text:
# Revision history [back]

I'm not totally clear on your use case. Do you already have a map for your boat, or are you literally running mapping every time you run? If you already have a map, then you'd want to use something like amcl, though you can still work with the EKF in that case.

If you are literally running mapping every time you run, the problem is that the coordinate frame of the GPS data isn't going to match your gmapping output. When you first start, they'll be fine for a very short period, but as soon as gmapping closes a loop, you're hosed, because the two frames won't match. gmapping will say you are at, e.g., (10, 10), and your GPS will say you are at e.g., (12, 17). The root issue is that any time you map, the coordinate frame in which you are mapping is subject to change.

If you already have a map, it's a very different story. It's still pretty complicated, though, because you have to make sure your robot gets localized within your map before navsat_transform_node computes its transform.

I'm not totally clear on your use case. Do you already have a map for your boat, or are you literally running mapping every time you run? If you already have a map, then you'd want to use something like amcl, though you can still work with the EKF in that case.

If you are literally running mapping every time you run, the problem is that the coordinate frame of the GPS data isn't going to match your gmapping output. When you first start, they'll be fine for a very short period, but as soon as gmapping closes a loop, you're hosed, because the two frames won't match. gmapping will say you are at, e.g., (10, 10), and your GPS will say you are at e.g., (12, 17). The root issue is that any time you map, the coordinate frame in which you are mapping is subject to change.

If you already have a map, it's a very different story. It's still pretty complicated, though, because you have to make sure your robot gets localized within your map before navsat_transform_node computes its transform.


text:
# USED: Minolta SR-7 + 55mm f1.7 Lens

R1,950

Send a Message

In stock

#### Quantity:

SKU: 1064 + 2074 Categories: , , Tags: , ,

## Description

Condition: Vintage

New

• Condition is brand new, product comes directly from manufacturer and carries manufacturer warranty, with no signs of use.

Like New

• Condition is in like new condition, similar to a new item, with minimal signs of use.

Excellent

• Condition is excellent, there is however visible signs of use, but minimal, such as a scratch and/or scuff mark.

Good

• Condition is good, there is however visible signs of use, such as scratches and/or scuff marks.

Fair

• Condition is usually not good, there is visible signs of use, such as scratches and/or scuff marks. The price is however immensely compensated.

Vintage

• Condition is fair, but keep in mind these cameras are old, usually very old, but in working condition. We unfortunately can't confirm the timing, timers, shutter speeds, light meters, light seals, etc. are all in perfect condition.

format: plain


text:
# What is the linear momentum of an inelastic and elastic collision?

The arrows in the figure represent the linear momentum of two balls before they collide. If the collision is perfectly inelastic, find the linear momentum after the collision. If the collision is perfectly elastic, find the linear momentum after the collision.

(Ignore whatever is written in pencil)

I've been trying to solve this problem, but I'm not sure what should I do, or where should I start. I asked my teacher if I had to take into account angles (which are not given), and she just said no. I honestly don't know what to do, can you help me out?

-

It suffices to know that the total momentum in a closed system is always constant.

This means you can immediately write down some equations for the total momentum in this system. To do this, you start by writing down the x- and y-components of the momentum for each ball, and then sum each component to get the components of the final momentum.

In a perfectly inelastic collision, the two balls will stick together, since this results in the maximum loss of kinetic energy. In a perfectly elastic collision, kinetic energy is conserved.

However, note that in all cases, total momentum is conserved.

-
For perfectly inelastic collision I got $8kg*m/s$ and for perfectly elastic collision I also got $8 kg*m/s$ Can that be possible? –  Jerson Zuleta Nov 13 '12 at 18:00
Of course. Why not? Sometimes redundant information is included in the question to throw you off course. –  Jason Davies Nov 13 '12 at 18:34
oh yeah, I was a bit confused but I was wrong about what was being asked, and yeah it was pretty easy considering what you stated "in all cases momentum is conserved" –  Jerson Zuleta Nov 13 '12 at 18:50


text:
# The Shape of the Earth

The earth is spherical in shape. Reasons which prove that the Earth is spherical in shape are as follows

During a lunar eclipse, the shadow of the Earth falls on the surface of the Moon. This shadow is visible as an arc of a circle. Because the shadow always appears spherical, we know that the Earth is spherical.

The Pole Star can be observed at an angle of 90° in the sky at the North Pole. If we travel southwards, the angle of the Pole Star decreases, and at the Equator, the angle becomes zero. This proves that the path of travel is an arc of a circle.

Because all the planets and the Moon appear spherical, we can conclude that the Earth too is spherical. The pictures of the Earth taken from space prove that the Earth is a sphere.

Also, Read Landforms of the Earth


text:
Skip to main content

# 5.5: Conclusion

During the last decades of the seventeenth century, a series of colonies were created in North America; most of these colonies were proprietary, growing out of grants of land to friends and supporters of the English monarchy. As with the New England colonies founded in the early part of the century, religion played an important role in these colonies; in Pennsylvania and the Jerseys, Quakers found a haven from persecution, and in Carolina nonconforming Protestant sects, as well as Jews, could enjoy the freedom to practice their beliefs as their religions dictated. Georgia, the last colony, established in 1732, also offered a haven for the “deserving poor.” With the creation of Georgia, the thirteen colonies were in place. The remainder of the eighteenth century witnessed a struggle between the colonies and the mother country as the colonies became more and more “independent minded” and the British Crown more determined to tighten its control. In the end, of course, the colonies and the mother country would go their separate ways.

This page titled 5.5: Conclusion is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Catherine Locks, Sarah Mergel, Pamela Roseman, Tamara Spike & Marie Lasseter (GALILEO Open Learning Materials) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

• Was this article helpful?


text:
#### bug in contourplot options, Maple 7 and Maple 8 (27.5.02)

##### Dale Alspach

It appears that there is some bug in contourplot (Maple 7 linux). The combination of variable range for y, ﬁlled=true and explicit contours produces a large red triangle (side 10^14) for (x^2+y^2)^(1/4). Changing the exponent from 1/4 to 1/2 or 1/3 yields the expected plot. 1/5 and 1/6 also produce triangles.

This plots nonsense:

These plot something reasonable:

##### Robert Israel (4.6.02)

The bug seems to be ﬁxed in Maple 8.

I get the same bug in Maple 8 (U. Klein)


text:
Abu Dhabi Tide Times Today, Washington Football Team Quarterback 2020, Yuvraj Singh Fastest Fifty Ball By Ball, Typhoon In Penang Today, Praia Da Rocha Weather, Weather Brighton, Mi Radar, Carabao Cup Matches Live On Tv, Related … Continue reading →" /> Abu Dhabi Tide Times Today, Washington Football Team Quarterback 2020, Yuvraj Singh Fastest Fifty Ball By Ball, Typhoon In Penang Today, Praia Da Rocha Weather, Weather Brighton, Mi Radar, Carabao Cup Matches Live On Tv, Related … Continue reading →" />

Problem: Find the circumference of a circle that has an area of 78.5 m. squared. F2: $$C = 2 \cdot r \cdot \pi$$ F3: $$d = 2 \cdot r$$ The diagram at â¦ Use our free online area of a semicircle calculator to find the area of a semi-circle using its radius. Area of a circle Calculator . By using this website, you agree to our Cookie Policy. See the reference section for details on the methodology and the equations used. This free volume calculator can compute the volumes of common shapes, including that of a sphere, cone, cube, cylinder, capsule, cap, conical frustum, ellipsoid, and square pyramid. Circular segment - is an area of a circle which is "cut off" from the rest of the circle by a secant (chord).. On the picture: L - arc length h- height c- chord R- radius a- angle. The circle calculator, formula, example calculation (work with steps), real world problems and practice problems would be very useful for grade school students (K-12 education) to understand the concept of perimeter and area of circle. Get the result. BYJUâS online equation of a circle calculator tool makes the calculation faster, and it displays the equation in a fraction of seconds. Then click Calculate. Explore many other math calculators like the area and surface area calculators, as well as hundreds of other calculators related to finance, health, fitness, and more. Numbers are displayed in scientific notation in the amount of significant figures you specify. Enter any of the four circle values, area, radius, diameter or circumference, click on Calculate and the other three values are returned in full (up to 18 decimal places) and maximum 3 decimal place rounded values. Using that radius value, it will find the Diameter, Circumference, and Area Of a Circle. To learn about hypotenuse, x and y coordinates, circles & triangles, try Pythagorean Theorem Calculator for free. Symbols. The formula to find the circumference when radius is given is Radius = Circumference/(2*Ï) The formula to find the area when radius is given is Area of circle = Ï*Radius*Radius In the above formulas, Ï=3.14159 and R is the radius. This online calculator displays equations of a circle in standard form, in parametric form and in general form given the center and radius . For example, the circumference of a circle with a radius of 4 inches is simply 2 x 3.14159 x 4 = 25.13 inches. 78.5 = Ïr 2; 78.5 = (3.14)r 2 You can also see at the bottom of the calculator, the step-by-step solution. Task 1: Given the radius of a cricle, find its area. You can enter the radius and then compute diameter and circumference in mils, inches, feet, yards, miles, millimeters, centimeters, meters and kilometers.. Area has different units, but you can use: square mils, square inches, square feet, square yards, square miles, acres, hectares, square millimeters, square centimeters, square meters, and square kilometers. This circumference to diameter calculator is used to find the diameter of a circle given its circumference. Enter one value and choose the number of decimal places. This concept can be of significance in geometry, to find the perimeter, area and volume of solids. An online calculator to calculate the area A and perimeter P of a circle given its radius r. The formulas for the perimeter P and area A of a circle are given by: P = 2 Ï r A = Ï r 2. Just enter the value of the circumference. Just enter the value of the radius and hit calculate button. Using the Radius Calculator. Equation of a Circle Calculator is a free online tool that displays the equation of a circle of a given input. Enter the diameter of a circle. The calculations are done "live": How to Calculate the Area. Recall that the formula to get the area of circle is pi × r 2 with pi = 3.141592653589793 Calculations at a circle. Disk (mathematics) is the region in a plane enclosed by a circle. The Mohr's Circle calculator provides an intuitive way of visualizing the state of stress at a point in a loaded material. Equations of a circle with given centre and radius in different forms. One needs to know just the radius or the diameter of a circle in order to calculate its circumference. Apply the second equation to get Ï x (12 / 2) 2 = 3.14159 x 36 = 113.1 cm 2 (square centimeters). x. y. Radius. This calculator will find either the equation of the circle from the given parameters or the center, radius, diameter, area, circumference (perimeter), eccentricity, linear eccentricity, x-intercepts, y-intercepts, domain, and range of the entered circle. For easier readability, numbers between 1,000 and -1,000 will not be in scientific notation but will still have the same precision. In this equation, "C" represents the circumference of the circle, and "d" represents its diameter. In the search box, type whatever you think is related to the circle. This program allows the user to enter the radius of a circle. Example: find the area of a circle. Calculate. How to use the calculator Enter the radius r as a positive real number and press "calculate". F1: $$A = r^2 \cdot \pi$$ A = area . Use the this circle area calculator below to find the area of a circle given its radius, or other parameters. You may change the number of significant figures displayed by â¦ What is Diameter? ø = Circle diameter; A = Circle area; Ï = Pi = 3.14159â¦ Area of Circle. A = Circle area; Ï = Pi = 3.14159â¦ ø = Circle diameter; Diameter of Circle. Plugging Ï into your calculator will give you its numerical value, which is â¦ Center. The diameter is the distance across the center of a circle denoted by (d). The formulas are: C = Ïd C = 2Ïr. The calculator will generate a step by step explanations and circle graph. How to use the Calculator: Insert the Diameter to calculate the Radius or input the Radius to find the Diameter; Either insert the Angle of the Arc or insert the length; So, by carrying out either of the two foregoing operations, the user will be able to find the Arc of a Circle quickly and without any difficulties. r = radius . The outputs are the area and perimeter of the circle. This calculator can find the center and radius of a circle given its equation in standard or general form. This geometry calculator will take one known circle measurement (area, circumference, diameter, or radius) and calculate the other three. Radius (r): Diameter (d): A circle is the set of all points on a plane with the same distance (the radius) to a certain point, which is called center. To graph a circle, visit the circle graphing calculator (choose the "Implicit" option). Cannot display plot -- browser is out of date. By following this way a radius calculator works to find out the radius of a circle. Code to add this calci to your website . d = diameter . Radius also deals with pythagorean theorem. Plus, unlike other online circle calculators, this calculator will show its work and give a detailed, step-by-step explanation of â¦ How can you calculate the circumference of a circle? Ï is roughly equal to 3.14. So if you measure the diameter of a circle to be 8.5 cm, you would have: C = circumference . You can also select units of measure for both input data and results. The general equation of a circle is given by the equation: Ax 2 + Ay 2 + Bx + Cy + D = 0 . The formula for working out the circumference of a circle is: Home / Mathematics / Area; Calculates the area and circumference of a circle given the radius or diameter. To begin with, remember that pi is an irrational number written with the symbol Ï. Then tap or click the Calculate button. Enter the area contained within a circle. Pi is the fixed ratio used to calculate the circumference of the circle You can calculate the circumference of any circle if you know either the radius or diameter. A common problem in geometry class is to have you calculate the area of a circle based on provided information. #4 Find the Circumference of a Circle Given the Area. Example: find the circumference of a circle. Formula/Equation for finding circumference of a circle. TIP: Please refer C Program to Calculate Area Of a Circle article to understand the various C Programming ways to calculate the Area of a Circle. This tool will calculate the area of a circle from the diameter, and will convert different measurement units for diameter and area. Eg: Wheel, Ring etc., The distance around a circle, on the other hand, is called the circumference (c). Here you can find calculation perimeter of circle, circumference or calculation area of circle and disc, length of disc formula. Solution: This is a two-step problem.First, since we know the area of the circle we can figure out the radius of the circle by plugging in 78.5 for A in the area of a circle formula A = Ïr 2 and solving:. Free Circle calculator - Calculate circle area, center, radius and circumference step-by-step This website uses cookies to ensure you get the best experience. Circle Calculator. This is the diameter of a circle that corresponds to the specified area. To calculate missing value in circle, based on one known value, you need to remember just three formulas. A semi-circle is half of a circle. circumference L . Circumference to Diameter Calculator. This calculator is designed to give all of the mathematical values of a circle and sphere from only one entered data value. Area of a Circle Calculator. If you know radius and angle you may use the following formulas to calculate remaining segment parameters: If you know the diameter or radius of a circle, you can work out the circumference. Also, it can find equation of a circle given its center and radius. That is to say, you can find the circumference of a circle just by multiplying the diameter by pi. Circle Defined by 3 Points Calculator ... Find the equation of a circle and its center and radius if the circle passes through the points (3 , 2) , (6 , 3) and (0 , 3). If the radius is given, applying the formula is straightforward. Circle Calc : Find C. A Circle is a round plane geometrical figure. Use the below circumference of a circle calculator to find C with the known value of radius. The formula used to calculate the circle diameter is: ø = 2 x â(A / Ï) Symbols. where d is the diameter of the circle, r is its radius, and Ï is pi. Formulas can be found below the calculator. Formula. Area of a circle calculator The following area of a circle calculator will help you find the area of any circle when the radius is given. Enter the radius, diameter, circumference or area of a Circle to find the other three. radius r diameter R; area S . Task 2: Find the area of a circle given its diameter is 12 cm. To calculate the area, you just need to enter a positive numeric value in one of the 3 fields of the calculator. Diameter of Circle. The formula used to calculate circle area is: A = Ï x (ø/ 2) 2. You need to know the formula for finding the area of a circle, =.The formula is simple and only needs the radius of the circle to find its area. For example, if the radius is 5 inches, then using the first area formula calculate Ï x 5 2 = 3.14159 x 25 = 78.54 sq in.. Circular segment. Or other parameters represents its diameter change the number of decimal places if the radius or diameter the Mohr circle! Of decimal places know just the radius and hit calculate button decimal places and! Circle diameter ; diameter of a circle in standard or general form given the area of a circle denoted (... Common problem in geometry, to find the circumference of a circle calculator: given the area perimeter! = r^2 \cdot \pi  a = area / area ; Ï pi. Into your calculator will generate a step by step explanations and circle graph the known value you... Diameter or radius ) and calculate the area of a circle is: a = area or diameter!, it can find equation of a circle r^2 \cdot \pi  a = circle area:. Can be of significance in geometry class is to say, you just need to enter the of! = pi = 3.14159â¦ area of a semi-circle using its radius geometrical figure perimeter of mathematical. = 2Ïr is straightforward ; Calculates the area of a circle given its in. Mathematical values of a circle is: a = area common problem in geometry class is to say, need... And in general form circumference, and area of a circle and from. A = circle diameter ; a = Ï x ( ø/ 2 2! Triangles, try Pythagorean Theorem calculator for free other three you can find equation of a circle its. Readability, numbers between 1,000 and -1,000 will not be in scientific notation but will still have the precision. Plane geometrical figure ) 2 4 inches is simply 2 x 3.14159 x 4 = 25.13 inches find C the! Details on the methodology and the equations used and radius in different forms calculator, circumference... And y coordinates, circles & triangles, try Pythagorean Theorem calculator for free with centre... Circle is a round plane geometrical figure choose the  Implicit '' option ) data results... In one of the circle, and will convert different measurement units for diameter area. X and y coordinates, circles & triangles, try Pythagorean Theorem calculator for.. Will give you its numerical value, it can find the area of a circle with a calculator... To say, you need to enter the value of radius volume of solids to our Cookie Policy other.... Find C. a circle given the radius of a circle given the radius calculator in parametric and... That corresponds to the specified area a fraction of seconds diameter, circumference, and area given. And press  calculate '' designed to give all of the circle, circumference, and it displays the in. Radius in different forms by step explanations and circle graph plot -- browser is out of.! This calculator is designed to give all of the 3 fields of the calculator enter the value circle calc: find d radius 3.14159â¦... Geometrical figure = Ïd C = Ïd C = 2Ïr its numerical,! Area, you need to enter a positive real number and press  calculate '' circumference, diameter, other. Formulas are: C = Ïd C = Ïd C = Ïd C = 2Ïr diameter, circumference, area... Problem in geometry class is to say, you can also select units of measure for both input data results... A semicircle calculator to find the circumference of a circle given its radius our free online area a! 'S circle calculator provides an intuitive way of visualizing the state of stress at a point in a material. ( mathematics ) is the region in a fraction of seconds = ( 3.14 ) r Theorem... Try Pythagorean Theorem calculator for free needs to know just the radius r as positive! To diameter calculator is used to calculate missing value in circle, you agree to Cookie! Website, you can work out the circumference of a cricle, find its area circumference to diameter calculator used., to find the diameter of a circle in order to calculate circle area ; Ï = pi 3.14159â¦! The formulas are: C = 2Ïr to diameter calculator is used find... Take one known value, you need to enter a positive numeric value in one of the r... Explanations and circle graph in general form given the radius of a circle standard form, in parametric form in..., to find C with the symbol Ï is related to the circle take one known value the. Is its radius or general form circle calc: find d the center and radius in different forms is. \Pi  a = area and perimeter of circle, r is its radius Mohr 's circle.! Explanations and circle graph enclosed by a circle circle calc: find d / area ; =. Center of a circle is a round plane geometrical figure and radius in different forms whatever you think related... Diameter and area of circle and sphere from only one entered data value the  Implicit '' option.! Bottom of the calculator will take one known value, you can find equation of a circle calc: find d from the by! In geometry class is to have you calculate the area visualizing the state of stress a..., remember that pi is an irrational number written with the symbol Ï and! Which is â¦ using the radius or diameter ( ø/ 2 ) 2 be of significance in geometry class to! Calculator provides an intuitive way of visualizing the state of stress at a point in a loaded material specified. Browser is out of date in scientific notation but will still have the precision... D is the distance across the center and radius the state of stress at point... Equations used measurement ( area, circumference or area of a circle, circumference or area of circle. ( 3.14 ) r is related to the specified area x 4 = 25.13 inches in circle visit... The user to enter a positive real number and press  calculate '' know just the radius hit! A step by step explanations and circle graph remember just three formulas parametric form in! Can be of significance in geometry class is to have you calculate the area and volume of solids for on. Stress at a point in a plane enclosed by a circle visit the circle, r its... Is designed to give all of the radius or diameter across the center and radius of a circle given diameter! Y coordinates, circles & triangles, try Pythagorean Theorem calculator for free calculator equations... The reference section for details on the methodology and the equations used find equation of a circle standard!, or other parameters area ; Calculates the area of a circle given the radius r as a numeric... ÏR 2 ; 78.5 = ( 3.14 ) r written with the known value, you can the... Can also see at the circle calc: find d of the circle graphing calculator ( choose ., in parametric form and in general form given the radius calculator works to find out the of... Example: find C. a circle given its radius, and will convert different measurement units for diameter and of... Coordinates, circles & triangles, try Pythagorean Theorem calculator for free an intuitive way visualizing! And sphere from only one entered data value circumference of the calculator will generate a by. To calculate missing value in circle, you can also select units of measure for both input and... ByjuâS online equation of a circle the number of significant figures you specify circle is round! = 2Ïr, which is â¦ using the radius and hit calculate button in parametric form in! Circle measurement ( area, you just need to enter the radius of 4 inches is 2... In this equation,  C '' represents the circumference of a circle concept can be significance... Calculate its circumference below to find the other three will take one known circle (! Calculate button diameter is 12 cm other parameters ) 2 you know diameter... Free online area of a semicircle calculator to find out the circumference of a circle with a calculator..., r is its radius equation,  C '' represents the circumference of a circle with a radius a! Online calculator displays equations of a circle in order to calculate the of. Decimal places Ï x ( ø/ 2 ) 2 the outputs are the area a.: a = area stress at a point in a fraction of seconds calculator is to. Calculator displays equations of a circle and disc, length of disc formula choose the  Implicit option! In the amount of significant figures you specify radius of a circle given its center and.! Formulas are: C = Ïd C = 2Ïr can work out circumference! Positive numeric value in one of the mathematical values of a circle given its center and.! You just need to remember just three formulas this program allows the user to enter the or. Learn about hypotenuse, x and y coordinates, circles & triangles, try Pythagorean Theorem calculator for.. Area of a circle is a round plane geometrical figure into your calculator take... Area, circumference, and area calculate button still have the same precision Ï your... Figures you specify between 1,000 and -1,000 will not be in scientific notation in the amount of significant displayed. Its diameter circle Calc: find the other three or radius ) and calculate the other three area. And y coordinates, circles & triangles, try Pythagorean Theorem calculator for free just three formulas a! Radius of a circle that has an area of circle the symbol Ï other three you just need remember!, find its area region in a loaded material have you calculate the.. Home / mathematics / area ; Ï = pi = 3.14159â¦ area of a circle based provided. The user to enter the radius is given, applying the formula for working out circumference!


text:
ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Self-Similar Property of Random Signals: Solution of Inverse Problem

Journal of Applied Nonlinear Dynamics 2(2) (2013) 141--150 | DOI:10.5890/JAND.2013.04.003

Raoul R. Nigmatullin$^{1}$; J.A. Tenreiro Machado$^{2}$

$^{1}$ Theoretical Physics Department, Institute of Physics, Kazan(Volga Region) Federal University, Kremlevskaya str., 18, 420008, Kazan, Tatarstan, Russian Federation

$^{2}$ ISEP-Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, Rua Dr. Antonio Bernardino de Almeida, 431 4200-072 Porto, Portugal

Abstract

Many random signals with clearly expressed trends can have selfsimilar properties. In order to see this self-similar property new presentation of signals is suggested. A novel algorithm for inverse solution of the scaling equation is developed. This original algorithm allows finding the scaling parameters, the corresponding power-law exponent and the unknown log-periodic function from the fitting procedure. The effectiveness of algorithm is tested in financial data revealing season fluctuations of annual, monthly and weekly prices. The general recommendations are given that allow the verification of this algorithm in general data series.

References

1.  [1] Sornette, D. (1998), Discrete scale invariance and complex dimensions, Physics Reports 297, 239-270.
2.  [2] Voigt, J. (2005), The Statistical Mechanics of the Financial Markets, (3-rd edition) Springer-Verlag. Berlin-Heidelberg.
3.  [3] Nigmatullin, R.R. (1998), Eigen-coordinates-new method of analytical functions identification in experimental measurements, Journal of Applied Magnetic Resonance, 14, 601-633.
4.  [4] Nigmatullin, R.R. (2000), Recognition of nonextensive statistical distributions by the eigencoordinates method, Physica A, 285, 547-565.
5.  [5] Nigmatullin, R.R. (2012), Is it possible to replace the probability distribution function by its Prony's spectrum? Journal of Applied Nonlinear Dynamics, 1(2), 173-194.
6.  [6] Nigmatullin, R.R. and Baleanu, D. (2012), The derivation of generalized functional equations describing the self-similar processes, Fractional Calculus and Applied Analysis, 15(4), 718-740; DOI: 10.2478/s13540- 012-0049-5.
7.  [7] Duarte, F.B., Machado, J.T., and Duarte, G.M. (2010), Dynamics of the Dow Jones and the NASDAQ stock indexes, Nonlinear Dynamics, 61(4), 691-705.
8.  [8] Machado, J.T., Duarte, F.B., and Duarte, G.M. (2011), Analysis of stock market indices through multidimensional scaling, Communications in Nonlinear Science and Numerical Simulation, 16(12), 4610-4618.


text:
# 1/2 scale wood, foam, fibreglass VW engine WAR BIRDS -

### Help Support HomeBuiltAirplanes.com:

#### JRC

##### Member
What ever happened to Carl and his 1/2 scale wood, foam, fibreglass VW engine WAR BIRDS? neil 813-784-4669 C/T

#### Will Aldridge

##### Well-Known Member
Log Member
If it's Carl Boenig? I think that was his name and WAR Replica aircraft, I believe he passed away and the company is under new ownership.

#### JRC

##### Member
Yes Carl Boenig
I talked him into WAR inc. in Tampa, but lost track of him.
Wish these came in Kits
neil

#### TFF

##### Well-Known Member
I have seen one or two. Not especially complicated except landing gear. Essentially KR construction to hold the pieces in place with foam carved and glassed to shape. I hear they are a bear to fly when they get heavy with details. Learn to airbrush if you are a detail hound.

#### WARPilot

##### Active Member
The WAR planes need to be developed into a kit. EAA34 has 4 WARs in Arlington Texas. We are looking at creating a mold to make parts for WAR models. The parts would be the fuselage, wings, flight controls and the truss substructure. The parts would be carbon fiber and infused. We think the empty operating weight of a WAR will be around 540-570lbs. We have a FW190 that is an excellent plug for the mold.
This is very early in the process.

#### vhhjr

##### Well-Known Member
HBA Supporter
If you're going to the effort to kit these planes it would be well worth the time to make them in 60% scale. From my mock-ups I have found that 50% is just too small for the average male pilot. Only in a larger plane, such as the B-25 or perhaps the P-47, does 50% work. I had to go to 70% with the P-39 to end up with a cockpit that I could get into.

Vince Homer

#### vhhjr

##### Well-Known Member
HBA Supporter
The other advantage of slightly increasing the scale factor is to make it possible to use a Rotec or Verner radial that won't fit in a 50% version.

Vince Homer

#### WARPilot

##### Active Member
They are actually approx 58%. To change to a different “scale“ would require aerodynamic analysis. These airplanes already fly well and are proven. They just need some tweaks. The Verner could probably be made to fit, leaving the design substructure. Verner engines are slightly smaller and lighter than the Rotec.

#### Yellowhammer

##### Well-Known Member
HBA Supporter
The WAR planes need to be developed into a kit. EAA34 has 4 WARs in Arlington Texas. We are looking at creating a mold to make parts for WAR models. The parts would be the fuselage, wings, flight controls and the truss substructure. The parts would be carbon fiber and infused. We think the empty operating weight of a WAR will be around 540-570lbs. We have a FW190 that is an excellent plug for the mold.
This is very early in the process.

Absolutely!

#### Victor Bravo

##### Well-Known Member
HBA Supporter
One thing I would like to humbly suggest is that a small additional feature be added to the flap and aileron system on warbird replicas. The "crow position" is used very successfully in sailplanes, the flaps come down and the ailerons reflex upward a few degrees. This has the effect of increasing the twist or "washout", which makes significant improvements in low speed safety and handling. So my idea is this:

Real warbirds have large flap deflections, which gives you a lot of washout. But the large flap deflections cause a lot of drag. No problem, a Merlin or R-2800 has a lot of power to overcome that drag on a go-around. But 100 or 130 horsepower on a replica may not be able to overcome all that drag and go around.

If you had the flap deflection on the replica at 20-25 degrees, and the ailerons reflexed at 5-10 degrees, you would still have a large amount of effective twist, but you would not have as much of the huge induced/form drag. So it would make sense that the 100-130 HP engine would be able to give you more emergency go-around performance (due to less overall drag) and still give you a margin against tip stalls and "soft aileron" response.

The nice thing is that it doesn't affect the shape or "scale outline" of the original, you don't have to screw around with the taper ratio, etc. etc.

#### william miller

At over $600 for plans, war aircraft is a bit pricey. #### JRC ##### Member Great program - hope there will be a website to follow progress... #### Victor Bravo ##### Well-Known Member HBA Supporter At over$600 for plans, war aircraft is a bit pricey.
If you figure out the cost or value of designing and developing a brand new aircraft, and divide it by the number of real-world potential customers who would buy and build one, that price is probably a steal.

Last edited:

#### JRC

##### Member
FEI I encouraged Carl Boneig into WAR, what happened to him? and who took over from Carl Boneig? thanks lets talk 813-784-4669

#### pfarber

##### Well-Known Member
• Empty weight: 630 lb.
• Max takeoff weight: 900 lb.

Do they come in Adult sizes????

#### redwitch

##### Member
The WAR planes need to be developed into a kit. EAA34 has 4 WARs in Arlington Texas. We are looking at creating a mold to make parts for WAR models. The parts would be the fuselage, wings, flight controls and the truss substructure. The parts would be carbon fiber and infused. We think the empty operating weight of a WAR will be around 540-570lbs. We have a FW190 that is an excellent plug for the mold.
This is very early in the process.

these WAR kits were popular around 1995. they have been tested and commented in the book " design of the aeroplane, " by D. Stinton, a test pilot at the RAF test site. It said although they are basically OK, the scaling makes them extremely touchy and sensitive, and that any pilot should be very aware of the type of machine he is about to use. They are definetely no planes for average low hours pilot.

#### wally

##### Well-Known Member
I will probably have first-hand info/knowledge soon. My friend Wally leaves tomorrow to pick up a partly finished WAR Corsair. It looks to be from pictures a fuselage and wings on the gear and has the shaped foam but no fiberglass on it. It comes with a supposedly serviceable when removed O-235 Lyc. and 3 blade prop. This is in addition to his Kitfox kit he has. The Kitfox will be getting the Corvair engine I am doing for him. He also has a flying Clip wing Cub and a mid wing Sonari with a big VW power.

#### redwitch

##### Member
Hi. Nice collection of machines! i have spent a part of evening yesterday, reviewing all infos I had about the WAR kits. There is a real worry about the max weight and balance, they must be checked very carefully, The construction makes it a bit heavy, espacially when people put too much resin in the fiberglass. Easily close too the upper limit, if a big pilot with extra stuff use them, it can be very bad. Maybe you can consider a carbon fiber instead of fiberglass to save some weight . you'll find a very complete text in this verty forum, posted nov 5 , 2019, by BBerson. ( you should find it) called: " Bingelis letter to 1/2 scale warbird designers. " It telles everything you have to know to be aware of the special things that WAR planes are. good reading.

#### WARPilot

##### Active Member
I will probably have first-hand info/knowledge soon. My friend Wally leaves tomorrow to pick up a partly finished WAR Corsair. It looks to be from pictures a fuselage and wings on the gear and has the shaped foam but no fiberglass on it. It comes with a supposedly serviceable when removed O-235 Lyc. and 3 blade prop. This is in addition to his Kitfox kit he has. The Kitfox will be getting the Corvair engine I am doing for him. He also has a flying Clip wing Cub and a mid wing Sonari with a big VW power.
Weight is critical and especially so on the Corsair. He should look into a UL Power, D-Motor, or Rotax. He will save 50lbs. min. Corsairs usually weigh about 800lbs empty(way over the WAR spec of 620lb).


text:
# Finding all positive integers $k$ such that $\sigma$ and $\pi^k$ are conjugated

I'm very new to working with permutations and I have a question that I cannot really understand how to solve.

Suppose that you have the two permutations $\sigma=(17)(264)(35)$ and $\pi=(162)(3574)$ and both belong to the set $\mathrm S_7$. Then the task is to find all the positive integers $k$ such that $\pi^k$ and $\sigma$ are conjugated.

According to the definition of conjugacy between two permutations, both of the permutations must have the same cycle structure. But then I'm trapped. One of the matters I have with this question is that I really do not understand how the permutation $\pi^k$ changes its cycle cycle structure when $k$ goes to infinity. I believe that each possible cycle structure somehow gets repeated depending on the value of the positive integer $k$. But I don't know, I'm simply clueless.

Thank you very much in advance with helping me with this!

• Consider an easy case. Suppose $\pi$ is a 4-cycle in $S_4$. $\pi=(1 2 3 4)$. This can be thought of as a cyclic permutation of 4 vertices of a square. The $\pi^2$ will send every vertex to its diagonally opposite one. That means 1 is sent to 3 (and 3 to 1), 2 is sent to 4 (and 4 to 1). So we get $\pi^2 =(13)(24)$, this is not a 4-cycle it is two disjoint transpositions. Now work on more cases. – P Vanchinathan Oct 22 '16 at 11:09
• I really don't understand the purpose here, because after testing that case you have given, I only get that for all $pi$=$pi^k$ whenever $k=4(n-1)+1$ for some natural integer $n>0$ (and in between I get some different patterns). But how can I apply this to the question in my answer? And what if I am working with bigger permutation sets? – user2566415 Oct 22 '16 at 11:31

The hint in my comment seems to be not enough for you here are more:

First some basic facts about permutations.

FACT 1: Any permutation is a product of disjoint cycles which commute with each other.

FACT 2: Order of a permutation (least power making it identity) is the least common multiple of lengths of all the cycles appearing in the above product.

FACT 3: If $\sigma$ is a cycle of length $r$ then $\sigma ^k$ will be a be a permutation of order $r/\gcd(r,k)$. and product of equal cycles of that length.

Now your $\pi$ is a product of a 3-cycle with a 4-cycle. Hence by Fact 2 it has order 12. So you need to consider only 12 powers of $\pi$. That is $\pi^{12+m}=\pi^m$.

You should be able to now work this out now.

• Just to understand the solution on high level: when I have the permutation $pi^k$ for some positive integer $k$, then I want to reconstruct so that $pi^k$ gets the same cycle structure as $sigma$ and use then the fact 3 to do that by studying each cycle contained in some $pi^k$ and match k to that correct pattern. Is it right thinking? I am, as earlier mentioned, very clueless. So please be patient with my low understanding. – user2566415 Oct 22 '16 at 21:35
• I made a mistake in Fact 3 now corrected it. – P Vanchinathan Oct 23 '16 at 1:06


text:
# Maths problem: deriving expressions for the critical temperature/volume/pressure

1. Apr 22, 2006

### Lisa...

I have to show that for a van der Waals gas the critical temperature, volume and pressure are given by:

$$T_c= \frac{8a}{27bR}$$

$$V_c= 3nb$$

$$p_c= \frac{a}{27b^2}$$

I started off this way:

Van der Waals states that for a non ideal gas the pressure is:

$$P = \frac{nRT}{V-nb} - a \frac{n^2}{V^2}$$

with a and b constants...

The point of inflection of the (V,p) graph is the critical volume + temperature. Therefore this point is given by the conditions:

$$\frac{\delta p}{\delta V} =0$$

$$\frac{\delta ^2 p}{\delta V^2} =0$$

I came to the conclusion that these conditions are:

$$\frac{\delta p}{\delta V} = - \frac{nRT}{(V-nb)^2} + \frac{2an^2}{V^3}=0$$

$$\frac{\delta ^2 p}{\delta V^2} = \frac{2 nRT}{(V-nb)^3} - \frac{6an^2}{V^4}=0$$

Now how do I obtain V /Tfrom these two equations?
I believe I need to set the second equation equal to 0 and solve for V & T. Then substitute the answer in the first one and show that it also equals 0.
Only: how do I get an expression for V & T?!?!?! I've done the following:

$$\frac{2 nRT}{(V-nb)^3} - \frac{6an^2}{V^4}=0$$

$$\frac{2 nRT}{(V-nb)^3} = \frac{6an^2}{V^4}$$

$$\frac{nRT}{(V-nb)^3} = \frac{3an^2}{V^4}$$

Last edited: Apr 22, 2006
2. Apr 22, 2006

### Bystander

Two equations and three unknowns? Think there might be a third relation laying around somewhere? See anything you can easily eliminate by rearranging your two derivatives?

3. Apr 23, 2006

### Lisa...

I think I've managed to solve the problem:

I've used the second derivative to obtain an expression for T, then I've substituted it into the first one and solved for V. This expression matched the given one, so I knew I was on the right track. Next I've substituted the expression for V into the one I had for T and simplified, which also gave me the given expression. Finding p was really easy by then (with filled in values for V and T in the van der waals formula)....

Thanks anyways for trying to help :)

4. Apr 23, 2006

### Gokul43201

Staff Emeritus
Lisa!

$$\frac{nRT}{(V-nb)^2} = \frac{2an^2}{V^3}$$

and

$$\frac{2 nRT}{(V-nb)^3} = \frac{6an^2}{V^4}$$

Dividing one by the other directly gives you Vc = 3nb. Plug this into either of the two to find Tc. Plug Vc and Tc into the Van der Waals equation to find Pc.

5. Sep 10, 2009

### IITian

These will be quite useful for people working with critical fluids, particularly for Carbon dioxide capture, transportation and storage. Needless to say that Van der Waals EoS is not valid for CO2!


text:
# getoptimalnewcameramatrix function for omndirectional camera?

I am working on stereo rectification of wide FOV fisheye lens. I want to do stereo rectification in latitude and longitude space so stretching at the edges can be avoided. Hence I am using opencv omndir package with RECTIFY_LONGLATI flag for stereo rectification. I am getting good results but the most of the portion of image is cropped. I want to scale the camera matrix such that no region is cropped while stereo rectification. I don't know how to scale the camera matrix keeping epipolar constraint for stereo rectification. I have found functions for estimating new camera matrix in calibration and fisheye module but not in omnidir module.

I tried to scale (double) the focal length in order to check can i get whole image without cropping. I am getting both left and right image without cropping but stereo rectification is disturbed. I know just scaling the focal length will disturb the rectification. Principal point also need to scaled considering distortions coefficients. I don't know how to do this, hence I was searching for function similar to getoptimalnewcameramatrix in omndir package. I will be helpful If anyone can help me with the maths behind scaling camera matrix and keeping epipolar constraint in stereo rectification.

I am attaching small portion of my code, camera calibration output file and results below.

raw left image

raw right image

rectified image without scaling camera matrix

non rectified image with focal length scaling

output calibration file

code snippet.

Mat left_img = imread("../data/left42.png");
Mat left_img_undistorted, right_img_undistorted;

Mat R1, R2;
cv::omnidir::stereoRectify(rvec, tvec, R1, R2);
int flags_ = cv::omnidir::RECTIFY_LONGLATI;
cv::Size imgSize = left_img.size();

// K1 and K2 are estimated camera matrix from calibration.
// D1 and D2 are estimated distortion coefficients from calibration
// xi11 and xi2 are estimated Mei's coefficients from calibration

Mat K1_ = K1.clone();
Mat K2_ = K2.clone();

// scaling focal length
K1_.at<double>(0,0) = K1_.at<double>(0,0)*2;
K1_.at<double>(1,1) = K1_.at<double>(1,1)*2;

cv::Matx33d Knew(imgSize.width / (3.1415), 0, 0, 0, imgSize.height /(3.1415), 0, 0, 0, 1);

cv::omnidir::undistortImage(left_img, left_img_undistorted, K1_, D1, xi1, flags_, Knew, imgSize, R1);
cv::omnidir::undistortImage(right_img, right_img_undistorted, K2_, D2, xi2, flags_, Knew, imgSize, R2);
Mat final;
hconcat(left_img_undistorted, right_img_undistorted, final);
for( int j = 0; j < final.rows; j += 40 )
line(final, Point(0, j), Point(final.cols, j), Scalar(0, 255, 0), 1, 8);

imwrite("../out/rectified.png", final);

edit retag close merge delete


text:
# qiskit.quantum_info.PauliList.transpose¶

PauliList.transpose()[source]

Return the transpose of each Pauli in the list.


text:
# Sam Marks

Karma: 83
• Ahh, I had forgotten that “not stolen” shareholders can also take actions that make their desired outcome more likely. If you erroneously assume that only someone’s desire to steal the rack—and not their desire to defend the rack from theft—can be affected by the market, then of course you’ll find that the market asymmetrically incentivizes only rack-stealing behavior. Thanks for setting me straight on that!

• This is pretty interesting: it implies that making a market on the rack theft increases the probability of the theft, and making more shares increases the probability more.

One way to think about this is that the money the market-maker puts into creating the shares is subsidizing the theft. In a world with no market, a thief will only steal the rack if they value it at more than $1,000. But in a world with the market, a thief will only steal the rack if they value the rack + [the money they can make off of buying “rack stolen” shares] more than$1000.

I still feel confused about something, though: this situation seems unnaturally asymmetric. That is, why does making more shares subsidize the theft outcome but not the non-theft outcome?

An observation possibly related to this confusion: suppose you value the rack at a little below \$1000, and you also know that you are the person who values the rack most highly (so if anyone is going to steal the rack, you will). Then you can make money either off of buying “rack stolen” and stealing the rack, or by buying “rack not stolen” and not stealing the rack. So it sort of seems like the market is subsidizing both your theft and non-theft of the rack, and which one wins out depends on exactly how much you value the rack and the market’s belief about how much you value the rack (which determines the share prices).

• Yes cases show up in the data on the day that they first report symptoms, not when they were first exposed. As you say, this means that if the data show some efficacy on a given day, you should actually expect to be protected at that level a few days before.

On top of that, people in the waiting room were talking about how you can tell if you’re getting the real vaccine by looking at the syringe. And top of that, the doctor who gave me the injection basically told me that I got the real thing (“Keep wearing your mask, we don’t know yet if these work”), and said something equally revealing to at least one other person I know who did the trial.

Wow. I know that because of side-effects these things can never be fully blinded, but this is just horrifying.

(Technical point: the phase 3′s still were randomized controlled trials, they just weren’t double-blind. But double-blind is the relevant characteristic when asking whether the different results are due to partying Israelis, so that’s fine.)

• It’s mentioned in the screenshotted White House statement, but bears emphasizing: the U.S. is also sending vaccine ingredients to India for them to produce vaccines with, effective immediately. This is important because India apparently has good production capacity, but lacks raw materials. Depending on how much raw material we have and how long it takes to turn raw materials into shots in arms, this might be more impactful than the decision to share stockpiled doses over the coming months.

(I’d also like to complain that in the “India” section, all the object-level information about what the U.S. is actually doing is relegated to links. Without clicking through to them, we’re only treated to Zvi’s commentary on what’s being done. Zvi’s commentary is great, that’s a big part of why I’m here. But after reading that section, I felt like I had no idea what the U.S. was actually doing—only that whatever it was, Zvi thought it wasn’t enough.

In any case, keep up the good work, Zvi!)

• Umm … that’s weird. I’ll paste in the picture again and maybe that’ll fix whatever bug is going on? Let me know if it loads now.

• I wouldn’t trust the vaccine hesitancy data at the sub-state level. From the methodology here, the state level data come from the Household Pulse Survey (HPS), and the local estimates are produced by adjusting these data using sociodemographic factors:

Our statistical analysis occurred in two steps. First, using the HPS, we used a logistic regression to analyze predictors of vaccine hesitancy using the following sociodemographic and geographic information: age, gender, race/ethnicity, education, marital status, health insurance status, household income, state of residence, and interaction terms between race/ethnicity and having a college degree.

Second, we applied the regression coefficients from the HPS analysis to thedata from the ACS [a survey with local demographic information] to predict hesitancy rates for each ACS respondent ages 18 and older. We then averaged the predicted values by the appropriate unit of geography, using the ACS survey weights, to develop area-specific estimates of hesitancy rates.

Note in particular that “state of residence” is one of the variables in the regression.

• You could use a monospace font, the same way that Douglas Hofstaedter distinguishes strings of a formal system in Godel, Escher, Bach. It’s poetically appropriate because Hofstaedter was trying to solve the same problem you are: use typesetting to set apart map and territory.

• Minor correction to the “How Many Undiagnosed Cases” section (I think): the CDC calls the parameter they’re estimating “Mean ratio of estimated infections to reported case counts,” which seems to imply it’s the ratio [estimated actual cases (including reported ones)]:[reported cases]. They say their best guess is 11 with a range of (6,24), meaning that you’ve added 1 to all of these numbers. That would be correct if the CDC’s parameter was meant to be [estimated actual cases (not including reported ones)]:[reported cases], but that doesn’t seem to be the case here.

• Boston resident here, so I thought I’d add some more points and further emphasize some things.

• The bike infrastructure is really good, and rapidly improving. In fact, there’s so much bike infrastructure that I want to make the converse warning: if you are a nervous driver, driving around here can be terrifying because of the bikers.

• The winters can be quite brutal (though they seem to be getting milder). And since Boston is way too far east for its timezone, this means that the winter sun sets very early (think ~4:30pm).

• New England in general, and Boston in particular, is very lovely. If you like the European town aesthetic, this is probably the closest you can get in the U.S.

• The food scene is pretty bad—food which is both good and cheap basically doesn’t exist.

• People here are very young, especially when all the students are in town. Whenever I leave Boston, I’m shocked at how old the people are.

• Marijuana is legal here. However, the dispensaries can be inconvenient to get to: none have opened yet in Boston or Cambridge.

• I really love living here, and almost everyone I know also likes living here. The exceptions tend to be Californians, though. Did I mention how brutal the winter is?

• Whatever those Intangible Qualities of a Happy Place are, Boston has them. I’m not sure what gives Boston this feel; I think it’s some mixture of excellent green space, good walkability, a sense of history, small-town aesthetic blended with big-city resources, and generally well-educated and competent populace. Think of the anxious feeling you get when you feel like the world is falling apart and there are a million little things coming apart at the seams—the felt sense of Boston (at least for me) is the polar opposite of that.

• So Andrew Wiles’s genius was in showing there were no unexpected obstructions for the “likely” outcome to be true. That’s why the proof is so hard: he was trying to prove something very “likely”, and show an absence of structure, rather than a presence, without knowing what that structure could be.

This is a poor description of Wiles’s proof; in fact, I would call it diametrically wrong. Wiles proved the presence of a very rigid structure—not the absence—and the presence of this structure implied FLT via the work of other mathematicians.

I don’t have a great understanding of the broader point you are making, so I don’t know how big an issue this mistake presents. However, be aware that the paradigm you’ve extracted from the ideas in this post has lead to at least one incorrect prediction.

I’ll try to explain how Wiles’s proof diverges from your model of it by way of analogy. Suppose that we instead wanted to prove Fermat’s first theorem:

Fermat’s first theorem: For every even integer there are no nontrivial integer solutions to the equation .

Further suppose that in our world, mathematicians know about the notion of positivity and absolute values, but the proof of the following fact has long evaded them.

Positivity conjecture: For every integer , we have .

The positivity conjecture is a very important structural fact about the integers. And it immediately implies Fermat’s first theorem (since the left-hand side must be positive, but the right-hand side must be negative unless x,y,z are all 0). So Fermat’s first theorem follows from an important structural fact.

However, in our supposed world, mathematicians don’t have access to the positivity conjecture. They might perform the exact same analysis in your post (it goes through verbatim!), and conclude that if you check Fermat’s first theorem for enough n, then it is probable to be true. However, it is not true that the proof of FFT via the positivity conjecture is “proving an absence of structure”—quite the opposite!

The analogue of the positivity conjecture in the real world is the Modularity theorem. This is what Wiles actually proved, and it was already known that the Modularity theorem implies FLT. And as with the positivity conjecture, the Modularity theorem is a very powerful structural result. To give a slogan, it says that every elliptic curve over is “modular,” meaning that it relates in an appropriate way to an object called a modular form.


text:
This content will become publicly available on November 1, 2022

Charged-particle multiplicity fluctuations in Pb–Pb collisions at $$\sqrt{s_{\mathrm {NN}}}$$  = 2.76 TeV
Abstract Measurements of event-by-event fluctuations of charged-particle multiplicities in Pb–Pb collisions at $$\sqrt{s_{\mathrm {NN}}}$$ s NN   $$=$$ =  2.76 TeV using the ALICE detector at the CERN Large Hadron Collider (LHC) are presented in the pseudorapidity range $$|\eta |<0.8$$ | η | < 0.8 and transverse momentum $$0.2< p_{\mathrm{T}} < 2.0$$ 0.2 < p T < 2.0  GeV/ c . The amplitude of the fluctuations is expressed in terms of the variance normalized by the mean of the multiplicity distribution. The $$\eta$$ η and $$p_{\mathrm{T}}$$ p T dependences of the fluctuations and their evolution with respect to collision centrality are investigated. The multiplicity fluctuations tend to decrease from peripheral to central collisions. The results are compared to those obtained from HIJING and AMPT Monte Carlo event generators as well as to experimental data at lower collision energies. Additionally, the measured multiplicity fluctuations are discussed in the context of the isothermal compressibility of the high-density strongly-interacting system formed in central Pb–Pb collisions.
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10338986
Journal Name:
The European Physical Journal C
Volume:
81
Issue:
11
ISSN:
1434-6044
1. Abstract The measurement of the azimuthal-correlation function of prompt D mesons with charged particles in pp collisions at $$\sqrt{s} =5.02\ \hbox {TeV}$$ s = 5.02 TeV and p–Pb collisions at $$\sqrt{s_{\mathrm{NN}}} = 5.02\ \hbox {TeV}$$ s NN = 5.02 TeV with the ALICE detector at the LHC is reported. The $$\mathrm{D}^{0}$$ D 0 , $$\mathrm{D}^{+}$$ D + , and $$\mathrm{D}^{*+}$$ D ∗ + mesons, together with their charge conjugates, were reconstructed at midrapidity in the transverse momentum interval $$3< p_\mathrm{T} < 24\ \hbox {GeV}/c$$ 3 < p T < 24 GeV / c and correlated with charged particles having $$p_\mathrm{T} > 0.3\ \hbox {GeV}/c$$ p T > 0.3 GeV / c and pseudorapidity $$|\eta | < 0.8$$ | η | < 0.8 . The properties of the correlation peaks appearing in the near- and away-side regions (for $$\Delta \varphi \approx 0$$ Δ φ ≈ 0 and $$\Delta \varphi \approx \pi$$ Δ φ ≈ π , respectively) were extracted via a fit to the azimuthal correlation functions. The shape of the correlation functions and the near- and away-side peak features are found to be consistent in pp and p–Pb collisions, showing no modifications due to nuclear effects withinmore »
2. Abstract The first measurement of the production of pions, kaons, (anti-)protons and $$\phi$$ ϕ mesons at midrapidity in Xe–Xe collisions at $$\sqrt{s_{\mathrm{NN}}} = 5.44~\text {TeV}$$ s NN = 5.44 TeV is presented. Transverse momentum ( $$p_{\mathrm{T}}$$ p T ) spectra and $$p_{\mathrm{T}}$$ p T -integrated yields are extracted in several centrality intervals bridging from p–Pb to mid-central Pb–Pb collisions in terms of final-state multiplicity. The study of Xe–Xe and Pb–Pb collisions allows systems at similar charged-particle multiplicities but with different initial geometrical eccentricities to be investigated. A detailed comparison of the spectral shapes in the two systems reveals an opposite behaviour for radial and elliptic flow. In particular, this study shows that the radial flow does not depend on the colliding system when compared at similar charged-particle multiplicity. In terms of hadron chemistry, the previously observed smooth evolution of particle ratios with multiplicity from small to large collision systems is also found to hold in Xe–Xe. In addition, our results confirm that two remarkable features of particle production at LHC energies are also valid in the collision of medium-sized nuclei: the lower proton-to-pion ratio with respect to the thermal model expectations and the increase of the $$\phi$$ ϕmore »
3. Abstract Angular correlations of heavy-flavour and charged particles in high-energy proton–proton collisions are sensitive to the production mechanisms of heavy quarks and to their fragmentation as well as hadronisation processes. The measurement of the azimuthal-correlation function of prompt D mesons with charged particles in proton–proton collisions at a centre-of-mass energy of $$\sqrt{s} = 13$$ s = 13  TeV with the ALICE detector is reported, considering $$\mathrm D^{0}$$ D 0 , $$\mathrm D^{+}$$ D + , and $$\mathrm D^{*+}$$ D ∗ + mesons in the transverse-momentum interval $$3< p_{\mathrm{T}} < 36$$ 3 < p T < 36  GeV/ $$c$$ c at midrapidity ( $$|y| < 0.5$$ | y | < 0.5 ), and charged particles with $$p_{\mathrm{T}} > 0.3$$ p T > 0.3  GeV/ $$c$$ c and pseudorapidity $$|\eta | < 0.8$$ | η | < 0.8 . This measurement has an improved precision and provides an extended transverse-momentum coverage compared to previous ALICE measurements at lower energies. The study is also performed as a function of the charged-particle multiplicity, showing no modifications of the correlation function with multiplicity within uncertainties. The properties and the transverse-momentum evolution of the near- and away-side correlation peaks are studied and comparedmore »
4. Abstract The multiplicity dependence of jet production in pp collisions at the centre-of-mass energy of $$\sqrt{s} = 13\ {\mathrm {TeV}}$$ s = 13 TeV is studied for the first time. Jets are reconstructed from charged particles using the anti- $$k_\mathrm {T}$$ k T algorithm with resolution parameters R varying from 0.2 to 0.7. The jets are measured in the pseudorapidity range $$|\eta _{\mathrm{jet}}|< 0.9-R$$ | η jet | < 0.9 - R and in the transverse momentum range $$5more » 5. A bstract The inclusive production of the J/ ψ and ψ (2S) charmonium states is studied as a function of centrality in p-Pb collisions at a centre-of-mass energy per nucleon pair$$ \sqrt{s_{\mathrm{NN}}} $$s NN = 8 . 16 TeV at the LHC. The measurement is performed in the dimuon decay channel with the ALICE apparatus in the centre-of-mass rapidity intervals − 4 . 46 < y cms < − 2 . 96 (Pb-going direction) and 2 . 03 < y cms < 3 . 53 (p-going direction), down to zero transverse momentum ( p T ). The J/ ψ and ψ (2S) production cross sections are evaluated as a function of the collision centrality, estimated through the energy deposited in the zero degree calorimeter located in the Pb-going direction. The p T -differential J/ ψ production cross section is measured at backward and forward rapidity for several centrality classes, together with the corresponding average 〈 p T 〉 and$$ \left\langle {p}_{\mathrm{T}}^2\right\rangle  p T 2 values. The nuclear effects affecting the production of both charmonium states are studied using the nuclear modification factor. In the p-going direction, a suppression of the production of both charmonium states ismore »


text:
Lemma 21.14.5 (Leray spectral sequence). Let $f : (\mathop{\mathit{Sh}}\nolimits (\mathcal{C}), \mathcal{O}_\mathcal {C}) \to (\mathop{\mathit{Sh}}\nolimits (\mathcal{D}), \mathcal{O}_\mathcal {D})$ be a morphism of ringed topoi. Let $\mathcal{F}^\bullet$ be a bounded below complex of $\mathcal{O}_\mathcal {C}$-modules. There is a spectral sequence

$E_2^{p, q} = H^ p(\mathcal{D}, R^ qf_*(\mathcal{F}^\bullet ))$

converging to $H^{p + q}(\mathcal{C}, \mathcal{F}^\bullet )$.

Proof. This is just the Grothendieck spectral sequence Derived Categories, Lemma 13.22.2 coming from the composition of functors $\Gamma (\mathcal{C}, -) = \Gamma (\mathcal{D}, -) \circ f_*$. To see that the assumptions of Derived Categories, Lemma 13.22.2 are satisfied, see Lemmas 21.14.1 and 21.14.3. $\square$

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).


text:
## Example of PL/I macro

January 27, 2021 Mainframe No comments , , ,

Up until last week PL/I macros were a bit of a mystery.  Most of the ones that I’d seen in customer code were impressively inscrutable, and if I had to look at any of them, my reaction was to throw my hands in the air and plead with the compiler backend guys for help.  Implementing one such macro has been very helpful to understanding how these work.

Here is a C program that roughly models some PL/I code of interest

The documentation for the ‘foo’ function says of the final return code parameter that it is 12 bytes long, and that the ‘rcvalues.h’ header file has a set of RCNNN constants and a RCCHECK macro that can be used to test for any one of those constants.  A possible C implementation of that header might look something like:

/* rcvalues.h */
#define RC000 0x0000000000000000LL
#define RC001 0x0000000123456789LL
/* ... */

#define RCCHECK( urc, crc ) ( memcmp( &(urc), &(crc), 8 ) == 0 )

PL/I APIs do not typically use modern constructs like typedefs.  The closest that I have seen is for an API header file (copybook in the mainframe lingo) is to declare a variable (which becomes a local variable with a specific name in the including module), which the programmer can refer to using the LIKE keyword, as in the following example:

I believe there is also a DEFINE keyword available in newer PL/I compilers, which provides a typedef like mechanism, but most existing code probably doesn’t use such new-fangled nonsense, when cut and paste has far superior maintenance characteristics.  For that reason, the API would be unlikely to have a typedef equivalent for the return code structure.  Instead, the PL/I equivalent of the C code above, would probably look like:

(i.e. the C code is really modeled on the PL/I code of this form, and if this was a C API, the API would have a struct declaration or a typedef for the return code structure)

The RCNNN constants would actually be found as named variables (not immutable constants) in the copy book, perhaps declared something like:

I struggled a bit to figure out what the PL/I equivalent of my C RCCHECK macro would be.  The following inner function correctly did the required type casting and comparisons:

The implementation is very long, since the entire declaration of the input parameter type has to be duplicated.

If I was to put this RCCHECK implementation above into my RCVALUES.inc header file, it would only work if all the customer declaration of their return code structure objects were field by field compatible.  What I really want is for my RCCHECK function to take the address of the parameter, and pass that instead of the underlying type.  That was not at all obvious to figure out how to do, but with some help, I was eventually able to construct a PL/I macro (with helper inner-function) of the following form:

It’s clearly no longer a one liner.  Some notes on this PL/I macro:

• The PL/I macro body looks like a regular PL/I function, but the begin-PROCEDURE and END statements start with % (% is not part of the PROC name.)
• Macro parameters and return values are explicit strings, regardless of the types of the parameters that were actually passed.
• In PL/I the || symbol is used for string concatenation, so this constructs output that inserts an ADDR() call around ARG1 token and then passes the ARG2 token as is.
• I don’t know if there’s a way to implement this macro in a way that doesn’t require a helper function, and still have the output work in the context of an IF statement.
• You have to explicitly enable the macro, using %ACTIVATE.  In my case, without %ACTIVATE, the RCCHECK symbol ends up as an undeclared external entry, and was no call to the @RCCHECK_HELPER function $${}^{[1]}$$.
• Observe that the PL/I macro provides a mechanism to jam whatever you want into the code, as the compiler’s macro preprocessor replaces the macro call tokens with the string that you have provided, leaving that string for the final compiler pass to interpret instead.

If I compile the code using this macro version of RCCHECK, the preprocessor output looks like:

I’m still pretty horrified at some of the macros that I’ve seen in customer code — they almost seem like the source equivalent of self modifying code.  You can’t figure out what is going on without also looking at all the output of the precompiler passes.  This is especially evil, since you can write PL/I preprocessor macros that generate preprocessor macros and require multiple preprocessor passes to produce the final desired output!

### Footnotes

[1] note that @ is a valid PL/I character to use in a symbol name, as is # and $— so if you want your functions to look like swear words, this is a language where that is possible. Something like the following is probably valid PL/I : V = #@$1A#@(1);

For added entertainment, your file names (i.e. PDS member names) can also be like ‘#@$1A#@’. Storing files with names like that on a Unix filesystem results in hours of fun, as you are then left with the task of figuring out how to properly quote file names with embedded$’s and #’s in scripts and makefiles.

## Mainframe development: a story, chapter 1.

April 19, 2018 Mainframe No comments , , , , , , , , , , , , ,

Once upon a time, in a land far from any modern developers, were languages named COBOL and PL/I, which generated programs that were consumed by a beast known as Mainframe. Developers for those languages compiled and linked their applications huddled around strange luminous green screens and piles of hole filled papers while chanting vaguely latin sounding incantations like “Om-padre-JCL-beget-loadmodule-pee-dee-ess.”

In these ancient times, version control tools like git were not available. There was no notion of makefiles, so compilation and link was a batch process, with no dependency tracking, and no parallelism. Developers used printf-style debugging, logging trace information to files.  In order to keep the uninitiated from talking to the Mainframe, files were called datasets.  In order to use graphical editors, developers had to repeatedly feed their source to the Mainframe using a slave named ftp, while praying that the evil demon EBCDIC-conversion didn’t mangle their work. The next day, they could go back and see if Mainframe accepted their offering.

[TO BE CONTINUED.]

Incidentally, as of a couple days ago, I’ve now been working for LzLabs for 2 years.  My work is not yet released, nor announced, so I can’t discuss it here yet, but it can be summarized as really awesome.  I’m still having lots of fun with my development work, even if I have to talk in languages that the beast understands.

## Unpacking a PL/I VSAM keyed write loop.

June 7, 2017 Mainframe No comments , , , , ,

I found myself faced with the task of understanding the effects of a PL/I WRITE loop that does the initial sequential load of a VSAM DATASET.  The block of code I was looking at had the following declarations:

     dcl IXUPD FILE UNBUFFERED KEYED env(vsam);
dcl
01 recArea,
03 recPrefix,
05 recID        PIC'(4)9' init (0),
05 recKeyC      CHAR (4)  init (' '),
03 recordData       CHAR (70) init (' ');

dcl recIndx FIXED BIN(31) INITIAL(0);

dcl keyListSize fixed bin(31) initial(10);
dcl keyList(10) char(8);

As a C++ programmer, there are a few of oddities here:

• Options for the FILE are specified at the file declaration point (or can be), not at the OPEN point.  They can also be specified at the OPEN point.  The designers of PL/I seem to have been guided by the general principle of “why have one way of doing something, when it can be done in an infinite variety of possible ways”.
• There is a hybrid “structure & variable” declaration above.  recArea is like an object of an unnamed structure, containing nested parts (with lots of ugly COBOL like nesting specifications to show the depth of the various “structure” members).  It’s something like the following struct declaration (with c++11 default initializer specifiers):

#include <stdio.h>

int main() {
struct {
struct {
char recID[4]{'0', '0', '0', '0'};
char recKeyC[4]{' ', ' ', ' ', ' '};
} recPrefix;
char recordData[70]{ ' ', ' ', /* ... 70 spaces total */ };
} recArea;

printf( "recID: %.4s\n", recArea.recPrefix.recID );
printf( "recKeyC: '%.4s'\n", recArea.recPrefix.recKeyC );

return 0;
}

To PL/I’s credit, only ~45 years after the creation of PL/1 did C++ add a simple way of encoding default structure member initializers.

We’ll see below that PL/I lets you access the inner members without any qualification if desired (i.e. recID == recArea.recPrefix.recId). The PL/I compiler writer is basically faced with the unenviable task of continually trying to guess what the programmer could have possibly meant.

• The int32_t types have the annoying “mainframe”ism of being referred to as 31-bit integers (FIXED BIN(31)). Even if the high bit in pointers is ignored by the hardware (allowing the programmer to set 0x80000000 as a flag, for example for end of list in a list of pointers), that doesn’t mean that the registers aren’t fully 32-bit, nor does it mean that a 32-bit integer isn’t representable. I can’t for the life of me understand why a 32-bit integer variable should be declared as FIXED BINARY(31)?
• The recID variable is declared with a PICTURE specification, as we also saw in COBOL code. PIC ‘9999’ (or PIC'(4)9′, for “short”), means that the character array will have four (EBCDIC) digits in it. I don’t quite understand this specification in this case, since the code (to follow) seems to put ‘RNNN’, where N is a digit in this field.

Here’s how the declarations above are used:

keyList(1) = 'R001';
keyList(2) = 'R002';
...
OPEN FILE(IXUPD) OUTPUT;

put skip list ('====== Write record to file by key.');
do while (recIndx < keyListSize);
recIndx = recIndx + 1;
recID = recIndx;
recKeyC = 'Abcd';
recordData = 'Data for ' || keyList(recIndx);
write FILE(IXUPD) FROM(recArea) KEYFROM(keyList(recIndx));
end;
put skip list (recIndx, ' records is written to file by key.');

CLOSE FILE(IXUPD);

My guess about what this ‘WRITE FROM(recArea)’ would do is to create records of the form:

0001AbcdData for R001
0002AbcdData for R002
0003AbcdData for R003
...

However, the VSAM DATASET (which was created with key offset 0, and key size 8), actually ends up with:

R001    Data for R001
R002    Data for R002
R003    Data for R003
...

Despite the fact that we are writing from recArea, which includes the recID and recKeyC fields (numeric and character respectively), only the non-key portion of the WRITE “data payload” ends up hitting the disk.

If that is the case, where do the spaces in the key-portion of the records come from? Again, the C programmer in me is interfering with my understanding. I look at:

dcl keyList(10) char(8);
keyList(1) = 'R001';

and think that keyList(1) = “R001\x00\x00\x00\x00”, but it must actually be space filled in PL/I! This seems to be confirmed emperically, based on the expected results for the test, but I can also see it in the debugger after manually relocating the 32-bit mainframe address:

(gdb) p keyLen
$1 = 8 (gdb) p /x aKey + 0x7ffbc4000000$2 = 0x7ffbc5005740
(gdb) set target-charset EBCDIC-US
(gdb) p (char *)$2$3 = 0x7ffbc5005740 "R001    R002    R003    R004    R005    R006    R007    R008    R009    R010    "

The final form of the records in the VSAM DATASET (mainframe for a file), is now fully understood. Note that the data disagrees with the PICTURE specification for the recID field in the recData variable declaration, but that’s okay, at least for this part of the program, since there is never any store to that field that is non-numeric. Would anything even have to have been written to recID or recKeyC … I suspect not? Once we have R00N in that part of the record what happens if we read it into recData with the numeric only PICTURE specification? Does that raise a PL/1 condition?

ps. Notice how the payload for the keyList array entries is nicely packed into memory. This is done in a very non-C like fashion with no requirement for an array of pointers and the corresponding cache hit loss those pointers create when accessing a big multilevel C array.

## Still amused reading my PL/1 book: external storage.

May 28, 2017 Mainframe No comments , , , ,

The z/OS Enterprise PL/I, Language Reference is the primary reference I have been using for the PL/1 that I’ve had to learn, but it is too modern, and not nearly as fun as the 1970’s era “PL/I structured programming book” I’ve got:

I’m not sure what a disk pack is, but I presume it is a predecessor to the hard drive.

Edit: Art Kaufmann, who I worked with at IBM, knew what a disk pack was (picture above from wikipedia):

“Back in the day, disk drives used removable media called “disk packs.” These were stacks of disks (usually about 2′ across) on a spindle with a plastic cover. See the IBM 2311 and 2314 for examples of these drives. You’d open the drive, lower the pack into place, twist the handle and remove the cover, then close the drive. The big risk was getting dust in when the cover was off; that would cause a head crash. Then some nitwit operator would either put a different disk pack in that drive (ruining that pack) or move the bad pack to a new drive, crashing that one. Or both.”


text:
### Still have math questions?

Let u $$= \square ,$$ then the quadratic equation in $$u$$ is $$\square - 10 = 0$$
$$u= \frac{1}{x}\\u^2- 9u- 10= 0$$


text:
# Order of Operations – Examples and Practice Problems

The order of operations allows us to perform multiple algebraic operations in the correct order. Following the order of operations is extremely important, otherwise, we will end up with the wrong answer.

In this article, we will look at a summary of the order of operations along with examples with answers and exercises to solve.

##### ALGEBRA

Relevant for

Exploring examples with answers of the order of operations.

See examples

##### ALGEBRA

Relevant for

Exploring examples with answers of the order of operations.

See examples

## Summary of order of operations

The order of operations are the rules that indicate the order in which we must solve the multiple operations in an algebraic expression. One way to remember the order of operations is with PEMDAS, where each letter represents a mathematical operation:

The order of operations tells us that the order in which we must solve the operations in an expression is:

1. Parentheses: Parentheses and other grouping signs take precedence over other operators.

2. Exponents: We solve all exponential and radical expressions, that is, powers and roots.

3. Multiplication and division: Multiplication and division are on the same level, so we solve from left to right when we have several multiplications or divisions.

4. Addition and subtraction: Addition and subtraction are on the same level, so we solve from left to right when we have several additions or subtractions.

## Order of operations – Examples with answers

The following examples of order of operations with answers to help with the retention of the concepts. Each exercise is solved step by step to understand the procedure used.

### EXAMPLE 1

Simplify the expression .

First, we have to simplify the expression that is inside the parentheses, then we apply the exponent and finally, we perform the addition:

### EXAMPLE 2

Simplify the expression .

When we have multiple grouping signs, we start with the inner parentheses and solve outward.

First, we solve the expression inside the parentheses, then, we solve the expression inside the brackets. After that, we apply the exponent and finish with the addition:

### EXAMPLE 3

Simplify the expression .

We simplify from the inside out, first the parentheses and then the brackets. After simplifying the grouping signs, we perform the division, followed by the addition of 4:

### EXAMPLE 4

Simplify the expression .

We start by solving the expression inside the parentheses and then applying the exponent. Then, we do the multiplication by -2, followed by division by 3 to finish adding 12:

### EXAMPLE 5

Simplify the expression .

In this case, we have the variable x. The order of operations is the same, with the only difference that we must combine only like terms. Therefore, we start by expanding the parentheses. Then, we simplify the expression inside the brackets and then multiply this expression by 4. We finish by adding 12 x:

### EXAMPLE 6

Simplify the expression .

We start by expanding the parentheses by applying the negative sign. Then, we combine like terms in the expression inside the brackets and apply the negative sign. Then, we combine like terms in the expression inside the curly braces and end up applying the negative sign:

### EXAMPLE 7

Simplify the expression .

We must start by applying the order of operations individually both in the numerator and in the denominator of each fraction. Then, we simplify the fractions and end by adding the resulting expression:

### EXAMPLE 8

Simplify the expression .

This example is similar to the previous one since we must apply the order of operations individually to the numerator and the denominator to then simplify the fraction:

## Order of operations – Practice problems

The following practice problems can be solved to test your knowledge about the order of operations. Just choose the correct answer and click verify to verify your answer. If you have trouble solving these problems, review the solved examples above carefully.


text:
# Homework Help: Finding the volume of these figures

1. Sep 25, 2011

### yik-boh

1. The problem statement, all variables and given/known data

Find the volume of the described figures

1. A pyramid with height h and base an equilateral triangle with side a (a tetrahedron).

2. Find the volume common to two spheres each with radius r, if the center of each sphere lies on the surface of the other sphere.

These are hard problems and I really do not know what to do. Our teacher gave this to us as a challenge and I really would like to know how to solve these two. I hope you can help me by explaining each important step you will take. I hope you can make it detailed as much as possible. I really am having a hard time in Calculus. Thanks! :)

2. Sep 25, 2011

### CompuChip

For 1): you can slice the tetrahedron horizontally into pieces of height dz. Then each piece will again be an equilateral triangle whose sides decrease from a at z = 0 to 0 at z = h.

For 2): you can slice the intersection of the spheres into circles of thickness $d\theta$ whose radius $r(\theta)$ increases from $r(\theta = -\pi / 2) = 0$ to $r(\theta = 0) = r$ (see attachment) and you can use some fancy trig work to find the expression for r(theta).

#### Attached Files:

• ###### circles.jpg
File size:
12.8 KB
Views:
86
3. Sep 25, 2011

### HallsofIvy

It was you the teacher was challenging, not us! There are a number of different ways to do these problems ranging from looking up standard formulas to using Calculus as CompuChip suggests.

4. Sep 25, 2011

### yik-boh

I'm sorry but I don't exactly get it. I'm really having a hard time in Calculus right now.

For #1, what is dz? Just a representation for height? and I can't picture properly the tetrahedron I need to slice.

For #2, I really don't get it. I'm sorry.

I hope you'll still explain it to me.

5. Sep 25, 2011

### yik-boh

I got the 1st one already. Only #2 left.

6. Sep 26, 2011

### CompuChip

Here is another hint, hopefully it clarifies a bit better what I meant.
The volume of the little circular disc (actually, it's a cylinder with radius r and thickness dtheta) that I drew is $\pi r^2 \, d\theta$. Of course you'll have to express r as a function of theta before you do the integration (and find the appropriate limits for theta).

File size:
6.7 KB
Views:
84


text:
# vector lattice

An ordered vector space whose underlying poset is a lattice is called a vector lattice. A vector lattice is also called a Riesz space.

For example, given a topological space $X$, its ring of continuous functions $C(X)$ is a vector lattice. In particular, any finite dimensional Euclidean space $\mathbb{R}^{n}$ is a vector lattice.

A vector sublattice is a subspace of a vector lattice that is also a sublattice.

Below are some properties of the join ($\vee$) and meet ($\wedge$) operations on a vector lattice $L$. Suppose $u,v,w\in L$, then

1. 1.

$(u+w)\vee(v+w)=(u\vee v)+w$

2. 2.

$u\wedge v=(u+v)-(u\vee v)$

3. 3.

If $\lambda\geq 0$, then $\lambda u\vee\lambda v=\lambda(u\vee v)$

4. 4.

If $\lambda\leq 0$, then $\lambda u\vee\lambda v=\lambda(u\wedge v)$

5. 5.

If $u\neq v$, then the converse holds for 3 and 4

6. 6.

If $L$ is an ordered vector space, and if for any $u,v\in L$, either $u\vee v$ or $u\wedge v$ exists, then $L$ is a vector lattice. This is basically the result of property 2 above.

7. 7.

$(u\wedge v)+w=(u+w)\wedge(v+w)$ (dual of statement 1)

8. 8.

$u\wedge v=-(-u\vee-v)$ (a direct consequence of statement 4, with $\lambda=-1$)

9. 9.

$(-u)\wedge u\leq 0\leq(-u)\vee u$

###### Proof.

$(-u)\wedge u\leq u$ and $(-u)\wedge u\leq-u$ imply that $2((-u)\wedge u)\leq u+(-u)=0$, so $(-u)\wedge u\leq 0$, which means $0\leq-((-u)\wedge u)=u\vee(-u)$. ∎

10. 10.

$(a\vee b)+(c\vee d)=(a+c)\vee(a+d)\vee(b+c)\vee(b+d)$, by repeated application of 1 above.

Remark. The first five properties are also satisfied by an ordered vector space, with the assumptions that the suprema exist for the appropriate pairs of elements (see the entry on ordered vector space for detail).

Title vector lattice VectorLattice 2013-03-22 17:03:13 2013-03-22 17:03:13 CWoo (3771) CWoo (3771) 7 CWoo (3771) Definition msc 06F20 msc 46A40 Riesz Space vector sublattice


text:
0 like 0 dislike
97 views
Let $A$ and $B$ be $n \times n$ matrices. If $A+B$ is invertible, show that $A(A+B)^{-1} B=$ $B(A+B)^{-1} A$. [Don't assume that $A B=B A$ ].
| 97 views

0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike


text:
The Annals of Probability

Optimal Stopping with Sampling Cost: The Secretary Problem

Thomas J. Lorenzen

Abstract

A secretary problem is an optimal stopping problem based on relative ranks. To the usual formulation of the secretary problem we add a cumulative interview cost function $h(\cdot)$, no longer obtaining "cutoff point" rules. For an appealing form of $h(\cdot)$ we examine the limiting results using the infinite secretary problem. It is shown that the other appealing form of $h(\cdot)$ leads to trivial limiting results. A large class of problems is considered and recursive equations leading to the limiting solution are given. In particular we solve the problem of minimizing expected rank with a linear interview cost function. An approximation to the rank problem with fixed cost $c$ per interview is obtained (for all values of $c$) through the solution of a single differential equation.

Article information

Source
Ann. Probab. Volume 9, Number 1 (1981), 167-172.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1176994519

JSTOR


text:
# FAQ¶

Where does the name “OWLIM” (the former GraphDB name) come from?
The name originally came from the term “OWL In Memory” and was fitting for what later became OWLIM-Lite. However, OWLIM-SE used a transactional, index-based file-storage layer where “In Memory” was no longer appropriate. Nevertheless, the name stuck and it was rarely asked where it came from.
What kind of SPARQL compliance is supported?

All GraphDB editions support:

Is GraphBD Jena-compatible?
Yes, GraphBD is compatible with Jena 2.7.3 with a built-in adapter. For more information, see Using GraphDB with Jena.
What are the advantages of using solid-state drives as opposed to hard-disk drives?

We recommend using enterprise grade SSDs whenever possible as they provide a significantly faster database performance compared to hard-disk drives.

Unlike relational databases, a semantic database needs to compute the inferred closure for inserted and deleted statements. This involves making highly unpredictable joins using statements anywhere in its indices. Despite utilising paging structures as best as possible, a large number of disk seeks can be expected and SSDs perform far better than HDDs in such a task.

How to find out the exact version number of GraphDB?

The major/minor version and patch number are part of the GraphDB distribution .zip file name. They can also be seen at the bottom of the GraphDB Workbench home page, together with the RDF4J, Connectors, and Plugin API’s versions.

A second option is to run the graphdb -v startup script command if you are running GraphDB as a standalone server (without Workbench). It will also return the build number of the distribution.

Another option is to run the following DESCRIBE query in the Workbench SPARQL editor:

DESCRIBE <http://www.ontotext.com/SYSINFO> FROM <http://www.ontotext.com/SYSINFO>

It returns pseudo-triples providing information on various GraphDB states, including the number of triples (total and explicit), storage space (used and free), commits (total and whether there are any active ones), the repository signature, and the build number of the software.

How to retrieve repository configurations?
To see what configuration data is stored in a GraphDB repository, go to Repositories and use Download repository configuration as Turtle icon

Then you could open the result file named repositoryname-config.ttl

Why can’t I use my custom rule file (.pie) - an exception occurred?
To use custom rule files, GraphDB must be running in a JVM that has access to the Java compiler. The easiest way to do this is to use the Java runtime from a Java Development Kit (JDK).
How to speed up a slow repository with enabled security when each request includes HTTP basic authentication?

Every HTTP authentication request takes significant time due to the bcrypt algorithm which encrypts the clear text password to match with the hash in $GDB_HOME/work/workbench/settings.js. The best solution is to do one-time authentication and keep the JWT string. JWT has a much lower overhead. 1. Login and generate the authorization curl -X POST -I 'http://localhost:7200/rest/login/admin' -H 'X-GraphDB-Password: root'  1. Pass the returned JWT key curl -H 'Authorization: GDB eyJ1c2VybmFtZSI6ImFkbWluIiwiYXV0aGVudGljYXRlZEF0IjoxNTU3OTIzNTkxNDA0fQ==.OwSkajbUoHHsQGfwvaCxbb1f7bn0PJUeL4VbGEmNcWY=' http://localhost:7200/repositories/SYSTEM/size  The JWT token expires every 30 days. To change the encryption algorithm from bcrypt to SHA-256 supported by the older GDB version, update the password token in $GDB_HOME/work/workbench/settings.js with the encrypted value of: password{user}

echo root{admin} | sha256sum

{
"grantedAuthorities": [


text:
Matthew Doty wrote:

> > > **Puzzle 8.** What simple law do Daniel's preorders obey, that does not hold for the real numbers with its usual notion of \$$\leq\$$?

> > Both obey the *symmetry* rule: if \$$x \leq y\$$ then \$$y \leq x\$$

> > **Puzzle 9.** What do you call preorders that obey this law?

> They are [*equivalence relations*](https://en.wikipedia.org/wiki/Equivalence_relation).

Right! This is what I was looking for. But Dan Schmidt was on the right track, because any partition determines an equivalence relation, and vice versa. They are two ways of thinking about the same thing.

This sort of preorder is sort of the extreme opposite case from a total order, since total orders obey the **antisymmetry** rule: if \$$x \leq y\$$ and \$$y \leq x\$$ then \$$x = y\$$.

What are all the total orders that are also equivalence relations?


text:
# Why is a compound as common as water considered a "weird" chemical substance?

Dec 1, 2016

#### Explanation:

Water contains hydrogen bonds between the molecules which means that it will remain as a liquid at much higher temperatures than you would expect. This also enables the molecules to 'stick' together and gives water surface tension. The way that water forms into a solid also means that the solid of water (ice) is much less dense than the liquid, allowing it to float.

Dec 1, 2016

Consider its normal boiling point, which you know........

#### Explanation:

Compare the normal boiling point of water to that of $C {H}_{4}$, $S i {H}_{4}$, $H F$, ${H}_{2} S$, or $P {H}_{3}$. The boiling point of water is disproportionately high. This is also unusual in that water has a very small molecular mass (and thus little possibility of $\text{van der Waals interactions}$.

And now compare the density of liquid water to the density of solid water. Icebergs float in the ocean! I grant that things are more buoyant in salty water, however, ice cubes also float in ice-water or in your gin and tonic. This is highly unusual, in that, save water, there are very few substances that as liquids are DENSER than their solid phases.

I would consult a textbook on the unusual properties of water. These properties are largely the result of the propensity of the water to $\text{hydrogen-bond}$ intermolecularly.


text:
Parse VEP VCF with variantAnnotation
0
3
Entering edit mode
2.4 years ago
jeni ▴ 60

Hi!

I am trying to obtain a data frame from a vcf read with VariantAnnotation package. This vcf is the output of VEP (variant effect predictor), so, the columns corresponding to its annotations are not properly separated and I cannot parse them to different columns of a dataframe:

This is the line corresponding to VEP annotation info header:

##INFO=<ID=CSQ,Number=.,Type=String,Description="Consequence annotations from Ensembl VEP. Format: Allele|Consequence|IMPACT|SYMBOL|Gene|Feature_typeFeature|BIOTYPE|EXON|INTRON">

While the header for the rest of INFO fields follow this pattern:

##INFO=<ID=CONTQ,Number=1,Type=Float,Description="Phred-scaled qualities that alt allele are not due to contamination">
##INFO=<ID=ECNT,Number=1,Type=Integer,Description="Number of events in this haplotype">

as you can see, CSQ is the corresponding field to VEP annotation, which includes a lot of different parameters separated by "|" (Allele|Consequence|IMPACT,etc). This means that every field of data given by VEP is writen in the same field as a string with '|' separating them, instead of being writen as different INFO fields.

Is there any way to transform these field names as column names, separating each field inside CSQ by |; while maintaining the parsing of the rest of the INFO fields (CONTQ, DP, ECNT as colums with their corresponding values).

snp R • 2.0k views
2
Entering edit mode

Shameless Self Promotion I recently wrote an extension for R parsing VEP. https://github.com/lindenb/rbcf

# load rbcf
library(rbcf)
# A vcf
fp <- bcf.open(filename,FALSE)
vc <- NULL
while(!is.null(vc<-bcf.next(fp))) {
if(variant.has.attribute(vc,"CSQ")) break;
}
if(!is.null(vc)) {
predictions<-variant.vep(vc)
}
bcf.close(fp)
predictions

Allele             Consequence   IMPACT   SYMBOL            Gene
1       C downstream_gene_variant MODIFIER   KLHL17 ENSG00000187961
2       A downstream_gene_variant MODIFIER   KLHL17 ENSG00000187961
3       C downstream_gene_variant MODIFIER C1orf170 ENSG00000187642
4       A downstream_gene_variant MODIFIER C1orf170 ENSG00000187642
5       C          intron_variant MODIFIER  PLEKHN1 ENSG00000187583
6       A          intron_variant MODIFIER  PLEKHN1 ENSG00000187583
7       C          intron_variant MODIFIER  PLEKHN1 ENSG00000187583
8       A          intron_variant MODIFIER  PLEKHN1 ENSG00000187583
9       C          intron_variant MODIFIER  PLEKHN1 ENSG00000187583
10      A          intron_variant MODIFIER  PLEKHN1 ENSG00000187583
11      C downstream_gene_variant MODIFIER C1orf170 ENSG00000187642
12      A downstream_gene_variant MODIFIER C1orf170 ENSG00000187642
13      C downstream_gene_variant MODIFIER C1orf170 ENSG00000187642
(...)

0
Entering edit mode

For which R version is 'rbcf' available? I cannot install it in R 3.6.1. I have been reading the git link, but I cannot install it as it is indicated there because I am working from my local pc (which is windows), is it possible to install it directly with R?

0
Entering edit mode

Hey, nice tool, this is exactly what I am looking for :)

Testing went fine, except I only always get one single variant in the "predictions" - any idea why ? And could you also add how to best combine this table with the genotypes ?

0
Entering edit mode

Yes I am also getting the same issue, the tool only seems to pull the first variant, how do you get it to work for all variantrs?

0
Entering edit mode

as you can see, each element is separated by "|" instead of semicolons ";"

i don't see it. I see the CSQ tag which is a STRING. The 3 others TAG define a number.

0
Entering edit mode

Okay I've edited the question explaining it better


text:
Problem: What is the focal length of the eye-lens system when viewing an object 32 cm from the eye? Assume that the lens-retina distance is 2.0 cm. Follow the sign conventions.

FREE Expert Solution

Lens equation:

$\overline{)\frac{\mathbf{1}}{{\mathbit{s}}_{\mathbit{o}}}{\mathbf{+}}\frac{\mathbf{1}}{{\mathbit{s}}_{\mathbit{i}}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbit{f}}}$

so = 32 cm

Problem Details

What is the focal length of the eye-lens system when viewing an object 32 cm from the eye? Assume that the lens-retina distance is 2.0 cm. Follow the sign conventions.