process of gradually adjusting the dose of a medication until the desired effect is achieved.

Titration setup: the titrant drops from the burette into the analyte solution in the w:flask. An indicator present then changes color permanently at the w:endpoint.

Titration is a common laboratory method of quantitative/chemical analysis which can be used to determine the w:concentration of a known w:reactant. Because volume measurements play a key role in titration, it is also known as volumetric analysis.

A w:reagent, called the titrant, of known concentration (a w:standard solution) and w:volume is used to react with a solution of the w:analyte, whose concentration is not known in advance. Using a calibrated w:burette to add the titrant, it is possible to determine the exact volume that has been consumed when the endpoint is reached. The endpoint is the point at which the titration is complete, often determined by an indicator (see below). In the classic strong acid-strong base titration the endpoint of a titration is when the pH of the reactant is just about equal to 7, and often when the solution permanently changes colour due to an indicator. There are however many different types of titrations (see below).

Many methods can be used to indicate the endpoint of a reaction; titrations often use visual indicators (the reactant mixture changes colour). In simple w:acid-base titrations a pH indicator may be used, such as w:phenolphthalein, which becomes pink when a certain pH (about 8.2) is reached or exceeded. Another example is w:methyl orange, which is red in acids and yellow in alkali solutions.

Not every titration requires an indicator. In some cases, either the reactants or the products are strongly coloured and can serve as the "indicator". For example, an oxidation-reduction titration using w:potassium permanganate (pink/purple) as the titrant does not require an indicator. When the titrant is reduced, it turns colourless. After the equivalence point, there is excess titrant present. The equivalence point is identified from the first faint pink colour that persists in the solution being titrated.

Due to the logarithmic nature of the pH curve, the transitions are generally extremely sharp, and thus a single drop of titrant just before the endpoint can change the pH significantly — leading to an immediate colour change. That said, there is a slight difference between the change in indicator colour and the actual equivalence point of the titration. This error is referred to as an indicator error, and it is indeterminate.

## Preparing a sample for titration

In a titration, both titrant and analyte are required to be aqueous, or in a solution form. If the sample is not a liquid or solution, the samples must be dissolved. If the analyte is very concentrated in the sample, it might be useful to dilute the sample.

Although the vast majority of titrations are carried out in aqueous solution, other solvents such as glacial ethanoic acid or ethanol (in petrochemistry) are used for special purposes.

A measured mass of the sample can be placed in a flask and then be dissolved or diluted. The mathematical result of the titration can be calculated directly. Sometimes the sample is dissolved or diluted beforehand and a measured volume of the solution is used for titration. In this case the dissolving or diluting must be done accurately because the mathematical result of the titration must be multiplied with this factor.

Some non-acid-base titrations require buffering to maintain a certain pH for the reaction. Therefore, buffer solutions are added to the reactant solution in the flask.

Some titrations require "masking" of a certain ion. This can be necessary when two reactants in the sample would react with the titrant and only one of them must be analysed, or when the reaction would be disturbed or inhibited by this ion. In this case another solution is added to the sample which "masks" the unwanted ion (for instance by a weak binding with it or even forming a solid insoluble substance with it).

Some reactions may require heating the solution with the sample and titration while the solution is still hot (to increase the reaction rate).

## Procedure

A typical titration begins with a conical flask containing a precisely known volume of the reactant and a small amount of indicator, placed underneath a w:burette containing the reagent. By controlling the amount of reagent that is added to the reactant, it is possible to detect the point at which the indicator changes colour. As long as the indicator has been chosen correctly, this should also be the point where the reactant and reagent neutralise each other, and by reading the scale on the burette the volume of reagent can be measured.

As the concentration of the reagent is known, the number of moles of reagent can be calculated (since ${\displaystyle concentration=moles/volume}$). Then, from the chemical equation involving the two substances, the number of moles present in the reactant can be found. Finally, by dividing the number of moles of reactant by its volume, the concentration is calculated.

## Types of titrations

Titrations can be classified by the type of reaction. Different types of titration reaction include:

• w:Acid-base titration is based on the neutralisation reaction between the analyte and an acidic or basic titrant. These most commonly use a pH indicator, a pH meter, or a conductance meter to determine the endpoint.
• A w:Redox titration is based on an oxidation-reduction reaction between the analyte and titrant. These most commonly use a potentiometer or a redox indicator to determine the endpoint. Frequently either the reactants or the titrant have a colour intense enough that an additional indicator is not needed.
• A w:Complexometric titration is based on the formation of a complex between the analyte and the titrant. The w:chelating agent w:EDTA is very commonly used to titrate metal ions in solution. These titrations generally require specialised indicators that form weaker complexes with the analyte. A common example is w:Eriochrome Black T for the titration of w:calcium and w:magnesium ions.
• A form of titration can also be used to determine the concentration of a w:virus or w:bacterium. The original sample is diluted (in some fixed ratio, such as 1:1, 1:2, 1:4, 1:8, etc.) until the last dilution does not give a positive test for the presence of the virus. This value, the w:titre, may be based on w:TCID50, w:EID50, w:ELD50, LD50 or pfu. This procedure is more commonly known as an w:assay.

## Measuring the endpoint of a titration

Main page: Endpoint (chemistry)

Different methods to determine the endpoint include:

• w:pH indicator: This is a substance that changes colour in response to a chemical change. An acid-base indicator (e.g., w:phenolphthalein) changes colour depending on the w:pH. Redox indicators are also frequently used. A drop of indicator solution is added to the titration at the start; when the colour changes the endpoint has been reached.
• A w:potentiometer can also be used. This is an instrument which measures the w:electrode potential of the solution. These are used for titrations based on a redox reaction; the potential of the working electrode will suddenly change as the endpoint is reached.
• w:pH meter: This is a potentiometer which uses an electrode whose potential depends on the amount of H+ ion present in the solution. (This is an example of an w:ion selective electrode. This allows the pH of the solution to be measured throughout the titration. At the end point there will be a sudden change in the measured pH. It can be more accurate than the indicator method, and is very easily automated.
• Conductance: The conductivity of a solution depends on the ions that are present in it. During many titrations, the conductivity changes significantly. (For instance, during an acid-base titration, the H+ and OH- ions react to form neutral H2O. This changes the conductivity of the solution.) The total conductance of the solution depends also on the other ions present in the solution (such as counter ions). Not all ions contribute equally to the conductivity; this also depends on the mobility of each ion and on the total concentration of ions (w:ionic strength). Thus, predicting the change in conductivity is harder than measuring it.
• Colour change: In some reactions, the solution changes colour without any added indicator. This is often seen in redox titrations, for instance, when the different oxidation states of the product and reactant produce different colours. Such titrations are known as 'self-indicating'.
• Precipitation: If the reaction forms a solid, then a w:precipitate will form during the titration. A classic example is the reaction between Ag+ and Cl- to form the very insoluble salt AgCl. Surprisingly, this usually makes it difficult to determine the endpoint precisely. As a result, precipitation titrations often have to be done as "back" titrations (see below).
• An isothermal titration calorimeter uses the heat produced or consumed by the reaction to determine the endpoint. This is important in biochemical titrations, such as the determination of how substrates bind to w:enzymes.
• Thermometric titrimetry is an extraordinarily versatile technique. This is differentiated from calorimetric titrimetry by the fact that the heat of the reaction (as indicated by temperature rise or fall) is not used to determine the amount of analyte in the sample solution. Instead, the endpoint is determined by the rate of temperature change.
• w:Spectroscopy can be used to measure the absorption of light by the solution during the titration, if the w:spectrum of the reactant, titrant or product is known. The relative amounts of the product and reactant can be used to determine the endpoint.
• w:Amperometry can be used as a detection technique (w:amperometric titration). The current due to the oxidation or reduction of either the reactants or products at a working electrode will depend on the concentration of that species in solution. The endpoint can then be detected as a change in the current. This method is most useful when the excess titrant can be reduced, as in the titration of halides with Ag+. (This is handy also in that it ignores precipitates.)

### Other terms

The term w:back titration is used when a titration is done "backwards": instead of titrating the original analyte, one adds a known excess of a standard reagent to the solution, then titrates the excess. A back titration is useful if the end point of the reverse titration is easier to identify than the end point of the normal titration. They are also useful if the reaction between the analyte and the titrant is very slow.

## Particular uses

• As applied to w:biodiesel, titration is the act of determining the w:acidity of a sample of WVO by the dropwise addition of a known base to the sample while testing with w:pH paper for the desired neutral pH=7 reading. By knowing how much base neutralizes an amount of WVO, we discern how much base to add to the entire batch.
• Titrations in the w:petrochemical or food industry to define oils, fats or biodiesel and similar substances. An example procedure for all three can be found here: [1].

# Sampling

## The importance of representative sampling

“The fundamental principle behind any sampling activity is that a small amount of collected material should be representative of all the material being monitored. The number and location of samples that are needed to make up a representative sample depends on how homogeneous the material is. If it is very homogeneous, only a few samples may be required. If the material is heterogeneous, many more samples will be required.”[1]

### Monitoring can be classified into types

1. Periodic measurements – measurements are made at periodic intervals; for example, once every three months. The sample is often withdrawn from the sampling site (extractive sampling). An instrumental or automated technique may be used, where the sampling and analysis of the substance is fed to an on-line analyser. Alternatively, a technique may be used where a sample is extracted on site and analysed later in a laboratory. Samples may be obtained over several hours, or may be so-called “spot” or “grab” samples collected over a period of seconds to several minutes.[1]
2. Intermittent measurements are made when convenient/possible. The timing between measurements may be semi-periodic (e.g. every day, sometime during working hours).
3. Continuous emissions monitoring systems (CEMs) are automated measurements carried out continuously, with few (if any) gaps in the data produced. Measurement may be carried out in situ, or extractive sampling may be used with an instrument permanently located at or near the stack. CEMs are also referred to as Automated Monitoring Systems (AMS), particularly in Europe.[1]

#### Should ambient air sampling be continuous or intermittent?

Consider:[2]

• the averaging period of the relevant quality criteria with which the data will be compared
• whether the impact is acute or chronic
• the detail required, e.g. short peaks averaged over three minutes, one-hour averages, daily averages, etc.

Short sampling programmes are unlikely to give data representative of long-term conditions. Meteorological conditions and source variations can have significant effects on pollutant concentrations. Where short-term peaks are of interest, these may be unusual events occurring for only a few days each year. Hence short-term monitoring campaigns are of very limited value for characterising air-pollution episodes.[2]

#### Comparison of continuous and periodic monitoring for water analysis

 Characteristic Continuous water monitoring systems (CWMs) Periodic monitoring Sampling period Monitoring covers all or most of the period that substances are discharged Snapshots of the long-term discharge profile Speed of results generation Almost always real-time output of results Real-time results if portable instrumental analysers used; delayed results if laboratory end-method used Stability Sensors may be prone to fouling or other malfunction Sample integrity needs to be maintained before analysis Availability Only a limited number of methods possible Comprehensive range of methods available Applicability May not be able to meet performance requirements at present Methods that will meet the performance of most regulatory requirements are available Reporting of results Results continuously averaged over (typically) one hour or 24 hours Results reported as daily average or instantaneous Capital cost Tends to be higher than equivalent periodic monitoring method Tends to be lower than equivalent CWMs

### Definitions of important terms

Sampling plane – the plane at 90° to the centreline of the stack, duct or channel at the sampling location.

Sampling point – the specific position on the sample plane from where the sample is extracted.

Isokinetic sampling – when the flow enters the sampling nozzle at the same velocity and direction as usual flow at the sampling point.

### Representative sampling of particulates, gases and liquids

Although a flowing gas or liquid might be thought of as being more homogeneous than, for example, a stockpile of coal; such flows can become heterogeneous. This may be due to differences in chemical composition, or differences in temperature and velocity, which may lead to stratification and swirling. Where the flow is also carrying particulates or aerosols along the duct or channel, there is likely to be even less uniformity. Here, special measures must be taken to ensure samples are representative.

If the flowing sample may be heterogeneous, samples must be obtained from multiple sample points across the sampling plane to give an overall average value.

If the emission rate is to be calculated, the flowrate will need to be measured; this will require velocity measurements to be made at several points across the sampling plane.

For extractive methods involving gases or liquids carrying particulates or aerosols, the sample must be collected isokinetically.

### Ambient air sampling

#### Where to sample?

Spatial considerations encompass both the location of monitoring positions relative to study area or emission source, and individual sampling site criteria, e.g. position relative to local emission sources and any interfering effects.

#### Data handling and data analysis.

Is the speed of results generation important? For example, results may be required in real time for public health warnings, whereas several weeks turnaround may be adequate for supplying routine results for authorisation compliance monitoring.

#### How to sample?

Both the type of sampling and analytical end method need to be considered. Sampling may be unidirectional or omnidirectional; in-situ, mobile or remote sensing. Method selection involves an appraisal of cost versus performance, the latter including limits of detection, sensitivity, speed of instrument response, susceptibility to interfering species and the overall uncertainty of the measurement.

#### Supplementary data collection.

Other information may be relevant to the study, for example meteorological conditions, process data and traffic flows. Meteorological conditions are obviously important in assessing the impact of a single source on its surroundings since they dictate the transport and dispersion of pollutants in ambient air. Many chemical transformations between reactive species in the atmosphere are also influenced.

### Soil sampling

If a property of the sample changes over time, then the analysis shall be carried out without as soon as possible.

If a sample has been stabilised, or preserved then this fact shall be recorded when the results are reported and details of the stabilising procedure or preserving agent shall be recorded.

When a sample has been dried and is subsequently analysed, sufficient information shall be provided to establish the stability of the parameter analysed. Such information shall provide justification for analysing the dried sample, rather than analysing the sample on a “wet-weight” or “as submitted” basis.

# Resources

Edexcel recommend the following resources except * which have been added to their list.


text:
less

I'm struggling to figure out a way to do this…I'm using less to view a large (~1GB) file. I want to jump to line "$n" in the file – preferably without having to wait for lines 1-($n-1) to scroll by in my terminal.

I would do this in vim using something like this:

localhost:~# vim myfile +\$n

Is there an equivalent command line option? If not, is there a way to do this once the file is open in less?

If the file is open you can type:

• 100g to go to the 100th line.

• 50p to go to 50% into the file.

• 100P to go to the line containing 100th byte.

You can use these from terminal by adding + in front of them:

less +100g bigfile.txt


text:
# Feed Varlist into Calculation

#### hlsmith

##### Not a robit
I have a dataset which I want to add a new variable (column) based on a calculation of existing variables in the set. But I want to repeat the process for eight variables and I AM hoping to do it in one step. So I would feed in a varlist into the line of code and generate the 8 new terms. See following where I run it twice, I would collapse this into one statement for the eight vars.

Code:
#FOR BEEF#
Food_3$Beef = (((((((Food_3$IM_Weekly_serving_2
* Food_3$IM_Attendance_2) + Food_3$Peds_Monthly_serving_2
* Food_3$Peds_Attendance_2)) *Food_3$beef)
/Food_3$kg_oz_conversion_2) *Food_3$Serving_conversion_2)
/Food_3$Passenger_Vehicle_2) #FOR LAMB# Food_3$Lamb = (((((((Food_3$IM_Weekly_serving_2 * Food_3$IM_Attendance_2)
+ Food_3$Peds_Monthly_serving_2 * Food_3$Peds_Attendance_2))
*Food_3$lamb) /Food_3$kg_oz_conversion_2)
*Food_3$Serving_conversion_2) /Food_3$Passenger_Vehicle_2)
End result would be the addition of these two variables (Beef and Lamb) into the dataset Food_3.

Last edited:

#### Dason

Code:
myfun <- function(x){
(((((((Food_3$IM_Weekly_serving_2 * Food_3$IM_Attendance_2)
+ Food_3$Peds_Monthly_serving_2 * Food_3$Peds_Attendance_2))
*x)
/Food_3$kg_oz_conversion_2) *Food_3$Serving_conversion_2)
/Food_3$Passenger_Vehicle_2) } Food_3$Beef <- myfun(Food_3$beef) Food_3$Lamb <- myfun(Food_3\$lamb)
Improvements could be made but that seems to do what you want?

I did that on my phone so apologies for lack of decent formatting

#### hlsmith

##### Not a robit
Thanks.

I'll check it out in morning. I was thinking there was an *apply approach or way to feed in a list. In SAS i would feed a varlist. I usually get intimidated writing functions since I am inexperienced and never have enough time.

#tested and the code snippet works.

Last edited:


text:
Covariates

Covariates are implemented using the new_covariate() function, wrapped in a named list. E.g. the following is the most basic specification:

dat <- sim_ode(
ode = model,
parameters = parameters,
regimen = regimen,
covariates = list("WT" = new_covariate(value = 70), "SCR" = new_covariate(value = 120))
)

The names in the covariate list-object should correspond exactly with the names of the covariates in the model.

Time-varying covariates

Time-varing covariates, such as creatinine values can be implemented easily as well. They just require the additional times argument:

dat <- sim_ode(
ode = model,
parameters = parameters,
regimen = regimen,
covariates = list("WT" = new_covariate(value = 70),
"CR" = new_covariate(
value = c(0.8, 1, 1.2),
times = c(0, 48, 72))
)
)

By default, PKPDsim assumes that you want to interpolate between measurements of the time-varying covariates. If you prefer to implement the covariate using last-observation-carried-forward (in other words a step function), specify the method = "LOCF" argument to the new_covariate() function.

Covariates for multiple patients

A table of covariates can be supplied to sim_ode() with covariate values per individual. It can handle both static and time-varying covariates. A covariate table could look like this:

id  WT   SCR  t
1   40   50   0
1   45  150   5
2   50   90   0
3   60  110   0

The id and t (time) columns can be omitted when only static covariates are to be used. Make sure that the headers used for the covariates match exactly with the covariate names specified in the model definition.

With the above data.frame called cov_table, the call to sim_ode() would then become:

sim_ode(ode = model, parameters = parameters, regimen = regimen,
covariates_table = cov_table)

A full example for a model with (simulated) covariates for a patient population would be:

library(PKPDsim)
parameters <- list(CL = 1,
V  = 10,
KA = 0.5)

n_ind <- 50
cov_table <- data.frame('id' = 1:n_ind,
'WT' = rnorm(n_ind, mean = 70, sd = 5))

model <- new_ode_model(
code = '
CLi = CL * pow((WT/70), 0.75)
Vi  = V * (WT/70)
dAdt[2] =  KA*A[1] -(CLi/Vi)*A[2]
',
declare_variables = c('CLi', 'Vi'),
covariates = c('WT'),
dose = list(cmt = 1),
obs  = list(cmt = 2, scale = 'V * (WT/70)')
)

regimen <- new_regimen(amt  = 30,
n    = 4,
type = 'bolus')

dat <- sim(ode        = 'model',
par        = parameters,
t_obs      = c(0.5, 2, 4, 8, 12, 16, 24),
n_ind      = n_ind,
regimen    = regimen,
covariates_table = cov_table,
output_include = list(covariates=TRUE))

Note: at current, PKPDsim does not handle missing covariate values. If you do have missing covariate data, probably the best approach would be to impute the values manually before simulation, e.g. based on the mean observed / known value, or the correlation between the covariates.


text:
D(f+g)=D(f)+D(g) and D(kf)=kD(f) for any $f,g \in P_n, k \in R$.
D(f)=0 if and only if $f \in P_2$.
D(Pn)= $P_{n-2}$ if n is greater than 2.


text:
coupon bonds valuation formula

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Appendix 5A The Term Structure of Interest Rates, Spot ...

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Bond valuation and bond yields | P4 Advanced Financial ...

View Notes - BOND VALUATION FORMULA from FINA 3313 at University of Texas, Arlington. Where If P > Face Value (Premium Bond) Yield to Maturity < CY < Coupon Rate (over maturity) If P <

The valuation of a bond can be broken down into two basic tasks: the valuation of the stream of coupon payments, and the valuation of the repayment of the face value of the bond. Valuing the stream of coupon payments is no different than valuing any other basic annuity. where F is the face value, r ...

Bond Valuation Price Sensitity and Hedging

Bond Discounting can be calculated from the cash flows attached to the particular bond. Bonds are the most important fixed income securities. A bond is a legal obligation to repay a loan’s principal and interest (Coupon). It is debt...

Bond valuation - Wikipedia

If r is the interest rate prevailing in the market, c is the coupon rate on the bond, t is the time periods occurring over the term of the bond and F is the face value of the bond, the present value of interest payments is calculated using the following formula:

View Notes - BOND VALUATION FORMULA from FINA 3313 at University of Texas, Arlington. Where If P > Face Value (Premium Bond) Yield to Maturity < CY < Coupon Rate (over maturity) If P <

Bond Yield to Maturity Calculator – DQYDJ

Bond Price | Formula | Calculation | Example

Bond Valuation - Jackson

4.2.2 Basic Bond Valuation

A zero coupon bond is a bond bought at a price lower than its face value, with the face value repaid at the time of maturity. It does not make periodic interest payments. When the bond reaches maturity, its investor receives its face value.

This free online Bond Value Calculator will calculate the expected trading price of a bond given the par value, coupon rate, market rate, interest payments per year, and years-to-maturity. Plus, the calculated results will show the step-by-step solution to the bond valuation formula, as well as a chart showing the present values of the par ...

Convexity of a Bond | Formula | Duration | Calculation

Bond Yield to Maturity (YTM) Formula - Moneychimp

Example of Yield to Maturity Formula The price of a bond is $920 with a face value of$1000 which is the face value of many bonds. Assume that the annual coupons are $100, which is a 10% coupon rate, and that there are 10 years remaining until maturity. 3. Valuation of bonds and equity - University of Scranton 3. VALUATION OF BONDS AND STOCK When the bonds have a definite maturity period, its valuation is determined by considering the annual interest payments plus its maturity value. The following formula can be used to determine the value of a bond: Zero Coupon Bond Calculator - Miniwebtool Description: The purpose of this calculator is to provide calculations and details for bond valuation problems. It is assumed that all bonds pay interest semi-annually. Future versions of this calculator will allow for different interest frequency. Bond valuation and bond yields | P4 Advanced Financial ... For Detailed Notes, please visit www Bond valuation formula coupon rate. ascentfinancials. com Bond Terminology Coupon rate: is the annual coupon amount Bond valuation formula coupon rate Zero Coupon Bond Calculator - Miniwebtool Coupon (bond) - Wikipedia valuation of corporate bonds - NYU Coupon (bond) - Wikipedia Pricing Bonds with Different Cash Flows and … A coupon bond is a form of debt obligation with coupons attached that pay annual or semi-annual interest payments and par value at maturity. A coupon bond comes with a coupon rate, which refers to the yield the coupon bond pays on its issuance date. Bonds with higher coupon rates provide higher yields. Thus, coupon All You Need to Know about Bond Valuation Formula ... Bond Valuation: Formula, Steps & Examples ... mainly when dealing with bonds. The coupon rate is the annualized coupon divided by par value. ... Coupon Rate: Definition, Formula & Calculation ... In deferred coupon bonds, initial coupon payments are deferred for a certain period while in accelerated coupon bonds, the coupon rate decreases over the life of the bond. Formula $$Coupon\ Payment \\= Face\ Value\ of\ Bond × \frac {r}{n}$$ Coupon Bond Valuation Formula - couponknow.com Bond Valuation Bonds usually pay a standard coupon amount, C , at regular intervals and this represents the interest on the bond. At the maturity of the bond, the final interest payment is made plus the principal amount (or par amount) is repaid. Bond valuation is the determination of the fair Coupon bond valuation formula. . . (This formula assumes that a coupon payment has just . . Coupon bond valuation formula. the bond's coupon dates and coupon amounts are known . . . Basic Bond Valuation - American University Problems andSolutions - wiley.com This makes the yield to maturity easier to calculate for zero coupon bonds, because there are no coupon payments to reinvest, making it equivalent to the normal rate of return on the bond. The Formula Basic convertible bonds calculations Bond Price / Value Calculator - Online Financial Calculator A zero coupon bond is a bond bought at a price lower than its face value, with the face value repaid at the time of maturity. It does not make periodic interest payments. When the bond reaches maturity, its investor receives its face value. BAII Plus Bond Valuation | TVMCalcs.com Chapter 9 Bonds and Their Valuation There is a lot you need to know about bond valuation formula, equation, and models. Meet our finance experts who are ready to help with your assignments today! financehomeworkhelp.org. Our Services ... There are bond valuation models of zero coupon bonds, annual, and semi-annual bonds. ... Stocks + Bonds; How to Calculate Coupon Rates; How to Calculate Coupon Rates. November 21, 2009. By: Eric Bank. Share; Share on Facebook; Coupon is bond lingo for an interest payment. When you buy a bond, you begin receiving periodic coupon payments for the interest you earned since the last coupon payment. ... The formula … This makes the yield to maturity easier to calculate for zero coupon bonds, because there are no coupon payments to reinvest, making it equivalent to the normal rate of return on the bond. The Formula Duration and Convexity - Faculty & Research Coupon Bond Valuation Formula - couponknow.com Description: The purpose of this calculator is to provide calculations and details for bond valuation problems. It is assumed that all bonds pay interest semi-annually. Future versions of this calculator will allow for different interest frequency. Coupon Bond - Guide, Examples, How Coupon Bonds … Bond Valuation Bonds are long-term debt securities that are issued by corporations and government entities. Purchasers of bonds receive periodic interest payments, called coupon payments, until maturity at which time they receive the face value of the bond and the last coupon payment. Convexity of a Bond | Formula | Duration | Calculation Asset Valuation Debt Investments: Analysis and Valuation BOND VALUATION - University of Texas at San Antonio Bond Value Calculator: What It Should Be Trading At ... Bonds have a face value, a coupon rate, a maturity date, and a discount rate. ... Ch 7. Bonds & Bond Valuation ... Bond Valuation: Formula, Steps & … A zero coupon bond is a bond bought at a price lower than its face value, with the face value repaid at the time of maturity. It does not make periodic interest payments. When the bond reaches maturity, its investor receives its face value. Bond Valuation - Jackson All You Need to Know about Bond Valuation Formula ... Power Point Presentation for Band Valuation and the Techincal knowledge abt valuation Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to … The Pricing of Bonds between Coupon Payments: From … A coupon bond is a form of debt obligation with coupons attached that pay annual or semi-annual interest payments and par value at maturity. A coupon bond comes with a coupon rate, which refers to the yield the coupon bond pays on its issuance date. Bonds with higher coupon rates provide higher yields. Thus, coupon 7/19/2018 · How to Calculate a Coupon Payment Two Parts: Gathering the Bond Information Calculating the Coupon Payment Community Q&A Bonds are a kind of debt instrument that offer investors a method of seeing a secure, predictable return. [1]Views: 131KBasic Bond Valuation - American Universitywww1.american.edu/academic.depts/ksb/finance_realestate/rhauswald/... · PDF fileBasic Bond Valuation Professor Robert B.H. Hauswald Kogod School of Business, AU ... Information needed to value level-coupon bonds: – Coupon payment dates and time to maturity (T) – Coupon payment (C) per period and Face value (F) ... – formula: ( )( ) 0 1 The above bond valuation formula assumes that the bond is a ‘fixed bond’e., has fixed cash flows or coupon payments. When people talk about bonds, they generally talk about fixed bonds unless mentioned otherwise. Bond Valuation: Formula, Steps & Examples ... mainly when dealing with bonds. The coupon rate is the annualized coupon divided by par value. ... Coupon Rate: Definition, Formula & Calculation ... Bond Discounting I Types I Examples I Formula I Bonds ... What is the formula for the forward price of a bond (assuming there are coupons in the interim period, and that the deal is collateralised) Please also prove it with an arbitrage cashflow scenario Coupon Bond Valuation: Basics - YouTube Bond valuation and bond yields | P4 Advanced Financial ... Bond Formulas - thismatter.com Duration and Convexity - Faculty & Research Coupon Bond Valuation: Basics - YouTube BOND VALUATION FORMULA - Where If P> Face … Join Curt Frye for an in-depth discussion in this video Calculating the value of zero coupon bonds, part of Excel 2007: Financial Analysis Getting back to our initial discussion of valuation of bonds, pre-requisites required of valuation are estimation of future expected cash flows and required rate of return for discounting these cash flows. ... Hence, the formula is, Following example provides an overview of the entire process of bond valuation. All the coupon payments at ... Bond valuation - SlideShare Zero Coupon Bond Calculator - Miniwebtool Bond Valuation final final.doc | Bond Duration | Bonds ... Zero Coupon Bond Calculator - Miniwebtool Types of Bonds - University of Waterloo Describe how the annual bond valuation formula is changed to evaluate semi-annual coupon bonds. Yield to call c. 7. A firm sells bonds with a par value of 1000 taka. VALUING FLOATING RATE BONDS (FRBS) - FIMMDA How to Calculate Bond Value: 6 Steps (with Pictures) - wikiHow Bond Discounting I Types I Examples I Formula I Bonds ... Bond Valuation - Investopedia VALUATION (BONDS AND STOCK) - College of Business Bond valuation and bond yields | P4 Advanced Financial ... A zero coupon bond is a bond bought at a price lower than its face value, with the face value repaid at the time of maturity. It does not make periodic interest payments. When the bond reaches maturity, its investor receives its face value. Valuation of Bonds and Stock - University of Manitoba Floating rate bond valuation - Breaking Down Finance Bond Discounting can be calculated from the cash flows attached to the particular bond. Bonds are the most important fixed income securities. A bond is a legal obligation to repay a loan’s principal and interest (Coupon). It is debt... Bond valuation (Zero coupon bonds) |Calculator - … Yield to Maturity - Approximate Formula and Calculator Convexity of a Bond | Formula | Duration | Calculation Getting back to our initial discussion of valuation of bonds, pre-requisites required of valuation are estimation of future expected cash flows and required rate of return for discounting these cash flows. ... Hence, the formula is, Following example provides an overview of the entire process of bond valuation. All the coupon payments at ... View Notes - BOND VALUATION FORMULA from FINA 3313 at University of Texas, Arlington. Where If P > Face Value (Premium Bond) Yield to Maturity < CY < Coupon Rate (over maturity) If P < Bond Valuation | Formula | Calculator | Example Bond Price The price or value of a bond is determined by discounting the bond's expected cash flows to the present using the appropriate discount rate. This relationship is expressed for a semiannual coupon bond by the following formula: How do I calculate yield to maturity of a zero-coupon bond ... Bond Formulas - thismatter.com The formula is complicated, but what it boils down to is: Duration = Present value of a bond's cash flows, weighted by length of time to receipt and divided by the bond's current market value. For example, let's calculate the duration of a three-year,$1,000 Company XYZ bond with a semiannual 10% coupon.

Bonds and the Term Structure of Interest Rates: Pricing ...

Coupon Bonds Formula - freecouponcodes.net

pricing formulae - Formula for forward price of bond ...

Duration and Convexity - Faculty & Research

Coupon Bond Valuation Formula - couponknow.com

Valuing Bonds. Present Value of Payments ... The formula for calculating a bond’s price uses the basic present value (PV) formula for a given discount rate. Bond Price: ... bond price is the sum of the present value of face value paid back at maturity and the present value of an annuity of coupon payments. For bonds of different payment ...

How to Calculate a Coupon Payment: 7 Steps (with …

Calculating the value of zero coupon bonds - lynda.com

Principles of Finance/Section 1/Chapter 4/Bonds/Valuation ...

Appendix 5A The Term Structure of Interest Rates, Spot ...

Types of Bonds - University of Waterloo

The valuation of a bond can be broken down into two basic tasks: the valuation of the stream of coupon payments, and the valuation of the repayment of the face value of the bond. Valuing the stream of coupon payments is no different than valuing any other basic annuity. where F is the face value, r ...

The bond in the previous example can be priced using this alternate bond valuation formula as follows: = 148.68 + 888.49 = \$1,037.17 c) Pricing Zero Coupon Bonds

Bond Discounting can be calculated from the cash flows attached to the particular bond. Bonds are the most important fixed income securities. A bond is a legal obligation to repay a loan’s principal and interest (Coupon). It is debt...

The valuation of a bond can be broken down into two basic tasks: the valuation of the stream of coupon payments, and the valuation of the repayment of the face value of the bond. Valuing the stream of coupon payments is no different than valuing any other basic annuity. where F is the face value, r ...

The valuation of a bond can be broken down into two basic tasks: the valuation of the stream of coupon payments, and the valuation of the repayment of the face value of the bond. Valuing the stream of coupon payments is no different than valuing any other basic annuity. where F is the face value, r ...

Bond Valuation - Investopedia

View Notes - BOND VALUATION FORMULA from FINA 3313 at University of Texas, Arlington. Where If P > Face Value (Premium Bond) Yield to Maturity < CY < Coupon Rate (over maturity) If P <

The Pricing of Bonds between Coupon Payments: From …

Chapter

Home » Basics Principles of Bond Valuation. Basics Principles of Bond Valuation. ... The company pays coupon income against Bonds or to the bond holders on the basis of its cash flows generated from the real assets. The bond’s value is calculated with the help of formula of net present value or present value. ... of bond, the IRR formula …

The above bond valuation formula assumes that the bond is a ‘fixed bond’e., has fixed cash flows or coupon payments. When people talk about bonds, they generally talk about fixed bonds unless mentioned otherwise.

Appendix 5A The Term Structure of Interest Rates, Spot ...

Bond Price / Value Calculator - Online Financial Calculator

Bonds and the Term Structure of Interest Rates: Pricing ...

Principles of Finance/Section 1/Chapter 4/Bonds/Valuation ...

BOND VALUATION FORMULA - Where If P> Face …

What is the discount factor formula for a coupon …

Pricing Bonds with Different Cash Flows and …

The above bond valuation formula assumes that the bond is a ‘fixed bond’e., has fixed cash flows or coupon payments. When people talk about bonds, they generally talk about fixed bonds unless mentioned otherwise.

WWWFinance - Bond Valuation: Campbell R. Harvey

Bond and Note Valuation and Related Interest Rate …

Bond Valuation II – Zero-Coupon Bonds. Date: May 9, 2015 Author ... If you do it right then you can enhance the formula for the present value of the vanilla bond with coupons because now you can discount each coupon at a different unique interest rate corresponding to the implied rate by the ZCB maturing on the date of the coupon …

Bond valuation under an arbitrage-free pricing approach considers each separate cash flow (coupons and principal) as a zero-coupon bond. The yield to maturity on a zero-coupon bond of similar maturity and equal credit rating is used as the discount rate.

Bond Valuation: Formula, Steps & Examples ... mainly when dealing with bonds. The coupon rate is the annualized coupon divided by par value. ... Coupon Rate: Definition, Formula & Calculation ...

Bond valuation (Zero coupon bonds) |Calculator - …

Appendix 5A The Term Structure of Interest Rates, Spot ...

Coupon tells you what the bond paid when it was issued, but the yield to maturity tells you how much it will pay in the future, and that's important. The Balance The Difference Between Coupon and Yield to Maturity

Bond valuation is the determination of the fair Coupon bond valuation formula. . . (This formula assumes that a coupon payment has just . . Coupon bond valuation formula. the bond's coupon dates and coupon amounts are known . . .

Bond Yield to Maturity Calculator – DQYDJ

pricing formulae - Formula for forward price of bond ...

Bond valuation (Zero coupon bonds) |Calculator - …

Bond Valuation | Formula | Calculator | Example

Bond Valuation Price Sensitity and Hedging

Bond Valuation: Formula, Steps & Examples - Study.com

Bond Price | Formula | Calculation | Example

How do I calculate yield to maturity of a zero-coupon bond ...

How to Calculate Bond Value: 6 Steps (with Pictures) - wikiHow

Stocks + Bonds; How to Calculate Coupon Rates; How to Calculate Coupon Rates. November 21, 2009. By: Eric Bank. Share; Share on Facebook; Coupon is bond lingo for an interest payment. When you buy a bond, you begin receiving periodic coupon payments for the interest you earned since the last coupon payment. ... The formula …

Asset Valuation Debt Investments: Analysis and Valuation

coupon bonds valuation formula


text:
Float from outstanding shares.

Hi there... I see no "Float shares" field (outstanding_shares-restricted_shares-tresury) from the fundamental Morningstar data. Is there a way to calculate on the fly from available data series...? IMO this is one of the most valuable fundamental data to have for an algo-trading (Along with Insiders transactions) as they are the available shares for public trading that "move the price" day to day basis (Volatility).

Thanks and good work Guys..! ;)

4 responses

Hey, could you clarify what you mean with "outstanding_shares-restricted_shares-tresury" ?

Hi John, I mean what float is by definition as described by Investopedia.
Actually, on Morningstar's "Quote" frontpage, this data for the majority of securities can be seen nearly at the bottom of page, under the "Short Interest [Security]" block of data.

Might available_for_sale_securities be what you want?

You may also want to look at ordinary_shares_number to get the number of issued shares, or shares_outstanding, etc. The morningstar data includes many share-metrics, which you can compose appropriately to get the result you need.

Thanks John... I think it's more complicated than that. From I was researching, companies only report to SEC (as fundamental) their stock float annually on their 10-K front page report. Float as reported at morningstar's page looks like an "in-house" calculation from fresh insider buy and sell's fillings (4-K's) and then added-sustracted from the officially reported Annual Filling. Maybe this "in-house" data are not part of the API service used on Quantopian.
Basically what I want to do is to start deploying (still learning python) a very simple algorithm proposed by Pascal Willain as an undisclosed method for his trading with volume that call's "Active Boundaries". Open Code for TradeStation can be publicly viewed (and used) in their own page


text:
Solve each equation. 5=frac{p}{4}

Solve each equation. $5=\frac{p}{4}$
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Roosevelt Houghton
To solve an equation for a variable, you need to use inverse operations to isolate the variable.
For the equation $5=\frac{p}{4},$ p is being divided by 4.
To isolate p, you must then use the inverse operation of dividing by 4, which is multiplying by 4.
Multiplying both sides of the equation by 4 then gives:
$5=\frac{p}{4}$ Given equation.
$4×5=\frac{p}{4}$ Multiply both sides by 4.
$20=p$ Simplify
The solution of the equation is then p=4.


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## Production of the X(3872) in charmonia radiative decays    [PDF]

Feng-Kun Guo, Christoph Hanhart, Ulf-G. Meißner, Qian Wang, Qiang Zhao
We discuss the possibilities of producing the X(3872), which is assumed to be a D \bar D^* bound state, in radiative decays of charmonia. We argue that the ideal energy regions to observe the X(3872) associated with a photon in e^+e^- annihilations are around the Y(4260) mass and around 4.45 GeV, due to the presence of the S-wave D \bar D_1(2420) and D^* \bar D_1(2420) threshold, respectively. Especially, if the Y(4260) is dominantly a D \bar D_1 molecule and the X(3872) a D \bar D^* molecule, the radiative transition strength will be quite large.
View original: http://arxiv.org/abs/1306.3096


text:
# Why does the graph of x^x undefined for x is less than or equal to 0?

by tahayassen
Tags: equal, graph, undefined
 P: 273 Let f(x)=(x)^(x) f(-1)=(-1)^(-1) =1/-1 =-1 But according to wolframalpha, f(-1) does not exist.
 P: 4 The function works only in integer point. For each non integer point the function goes in Complex Set, and so isn't defined on real. Easilly, to avoid the calculator have problem on any other point lesser then 0, the programmer block each of that point with "does not exist" message. Fruthermore I can rewrite the f(x) in this way: f(x)=exp(x*ln(x)). And ln(x<0) is undefined.
 P: 45 http://www.wolframalpha.com/input/?i=f%28x%29+%3D+x%5Ex If you look at the graph of the function itself (without plugging anything in) you will see that it shows that at x=-1 it is imaginary.
P: 66
Why does the graph of x^x undefined for x is less than or equal to 0?

 Quote by G.I. Fruthermore I can rewrite the f(x) in this way: f(x)=exp(x*ln(x)). And ln(x<0) is undefined.
ln (-x) = ln(x) + $i \pi$

 Quote by tahayassen Let f(x)=(x)^(x) But according to wolframalpha, f(-1) does not exist.
http://www.wolframalpha.com/input/?i=%28-1%29^%28-1%29

It says "negative 1". :)
P: 2,751
 Quote by Best Pokemon http://www.wolframalpha.com/input/?i=f%28x%29+%3D+x%5Ex If you look at the graph of the function itself (without plugging anything in) you will see that it shows that at x=-1 it is imaginary.
That graph show that the imaginary part of f(-1) is 0 and that the real part is -1. That is, f(-1) = -1 + 0i.

It's as the first reply said, f(x)=x^x is not (in general) a real valued function for x<0, though it is real for the negative integers.
 P: 273 So it's a matter of limitations of computers/programming that x<0 doesn't exist for the real-valued plot? Why does the real part for x<0 exist on the complex-valued plot?
 P: 66 Remember x^x = (e^(log(x)))^x = e^(x*log(x)) log (-x) = log(x) + $i\pi$ This means that you'll have the magnitude x^(-x), and the angle x*i*pi. With the angle you'll have: cos (x*pi) * x^(-x) for the real portion and sin (x*pi) *x^(-x) for the imaginary portion. Correct this if I made a mistake.. tired. :)
 P: 295 Knowing that $z=r\exp(i\theta + 2ki\pi)$ where $r=|z|=\sqrt{\Re^2(z)+\Im^2(z)}$, $\theta=\mathrm{arg}(z)=\mathrm{atan2}(\Im(z),\Re(z))$ and k is an arbitrary integer, one has $\log(z)=\log(r) + i\theta + 2ki\pi = \log|z| + i\mathrm{arg}(z) + 2ki\pi$. Now, we consider our function for an arbitrary negative integer, with the principal branch of the complex logarithm (k=0): $$(-x)^(-x) = \exp((-x)\log(-x)) = \frac{1}{\exp(x\log(-x))} = \frac{1}{\exp(\log(x)+xi\pi)}= \frac{1}{x(\cos(x\pi)+i\sin(x\pi))}$$ Now, note that if x was not an integer, we would be stuck here. However, we know for integer x, $\cos(x\pi) = (-1)^x$ and $\sin(x\pi) = 0$, which leaves us with our final answer: $$= \frac{1}{x(-1)^x}$$ So why did I go through this? I wanted to show why Wolfram does not display the graph for $x \leq 0$. The function is defined as a real value only in the positive reals and the negative integers. For negative reals, we get the ugly-looking answer $\displaystyle \frac{1}{x(\cos(x\pi)+i\sin(x\pi))} = \frac{\cos(\pi x)-i\sin(\pi x)}{x}$, which can't be simplified further.
P: 1,716
 Quote by tahayassen Let f(x)=(x)^(x) f(-1)=(-1)^(-1) =1/-1 =-1 But according to wolframalpha, f(-1) does not exist.
P: 66
 Quote by Millennial So why did I go through this? I wanted to show why Wolfram does not display the graph for $x \leq 0$.
I saw the graph on Wolfram Alpha. Really nice pretty one if you constrain the x variable:
http://www.wolframalpha.com/input/?i...tupperrange---

Note... I am a fan of the Alpha. I also think the borderline ASD having character in Alphas is pretty awesome... and hilarious. Do you like strange tangents? :p

 Quote by Millennial The function is defined as a real value only in the positive reals and the negative integers. For negative reals, we get the ugly-looking answer $\displaystyle \frac{1}{x(\cos(x\pi)+i\sin(x\pi))} = \frac{\cos(\pi x)-i\sin(\pi x)}{x}$, which can't be simplified further.
It's actually (so you don't confuse people- look at the first post):
$$\dfrac{\cos(\pi x)-i\sin(\pi x)}{x^x}$$
or (rewritten version of my post above your post):
$${x^{-x}}\times \left({\cos(\pi x)-i\sin(\pi x)}\right)$$

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