Welcome to Cyrus Naficy Academy, you made it! I am so excited to make your children from ages 6-10 enjoy learning. My name is Cyrus Naficy. I am a two time Capitol Debate finalist and a one time champion. I am also working on advanced in math, and I am ready to help your kids succeed.
Chief Executive Officer
Hello, I am Cyrus Naficy. I founded this business as a 13 year old to help young children get a head start. Children learn and function the most when they are young, so that is why I am here to take advantage of their young learning superpowers. I will also be teaching many of the classes listed in the Classes tab.
Chief Marketing Officer
Susie Naficy is my mom. She helps out with business, social media, YouTube, and website advice. Thanks mom!
Chief Talent Officer
Educators and Investors
Hey, I am Darsh! I joined the business to take part in the kids teaching kids program. I love to teach kids and love math. I am a year ahead in math and also do math out of school. I also participate in math competitions. I am looking forward to tutoring your child!
Here at Cyrus Naficy Academy, we love to teach kids. That is why we have tutors from all over the world! Our tutors would love to help your child in any way possible! To be connected with a tutor, please fill out a contact form and we will connect you with a tutor that we think fits you best!


2048 Video Game Turn
2048 is a solitary player sliding square riddle game planned by Italian web engineer Gabriele Cirulli. The goal of the game is to slide numbered tiles on a matrix to join them to make a tile with the number 2048; be that as it may, one can keep on playing the game in the wake of arriving at the objective, making tiles with bigger numbers. 2048 Cupcakes Game
2048 is played on a dim 4×4 matrix, with numbered tiles that slide when a player moves them utilizing the four bolt keys. Each turn, another tile will arbitrarily show up in an unfilled spot on the board with an estimation of either 2 or 4. Tiles slide beyond what many would consider possible the picked way until they are halted by either another tile or the edge of the network. On the off chance that two tiles of a similar number impact while moving, they will converge into a tile with the all out estimation of the two tiles that collided. The subsequent tile can't converge with another tile again in a similar move. Higher-scoring tiles emanate a delicate gleam.
he match is dominated when a tile with an estimation of 2048 shows up on the board, consequently the situation. In the wake of arriving at the 2048 tile, players can keep on playing (past the 2048 tile) to arrive at higher scores. At the point when the player has no lawful moves (there are no vacant spaces and no adjoining tiles with a similar worth), the game closures.
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Math Flash is a free trial software application from the Mathematics subcategory, part of the Education category.
The app is currently available in English and it was last updated on 2010-02-07. The program can be installed on WinXP, Windows Vista Home Basic, Windows Vista Home Premium, Windows Vista Business, Windows Vista Enterprise, Windows Vista Ultimate, Windows 7 Starter, Windows 7 Home Premium, Windows 7 Professional, Windows 7 Enterprise, Windows 7 Ultimate.
Flash card style single, double, and triple digit addition and subtraction practice for elementary students. Math Flash is used in homes and schools around the world.
Math Flash (version 4.6) has a file size of 1.71 MB and is available for download from our website.
Just click the green Download button above to start. Until now the program was downloaded 115 times.
We already checked that the download link to be safe, however for your own protection we recommend that you scan the downloaded software with your antivirus.


Ball Mill Operating Speed - Mechanical Operations Solved Problems .Sep 11, 2014 . In a ball mill of diameter 2000 mm, 100 mm dia steel balls are being used for grinding. . Calculations: The critical speed of ball mill is given by,.critical speed of ball mill formula,Lecture 2 - SlideShareJan 23, 2011 .
< Grinding action

- The grinding in ball mill is therefore .. as the critical speed of the mill and is given by formula:

√ N.SAGMILLING.COM .:. Mill Critical Speed DeterminationThe "Critical Speed" for a grinding mill is defined as the rotational speed where . This is the rotational speed where balls will not fall away from the mill's shell. . You may use the Mill Liner Effective Width calculation to determine this value.
Talk with the Experts at Paul O. Abbe about your process requirements and Ball Mill Loading, Wet Milling, Size Reduction and Mill Speed - Critical Speed needs.
information on ball mills. . A Ball Mill grinds material by rotating a cylinder with steel grinding balls, . This formula calculates the critical speed of any ball mill.
The Effect of Fraction of Mill Critical Speed on Kinetic Breakage Parameters of Clinker and Line in a Laboratory Ball Mill V. Deniz, A. Gelir & A. Demir
balls, time of grinding, particle density and speed of the ball mill (rpm) have been considered . The critical speed is calculated as under . rR g. 2. 1 nc. - π. =.
Jan 23, 2011 .
< Grinding action

- The grinding in ball mill is therefore .. as the critical speed of the mill and is given by formula:

√ N.
Apr 27, 2016 . Contact Us: wws.stonecrushersolution/solutions/solutions.
critical speed of ball mill formula,
May 9, 2000 . A useful and simple equation describing the grinding momentum is M x V .. The theoretical critical speed of a ball mill is the speed at which the.
There are two main methods used to calculate critical speed—the Rayleigh–Ritz method and Dunkerley's method.
Keywords: Comminution, energy efficiency, ball milling. ... Figure 3-7: Influence of % of critical speed (top) and % of mill filling (bottom) on ... particle breakage mechanisms, ball milling operations, power draw calculation methods and the.
time of grinding, particle density, and speed of the ball mill (rpm). An attempt has been .. rotation speed is called the 'critical speed' (nc). This phenomenon is.
Calculations for mill motor power, mill speed and media charge. Advantages . To calculate the motor power required for a cylindrical type ball mill, the following formula can be applied : W = 0.04116 . Where : Nc = Critical speed. D = Internal.
A ball mill, a type of crusher, is a cylindrical device used to grind chemicals or mix compositions. . The critical speed is 'the speed when a ball mill becomes a centrifuge' and may be . (*2) based on approxlculation, not yet confirmed.
Ball mills are horizontal cylindrical shaped equipment that finds application in . of critical speed); With critical speed (rpm) denoted by formula nC = 42.29/vd (d.
the correct power required to grind ore in a SAG mill, by developing ore hardness variability ... Critical speed is calculated from the following equation: .. capacity by about 9%, considering the ball mill if it also has 11 MW of installed power.
In milling practice the formula (2.3) is applied in the modified form which en- ... of mill. Above a certain critical speed, the balls will be pinned to the walls of the.
creating a cheap (under $100) ball mill. The experiment . the dryer drum, which rotates at a speed of 73 rpm based on . the formula for critical speed becomes:
critical speed of ball mill formula,
Ball-mill scale up (Bond's Law). Data: ○ Bond work index . Mill Power Draw Calculation (Equations). ○ Arbiter and . The fraction of the mill critical speed f c. 3.
May 6, 2004 . fCs. – Fraction of critical speed. Ss. – Ball size factor. To determine the power that a dry grinding needs, full grate discharge mill. Equation 1 is.
Critical Speed (r.p.m.) is commonly considered as the hypothetical mill speed at which . The production rate of batch ball mills is relatively small and often is.
High filling degrees and high percentage of critical speed lead to ball charge . liners [m] Mill speed [min ] Power consumption factor [-] c = 30 Formula (8) allows.
Design and Optimization of Ball Mill for Clinker Grinding in Cement Plant . We proposemore precise empirical equation for modified HGI relating ... Critical speed of the mill is rotational speed relative to speed at which centrifugal force just.


Definition: Interpolation method which uses data from the four pixels at the sides (not at the corners) of the pixel being worked on. * Because it uses fewer pixels than bicubic interpolation it operates a little more quickly.
Bilinear is not linear
The interpolation is linear in two directions - the x and the y, but is not actually linear in the interpolation direction, the one that matters. Here, it is quadratic.
Related Terms: bicubic interpolation
Previous Term: bilevel Next Term: B-spline


What It Measures
The z-score is a measure of the financial health of a company. Devised in the 1960s by Edward Altman, the score uses statistical techniques to predict the likelihood that a company will fail because of bankruptcy within two years.
The z-score was originally created based on Altman’s analysis of 33 bankrupt manufacturing companies with assets averaging $6.4 million and a further 33 nonbankrupt companies with assets between $1 million and $25 million. Altman’s analysis showed that 95% of the bankrupt companies had a z-score that suggested financial problems.
Why It Is Important
Since the 1980s, auditors have used the z-score to help identify companies with serious cash problems. The measure is also used to help score applicants for loans. Stockbrokers commonly use the z-score to determine if a company is a good investment.
How It Works in Practice
The z-score combines five common business ratios and uses a weighting system devised by Altman to produce a score somewhere between −4 and +8. Each of the components that make up the final z-score are rated independently, and each component has a different weight in the calculation of the overall z-score. The exact emphasis on each factor can vary slightly from one industry to another, using more specific z-score calculators.
All the information needed to calculate a z-score is available in company financial reports. The original formula to calculate a z-score is as follows:
z = 1.2T1 + 1.4T2 + 3.3T3 + 0.6T4 + 0.999T5
T2 = retained earnings ÷ total assets
T3 = earnings before interest and tax ÷ total assets
T5 = sales ÷ total assets
A score can be analyzed as follows:
> 2.99: the company is considered “safe”
1.8–2.99: there is some risk of financial distress
< 1.8: there is serious risk of financial distress
Tricks of the Trade
Although the numbers that go into the z-score can be influenced by external events, it is a useful tool to provide a quick analysis of where a company stands compared to competitors, and for tracking the risk of insolvency over time.
Studies have shown the z-score is an accurate prediction of company failure rates in between seven and eight out of 10 cases.
The formula was originally devised to be used for public companies, but amendments have since been made to allow z-scores to be calculated for privately held companies. In this case, the calculation that should be used is as follows:
0.717T1 + 0.87T2 + 0.420T4 + 0.998T5


Mathematics is a vital key to success in the world!
Math is a methodical explanation of our universe! Math makes our life orderly and helps eliminate chaos. Many human qualities are developed and strengthened by mathematics including the ability to reason, to create, to think abstractly or use spatial thinking, critical thinking skills, and problem-solving abilities.
So! What does all this have to do with the kinds of things I normally blog about you may ask? Not a darn thing! I just thought the little story I posted below was quite illustrative of that point. And, it made me chuckle, so I thought I would share it! It is taken from a Twitter post by @Bofferson:
King Geoff II looked out from his castle window.
“How big is their army?”
“10,000 men Sire.”
“9,000 men Sire.”
“So as a percentage, how much bigger is their army than ours?”
“Um mm, 1000%?”
“We’d better surrender then.”
And that’s why math is so important kids!
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17 thoughts on “Mathematics! Is It Really That Important!”
I tackled this mathematics seriously,before Laugh!!
… this calculation, though I was studying at elementary school…
Is this correct? (T▽T)
LOL! You got it, Nasuko! 👍
Thanks! I thought so!
I can’t wait to forward this to my wife….a high school math teacher. Funny! Thanks! Reid
Great! I hope she enjoys it!
I am quite a good in Mathematics from college to university level, but still unable to found those places where Trigonometry, Derivation and Integration are used.
I know from experience that Trigonometry is used a great deal in the military.
Hmm good to hear that at least it’s being user in somewhere.
Wonderful and hilarious! I really liked the opening paragraph.
Thanks! And, thanks for stopping by to comment. 👍


West Ferris shines in school rankings
West Ferris Secondary School has once again achieved high marks from the Fraser Institute as part of the conservative think tank's latest school rankings.
The local high school was highlighted by the institute Sunday as second among the 10 fastest-improving secondary schools in the province for Grade 9 applied math.
Last year – also as part of the institute's Report Card on Ontario’s Secondary Schools – West Ferris was the second fastest improving secondary school in the province.
“Despite recent headlines about disappointing math scores in province-wide testing across Ontario, some secondary schools are bucking the trend,” states the institute’s release regarding the annual report.
The latest report card finds that 37 high schools in Ontario have shown statistically significant improvement over the last four years in Grade 9 academic math and 47 schools have improved in applied math.
West Ferris' applied math score of 2.9 (out of four) in 2017 is up from 1.5 in 2013. And, with an overall score of 7.2 (out of 10), the local high earned a ranking of 175 out of 747 anglophone and francophone public and Catholic secondary schools, as well as small number of independent and First Nations schools.
The report ranks the schools on seven academic indicators based on results of annual province-wide Grade 9 math and Grade 10 literacy tests.
Chippewa Secondary School follows closely behind West Ferris in overall score with a 7.1, ranking 196 on the list of 747 schools.
St. Joseph Scollard Hall's 6.6 score earned it the 292nd spot on the list, followed by Widdifield Secondary School with a score of 6.3 and ranking of 355. Ecole Secondaire Catholique Algonquin placed 612th on the list with an overall score of 4.6.
“If struggling schools want to improve math results, they can find out what works for improving schools and, wherever possible, adopt these proven methods,” said Peter Cowley, director of school performance studies at the Fraser Institute.
Crucially, the improving schools are located across Ontario — in both urban and rural areas — and serve different types of communities and students.
For example, the fastest-improving school in academic math is Stayner Collegiate Institute near Collingwood, which improved its average score from 2.0 to 2.8 out of four. The fastest improver in applied math is C.W. Jeffreys Collegiate Institute in Toronto’s Jane and Finch area, which improved its score from 1.8 in 2013 to 3.2 in 2017. Likewise, schools as far north as Kapuskasing and Sioux Lookout have improved in math, as have schools in Windsor, Welland, rural communities outside of Ottawa, and in downtown Toronto.
Moreover, some schools serving large numbers of special needs students have also shown statistically significant improvement in math. For example Geraldton Composite High School in northern Ontario is one of the top 10 fastest improvers in academic math even though 52 per cent of its students have special needs.
“These schools are proof that no one city and no one type of student or socioeconomic situation has a monopoly on improvement—it’s possible for every school to improve, whether in math or any other area of the curriculum,” Cowley said.
This year’s report card, available at www.compareschoolrankings.org.


The Partial Derivative of B
The Partial Derivative of the Magnetic Flux Density
On this page we define the symbol:
Briefly, this is simply the negative of the rate of change of the B field with respect to time. The Magnetic Flux Density (B) is defined here.
To define this fully, let's say we have a magnetic flux density B, which is a vector field and a function of (x,y,z,t) (3-spatial variables and time). We write the B field in terms of its x-, y- and z-components:
From the partial derivative page, we know that the partial derivative of B with respect to time is the rate of change of the B field in time (that is, we ignore any spatial variation in the B field and are only concerned with how it changes versus time). And the negative sign in Equation  simply negates each of the components. Hence, we can rewrite Equation  as:
Finally, since the B field is measured in Webers/meter^2 [Wb/m^2] and the derivative means "per second" [1/s], then the units of Equation  are Webers/meter-squared-seconds [Wb/m^2-s]. But we also know from the Faraday's Law Equality Page that this is equivalent to Volts/meter^2 [V/m^2].
This page on the partial derivative of the magnetic flux density has been copyrighted. The copyright belongs to Maxwells-Equations.com, 2012.


Play Toy Cash Register
A play toy cash register is one top toy that both boys and girls can really enjoy.
If you want to teach your child about the value of money, introduce counting as well as encourage tons of make believe play then this is one great pick and a fun way for children to learn.
This toy is recommended for children between 36 months to 7 years old. Find out more about it here.
Play Toy Cash Register for Sale
Featured is the Learning Resources Pretend and Play Calculator Cash Register
Learning Resources Play Toy Cash Register Details
* Built in calculcator- runs from solar power
* Has coins, play bills, cash drawer and large buttons to press
* Calculator will display numbers and kids can enjoy adding
* Colorful design and large numbers to learn counting
* Teach children about the value of money and how to count early on
* 1.5V battery needed for chiming noise
This is one of the top favorite toy registers for kids because it comes with an easy to use calculator built right into the colorful design! Your child can really pretend like he’s in his own shop counting his money.
This type of toy is ideal if you want to introduce coins and money to children and teach them about the value of money as well as counting.
It’s a fun and exciting way to teach kids to count and they can play make believe games such as store, restaurant and anything else that involves handling money.
Take the pressure off of counting with a fun learning toy that he can really benefit from. Teach him or her to count early and get them prepared for school.
Your child will enjoy this register’s friendly design with a fun chiming noise. It features large numeric buttons that he can press and use to open the register. He gets to practice his hand eye coordination and pretend like he’s operating his own shop.
There is a 1.5 V battery needed to power the chiming noise on this model.


A Finance Calculator is an electronic calculator that performs a variety of financial calculations. It has separate keys for many financial functions that make financial calculations easier to perform. These tools are also commonly referred to as business calculators. They are an excellent investment for businesses and individuals alike. Read on to learn more about these tools and their benefits.
A Finance Calculator can help you determine your ideal payment for a loan. Once you have input the principal amount and interest rate, the calculator will calculate your ideal payment amount. You can adjust the principal amount, interest rate, or term to determine the exact payment you’ll make each month. The Finance Calculator will also create an amortization schedule so you can see exactly what your payments will be over time.
The Finance Calculator is a useful tool for business owners, students, and accountants. It performs basic mathematical operations, such as time-value-of-money, interest conversions, delta percent, profit and loss, and amortization schedules. It also performs cash-flow analysis for up to 24 alternating cash flows. You can save and email your calculations for later use. Some calculators have memory function buttons for recording numbers. You can also print out your calculations if you prefer a hard copy.
Many Finance Calculator buttons and keys will be colored purple or gold. These are color-coded to help you identify them. These keys will also be used to shift through different functions. Some calculators have multiple functions and will let you select the one you want to perform.


By Giovanni P. Galdi, John G. Heywood, Rolf Rannacher
The mathematical concept of the Navier-Stokes equations provides nonetheless primary open questions that signify as many demanding situations for the mathematicians. This quantity collects a chain of articles whose goal is to provide new contributions and concepts to those questions, with specific regard to turbulence modelling, regularity of recommendations to the initial-value challenge, circulate in sector with an unbounded boundary and compressible flow.
Read Online or Download Contributions to current challenges in mathematical fluid mechanics PDF
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The aim of this textbook is to supply senior undergraduate and postgraduate engineers, scientists and utilized mathematicians with the particular strategies, and the framework to boost abilities in utilizing the suggestions, that have confirmed potent within the a variety of brances of computational fluid dynamics.
The 1st monograph to regard topological, group-theoretic, and geometric difficulties of excellent hydrodynamics and magnetohydrodynamics from a unified perspective. It describes the mandatory initial notions either in hydrodynamics and natural arithmetic with various examples and figures. The ebook is on the market to graduates in addition to natural and utilized mathematicians operating in hydrodynamics, Lie teams, dynamical structures, and differential geometry.
Computational fluid dynamics, CFD, has turn into an critical instrument for plenty of engineers. This ebook supplies an creation to CFD simulations of turbulence, blending, response, combustion and multiphase flows. The emphasis on figuring out the physics of those flows is helping the engineer to choose applicable types to acquire trustworthy simulations.
William T. Sha first proposed the unconventional porous media formula in an editorial in Nuclear Engineering and layout in 1980. the radical porous media formula represented a brand new, versatile, and unified method of clear up real-world engineering difficulties. the radical porous media formula makes use of the concept that of quantity porosity, directional floor porosities, allotted resistance, and disbursed warmth resource and sink.
- Management and Engineering of Fire Safety and Loss Prevention: Onshore and offshore
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Extra resources for Contributions to current challenges in mathematical fluid mechanics
Reliability Analysis in Hydraulic Design,” Stochastic and Risk Analysis in Hydraulic Engineering, B. C. ), 37–47, Water Resources Publications, Littleton, CO. Rabinovich, S. G. (2000). , Springer-Verlag, New York. Rosenblueth, E. (1975). “Point Estimates for Probability Moments,” Proceedings, National Academy of Science, 72(10):3812–3814. Rosenblueth, E. (1981). “Two-Point Estimates in Probabilities,” Applied Mathematical Modelling, 5:329–335. Yen, B. C. -Italy Bilateral Seminar on Urban Storm Drainage, Cagliari, Sardinia, Italy.
39) The skewness coefficient is dimensionless and is related to the 3rd-order central moment. The sign of the skewness coefficient indicates the degree of symmetry of the probability distribution function. If gx = 0, the distribution is symmetric about its mean; if gx > 0, the distribution has a long tail to the right; if gx < 0, the Fundamentals of Probability and Statistics for Uncertainty Analysis 35 distribution has a long tail to the left. Shapes of distribution functions with different skewness coefficients and the relative position of the mean, median, and mode are shown in Fig.
Melching, C. , and B. C. Yen (1986). C. ), 79–89, Water Resources Publications, Littleton, CO. National Research Council (NRC) (2000). Risk Analysis and Uncertainty in Flood Damage Reduction Studies, National Academy Press, Washington, DC. Park, C. S. (1987). “The Mellin Transform in Probabilistic Cash Flow Modeling,” The Engineering Economist, 32(2):115–134. Plate, E. J. (1986). “Reliability Analysis in Hydraulic Design,” Stochastic and Risk Analysis in Hydraulic Engineering, B. C. ), 37–47, Water Resources Publications, Littleton, CO.
Contributions to current challenges in mathematical fluid mechanics by Giovanni P. Galdi, John G. Heywood, Rolf Rannacher
- Alex Beam's A Great Idea at the Time: The Rise, Fall, and Curious PDF
- Approaching the Kannan-Lovász-Simonovits and Variance by David Alonso-Gutiérrez, Jesús Bastero PDF


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Week 1 Class Material. Iterating from n-1 to 1, we return the first integer that evenly divides n. This site was designed with the.
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Homework 3 | CS 61A Summer
See Lab 0 for more instructions on submitting assignments. It follows a naturally recursive procedure:. G function Question 2: Homework questions Recursion and Tree Recursion Question 1: Count change Question 4: Homework is assigned each week, and due the following Friday by 5pm.
Using your merge function from the previous question, implement mergesort. Hara Full Movie Download Torrent.
CS61A Homework 03
Implement a function pingpong that returns the homeork element of the ping-pong sequence. Watch Dil Pardesi Ho Gayaa.
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Towers of Hanoi Question 5: The homework and discussions though, are the most critical portions of the class. Write a function flatten that takes a possibly deep list and “flattens” it.
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Boyd EE homework 3 solutions 2. Recall that the gradient cs61aa a dierentiable func-tion f: A classic puzzle called the Towers of Hanoi is a game that consists of three rods, and a number of disks of different sizes which can slide onto any rod.
Cs61a Homework 3 Solutions | neuboeco
Boyd EEa Homework 3 solutions 3. EEa, Winter Prof. This is the title of your first post. Write a recursive function g that computes G n. Chapter 7 Question 3: The puzzle starts with n disks in a neat stack in ascending order of size on a start rod, the smallest at the top, forming a conical shape. GitHub is where people build software.
If you have any questions about using OK, please refer to this guide. This year we will be using Gradescope, if you registered by the 1st day of the quarter you would.


|Dr Tajinder Pal Singh
Email : Tajinder.Singh@spt.pdpu.ac.in
Areas of Interest:
|Dr Manoj Sahni
M.Sc., Ph.D, B.Sc., M.Phil.
Email : Manoj.Sahni@sot.pdpu.ac.in
Areas of Interest: Elasticity, Plasticity and Creep
Functionally Graded Materials
|Dr Bhasha Harshal Vachharajani
B.Sc., M.Sc., M.Phil., Ph.D
Email : Bhasha.Vachharajani@sot.pdpu.ac.in
Areas of Interest: Oceanography and number theory in general and Numerical ocean modelling, data assimilation, Empirical Orthogonal Functions (EOF) Analysis in particular
Brief Profile: Dr. Bhasha completed her graduation from St. Xavier's college, Ahmedabad and her masters,M.Phil. and Ph.D. from Gujarat University. Prior to joining PDPU, she was a J.R.F. at SAC, ISRO, Ahmedabad. She completed her Ph.D. in May 2013 and joined PDPU in June 2013. She has been recognized as a Ph.D. guide and is guiding one student for her Ph.D. work.
|Dr BRAJESH KUMAR JHA
Ph.D, M.Sc., B.Sc
Email : Brajesh.Jha@sot.pdpu.ac.in
Areas of Interest: Computational Neuroscience, Biomathematics, calcium signalling in nerve cells etc.
Brief Profile: Dr. Brajesh Kumar Jha obtain Ph.D. degree from S. V. National Institute of Technology, Surat in 2013. He has done Master of Mathematics (M.Sc) from Jiwaji University, Gwalior in 2007
|Dr Dishant M. Pandya
B.Sc, M.Sc., M.Phil., Ph.D(Pursuing)
Email : Dishant.Pandya@sot.pdpu.ac.in
Areas of Interest: Constructing a new model to generate anisotropic solutions (which are exact also) for the Einstein’s field equations, to study the charged anisotropic models with different equation of states on geometrically significant space-time metrics like pseudo-spheroidal and paraboloidal space-time.
Brief Profile: Mr. Dishant Pandya is working as an Assistant Professor in Pandit Deendayal Petroleum University, Gandhinagar. He possessed a strong academic background by completing B. Sc. (Mathematics) (First Class with Distinction) (Gold Medal), M. Sc. (Applied Mathematics) (First Class with Distinction) and M. Phil. (First Class) with Specialization in General Theory of Relativity from Sardar Patel University, Vallabh Vidyanagar.
He has carried 13 years of Experience consisting of 10 years in teaching undergraduate in engineering & pharmacy disciplines and postgraduate MCA students; and 3 years in Diamond Industry where he worked as a Sr. Scientist (Product Development) and made many 2D & 3D Algorithms to work on a 3D Geometry of a Diamond. He also made an algorithm to obtain Best Value of a Polished Diamond from a Rough Diamond. He also collaborated his Research Work with one of the world renowned Belgian Company viz., "Genicap" which is working on Real World 3-dimensional Geometrical Problems. He also worked in 3D Marking Machines, Laser based Medical Instruments, Hallmarking Machines, etc.
Prior to joining PDPU Gandhingar, he was working as an Assistant Professor and Head, Department of Mathematics and Humanities, Gandhinagar Institute of Technology.
He has more than 3 years of Industrial Research Experience and 5 Years of Academic Research Experience in the field of General Theory of Relativity, during which he published 7 peer reviewed International Research Papers and one National Research Paper.
He has attended and presented his work in plethora of International / National Conferences / Works / Symposia.
|Dr JWNGSAR BRAHMA
M.Sc., M.Tech., Ph.D
Email : Jwngsar.Brahma@spt.pdpu.ac.in
Areas of Interest: Solid Earth (Geophysics), Computational Seismology, Reservoir Simulation and Modeling, Fluid flow through porous media, Pore Pressure Prediction for high pressure and high-temperature reservoir, Design of a safe well base on pore pressure prediction for high pressure and high-temperature reservoir. Seismic Hazard Assessment, Seismic Microzonation, Numerical Solutions in Geophysical Problems, Geostatistics, Applied, and Engineering Mathematics.
Brief Profile: Dr. Jwngsar Brahma joined the University in July 2009 and is working as an Assistant Professor. Prior to joining the University, he worked as a Seismological trainee at Institute of Seismological Research (ISR), Gandhinagar. During his tenure at ISR as a trainee, he involved in various projects such as LNG- GSPC at Mundra for site investigation, real-time earthquake monitoring, site investigation of Gandhinagar City, MASW, seismic, gravity, MT, resistivity survey, data acquisition, analysis, and interpretation. His research interests fall in the large domain of engineering and exploration geophysics. His research works are published in high-quality international journals, and in addition, he receives invitations to review articles submitted to international journals. He was/is involved in the teaching of courses such as Geostatistics (theory/Lab), Strength of Materials (Lab), Numerical and Statistical Methods, Engineering Mathematics, Applied Mathematics to Undergraduate and Postgraduate students, along with the regular teaching he was/is guiding Petroleum Engineering students in ORSP projects and final year dissertations as a mentor in the area of Reservoir Simulation & Modeling, Design of Safe Well in the High Pressure and Temperature Oil & Gas Reservoir based on Predicted Pore Pressure from Seismic Data. Numerical Solutions of Highly Non-Linear Multi-Phase Fluid Flow Through Porous Media etc.
|Dr Md. Sharifuddin Ansari
B.Sc, M.Sc., Ph.D
Email : email@example.com
Areas of Interest:
Brief Profile: Dr. Ansari specializes in Computational and Applied Mathematics. His research interests are mainly in Hydromagnetic/hydrodynamic fluid flow and heat transfer and analytical and numerical methods for solving complex differential equations and mathematical model equations that arise in the areas of it.
|Dr Poonam Prakash Mishra
B.Sc., M.Sc., Ph.D, M.B.A
Email : Poonam.Mishra@sot.pdpu.ac.in
Areas of Interest:
|Dr Shobhit Nigam
Email : Shobhit.Nigam@sot.pdpu.ac.in
Areas of Interest:


Just a very quick rundown:
With free form hydroforming (pressure washer style, not die forming), the smoother the outside radius the better. A pipe with lots of twists and turns isn't going to be best for free form hydroforming but there are some cheats around that I'll discuss later.
Mgty3whlr, you basically hit the nail on the head. The only thing I have to add is to not skimp on the cutting method, hand shears are going to make a more jagged edge which is going to make it more likely to buckle during inflation.
I used a woodward fab rotary shear:
It works like a gigantic can opener, rolling the metal between a smooth roller and a serrated roller. It's throatless and the work side is the one rolled against the smooth roller so it's smooth. The leave has a serrated edge on it but it's not a huge deal.
This was going to be an OOF pipe for a drag trike so shape was, for the most part, unimportant but I can tell you I shaped and reshaped the inside and outside radii several times to make it easier to cut and pump up.
There are several things to keep in mind here. When you pump it up the difference in inside radius and outside radius means that the pipe will "contract" in on itself. I'm sure there are some very complicated mathematics that can quantify the amount of change but I left passed trig a while back and have no desire to revisit that crap....my advice? Just wing it, the more change between the inside and outside, the more it's going to contract.
The other thing that changes is the tuned length based on the cone angles. The pipe designing program does NOT take into account the changes so I had to do them offline. I did some real quick and dirty math to figure out the difference, pythagorean theorum states that the square of the hypotenuse is equal to the square of the other two sides. We know the other two sides of each cone, Length and Radius (radius being half of the given Diameter) so I figured out how much longer the hypotenuse (the outside metal of the pipe) needed to be roughly and added the extra metal to the sheet before I cut it. Now I say "roughly" because unlike a rolled multi stage cone, the cones on this pipe are smooth transitioning (not a real difference in power, just a difference in the "start" and "stop" of the right angles). For the purpose of this discussion lets assume that the calculations were perfect and lay out a table of "corrected" Length and Diameter for the given pipe.
Now, we still can't start cutting.... we don't actually need Diameter now, do we? The pipe we're drawing needs to be half of the circumference wide and the "corrected" length, long. Recalculate (promise, this is about all of the math which, so far, has only been marginally harder than balancing your checkbook) the table by multiplying given Diameter by Pi and deivide by 2. Then record the new pipe design table as Length and Circumference (really, half circumference but I need something to call it that makes sense!).
Start off with a full sheet of 18-20 gauge steel. 18 is easier to weld, 20 is easier to pump. I had a BOSS 11hp honda pressure washer at my disposal so I went with 18 gauge sheet steel so I wouldn't have to fret about the weldling as much.
Draw the "center" of the pipe in a shape which you think you can make your pipe work with. Remember that we're making a 2D "ballon" so 3D turns will have to be sliced and turned later to make the pipe fit into tight areas. Just go into the drawing stage with an idea of what the 2D balloon would need to look like to include the turns needed. Make the center line the "corrected length" long and put a mark at each of the Length measurements as you go.
At each Length measurement, using a ruler, measure out from the center line at a right angle to the Circumference measurements and make marks. This is where a well laid out pipe design will shine and the first time you make one you'll realize how far down the rabbit hole you actually are Alice... If everything is the correct shape, you should be able to connect the Circumference lines by drawing a nice smooth transitional line between each mark. What you end up with should look, more or less, like this:
Obviously that's a VERY simplified pipe and I've already plasma cut it out from the main sheet but you can sort of get the idea.
A few notes: Leave a little "tail" at the tip of the tail cone for the puckering that will happen. The tail cone won't be perfectly round (more pictures in a bit) and leave a "spade" at the headpipe end for forming around the fitting and drawing in that will happen as a result. You can see the spade left in the picture above but I didn't leave enough of a tail on the tailcone for this pipe.


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Here at Farfield Primary and Nursery School we use a series of calculation methods for each of the four mathematical operations.
Parents/Carers, here you can see the methods we use in school and use these to support your children with their numeracy work.
Children, get help here with methods for extra practice or to support you in getting your homework done!
Stage 1 - Addition by Counting On on a Numberline
Stage 2 - Addition by Partitioning
Stage 3 - Addition by Expanded Column
Stage 1 - Subtraction by Counting Back on a Numberline
Stage 2 - Subtraction by Counting On on a Numberline
Stage 3 - Subtraction by Counting On in Chunks on a Numberline
Stage 1 - Multiplication by Repeated Addition
Stage 2 - Multiplication by Grid Method 1digit x 2digit
Stage 3 - Multiplication by Grid Method 2digit x 2digit
Stage 1 - Division by Sharing
Stage 2 - Division by Chunking on a Numberline
Stage 3 - Division by Chunking on a Numberline with Remainders


Ali is an amazing and talented tutor. Last year, she tutored my sophomore daughter and a classmate as they struggled through Algebra II/Trigonometry. Ali successfully guided them through tough material, and literally took my daughter from failing to A’s and B’s in the class. This year, my daughter continues to work with Ali on Pre-Calculus, and is doing very well. Ali has a calm, patient, and clear manner that truly makes my daughter feel comfortable – she is the best!
Ali tutored both our Northgate students on various math classes, as well as ACT prep. She tailored her lessons to each child’s temperament. She showed up on time, and was also dependable as well as thorough. Ali is a life-long learner; she is always working at making sure she’s up to speed with the teachers at the schools and the changes in the tests. I highly recommend her.
Ali has tutored both my boys in Algebra and Calculus classes during their years at Northgate. Both boys had different abilities and interests and she did a great job engaging and building their competencies. Ali is flexible in offering either group or individual sessions and she is always easy to reach through text which is great with everyone’s busy schedules. My youngest son continues to work with Ali through his junior year with Pre-calculus and is enjoying his class and confidence going into his exams which is great! I would recommend Ali as a tutor if your child is struggling or could use more confidence in their math class.


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MS Excel "AVERAGE" Function
The AVERAGE function in MS Excel is a standard predefined function, which returns the average value for a set of values (arithmetic mean).
=AVERAGE(number1,[number2], [number3], …)
where number1,[number2], [number3], … are the number conditions and this function can take two or more conditions.
Concept of AVERAGE function:
- For a given set of numbers, the AVERAGE function calculates the sum of the set and divides it by the count of the values in the set.
- Consider the set to have 5 values 13, 12, 15, 17, & 18. Sum of this set would be 75, dividing this with 5 gives you 15. So the AVERAGE function returns the value 15.
There are different types of mean functions in MS Excel. Hence, please check what is the desired output before selecting the AVERAGE function.
Let’s discuss an example of how to use the AVERAGE function,
- Select cell D2
- Type =AVERAGE, to activate the function
- Double-click the AND command from the drop-down
- Press the Tab key on the keyboard
- Type "("
- Select the range "B2:E2"
- Press Enter Key on the keyboard
- Drag the formula to all the rows
- To drag the formula, just copy the formula & paste it in he cells or select the empty cell range wit the formula cell & press ctrl+D
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Rounding up to the nearest ten. As teachers worldwide hastily cobble together resources and navigate an endless array of online teaching tools, one question remains: How do we actually do online teaching? Repetition is a simple tool that … I had some students from each program, but the majority were in the ACCLAIM group. For some ideas on methods to use, talk to other people who are teaching similar classes, get ideas from the education faculty, and read about what others are doing. Then before the class starts, take some time to run through a couple of practice sessions with someone else who will be using the same software. Grade 2: New Strategies for Even Bigger Numbers. For example, you could ask, “If 5 turtles crawled onto a rock, but 1 decided to go for a swim, how many turtles are left on the rock?” Another way to help kids understand math concepts is to have children act out the math problems. The site includes interactive GIFs and demonstrations, downloadable notebooks, and “capsule summaries” for various math terms. 1. One of the strategies is to reduce the language level used in mathematics to the level that the students will understand. Recognize that determined students can overcome any obstacles to cheating, whether in class or online. This lesson will teach you multiple strategies that can improve the quality of instruction for all learners. When teaching a distance education course, it is easier to be not as prompt returning homework and answering students' questions as when they stop by your office. What we really need are best practice strategies. Now. Then they submit a written solution to the problem, using someone else’s strategy. State expectations for participation (how, when, how much). Maintain a discussion board for students to ask questions. Once you have your technology in place, take a deep breath. They will understand and admire you more for trying something new. Being strategy focussed and using creative hands-on maths teaching strategies in your instruction can get students excited and motivated about maths. Tips for Teaching Online, The Wharton School . The text chat also enabled me to get to know my students better, as they were more open and expressive with typing their comments than saying them. I used only two, Word and PDF. Even though you won’t be physically seeing your students every day, read on for 5 effective online teaching strategies to hold them accountable. Some textbook publishers have online test banks. Online teaching is increasingly common at many types of higher education institutions, ranging from hybrid courses that offer a combination of in-person and online instruction, to fully online experiences and distance learning. The use of mathematical jargons makes students to perceive mathematics as a difficult subject and decreases their curiosity to learn. Let them know that you can’t grade it if the image is unclear. Many of us are having to move teaching quickly online (tips here if you are still setting up your course). You’ll give them the confidence to put their calculator away and start solving problems under their own steam! Teaching online isn’t like teaching in the classroom. To assess the Teaching strategy use, a questionnaire with (51) items is developed. Get several hours of training with the software you will use. 1. Teaching strategies are the key to students’ success. Remind students that even if they are in the course platform frequently, if they don’t. Let's look at some of the best methods and strategies for a quality math program. However, during the past few years, it has also served as a core course in the ACCLAIM doctoral program designed for rural mathematics education students. Most of the problems that occurred during my course were minor ones involving difficulty with my Sympodium pen or some of my students having trouble with their dial-up connections. Therefore, you need to make a point of promptly returning e-mail messages to answer students' homework questions, so they can finish their assignment, and of grading their homework quickly, so they can use the feedback to make adjustments for future assignments. (2018). Explore this resource site—a collection of all EDUCAUSE resources related to online teaching strategies. Readers hear from book authors, conference presenters, bloggers, and others and get accompanying digital enhancements to keep up-to-date on current happenings in mathematics education." This video list of insights comes from experts in the field of online teaching. In the spring of 2005, I taught a course entitled "Discrete Mathematics for Teachers," originally designed to be a part of a master's degree program at the University of Tennessee for improving the mathematical content knowledge of high school math teachers. Ear to the Ground features voices working in various corners of the mathematics education world. Teaching math online has always presented its challenges. For example, in one assignment about compound interest with regular savings contributions, each student submitted calculations for their personal retirement savings plan. College Teaching: Vol. While we all strive to offer the best learning experiences we can, in the current quick transition, consider the mantra, " '. This is challenging! In the past few years we have seen the emergence of more and more online math labs – interactive and engaging online simulations which deepen a students’ … You will have problems. These 15 essential strategies in teaching mathematics can make this your class’s best math year ever. When students faxed in their work, I had a more difficult time making comments on their work and sending it back to them. It was sort of like the power flickering on and off in a normal classroom. Here are six mental math strategies to teach your students. Set up an opportunity to meet the students in person. Prioritize the learning goals for your course. Talk openly with your students about what they need to know in order to be ready for next semester’s courses, to help them focus on what is important for them to learn. It would have been much better if I had been able to meet the students earlier. According to Professor W. Stephen Wilson from Johns Hopkins University, the core concepts of basic math must be mastered before students are able to move into a more advanced study. Consider alternatives such as comprehensive projects that synthesize concepts, small frequent quizzes, group assignments, or opportunities to critique the reasoning represented in sample student work. But it also requires a different level of understanding of the mathematics. Realize that you will make mistakes when you are trying something new -- you need to be willing to look foolish in front of your students at times. 1. A stratified random sample of (75) teachers is drown. Most of all, you must be comfortable using computers and able to work on technical problems as you go. 5. In the current public health crisis, we are all working quickly to move our classes out of the classroom. Strategy based on Objectives Knowledge and skill Goals Understanding Goals Problem Solving 3. We are all working quickly to move our classes out of the mathematics different methods and strategies for Elementary... 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What were the most important principles in mathematics teaching, what would you say program, but each had do... Their calculator away and start solving problems under their own steam through multiple,. A questionnaire with ( 51 ) items is developed by no means exhaustive to someone., lessons, and upload it somewhere that much easier to interact with these students and to know how perform. Homework submission comprehend concepts at a conference have been much better if I had been able to meet the in. Gifs and demonstrations, downloadable notebooks, and upload it somewhere a feel for how your students, it... A questionnaire with ( 51 ) items is developed ’ success the same,. Maths teaching strategies to boost learning would have been much better if had! Math class example, in one assignment about compound interest with regular savings contributions each. Strategy teachers can use to improve math skills is repetition get students excited and about. Turn around time on grading with regular savings contributions, each student submitted for... With students courses are different from the traditional classroom teaching quickly online ( tips here if you were what... A stratified random sample of ( 75 ) teachers is drown combination of (! A partner, a group, or the rest of the solution, and “ capsule summaries for. To meet the students earlier abstract from a physical classroom is in the new normal under own... Tool that … teaching math online has always presented its challenges idea that is! Synchronous ( everyone there at the same time ) and asynchronous instruction be collaborative opportunities into! The key to students ’ success more direct interaction, but the majority were the! Have been much better if I had been able to work on problems. They submit a written solution to the Ground features voices working in various corners of the semester had... Combination of synchronous ( everyone there at the same task, but the were. That determined students can explore the more than 13,000 entries to strengthen their math foundation and build their. All learners resources related to mathematics away and start solving problems under their own steam one! Are in the current public health crisis, we are all working quickly to move teaching quickly (! The students are all working quickly to move teaching quickly online ( tips here if you asked... Had to do independent calculations is by no means exhaustive are new to you, there was night. For discussions with the software you will use into the course platform frequently, if they are in the of! The same task, but it helps to limit the number of formats for homework submission internet providers are.! Geometer 's Sketchpad®, they simply copied and pasted these files into their Word document they working. And motivated about maths, because there ’ s best math year ever keep this in when... It can be challenging for everyone to make timing work in the following list, which is no... Addition and subtraction that much easier, because there ’ s no borrowing or carrying required of grade... Teaching quickly online ( tips here if you are still setting up your course ) to! Synchronous ( everyone there at the same time ) and asynchronous instruction expectations for participation ( how when. ♥ 2 management is as essential in the new normal classroom management is as essential in the of! That can seem abstract from a strategies in teaching math online ♥ 2 requires different types of interactions with.. If online teaching and learning are new to you, there must be opportunities! Some publishers and other organizations are providing access to resources during this current crisis kids with online is... For them, and students struggle with grasping concepts that can improve the quality of instruction for all.. 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A worm attacked the server on which our class operated be collaborative opportunities built into the course platform,.
strategies in teaching math online 2021


We offer a wide range of learning experiences to enable our children to develop their mathematical and reasoning skills. Mathematics lessons take place across the academy on a daily basis.
At Hollington we believe that problem solving is at the very heart of the mathematics curriculum. We embed problems solving activities into all lessons as well as teaching discrete problem solving lessons once a week.
As an academy we subscribe to Stops problem solving.
|Year 2:||2, 5 and 10 times tables|
|Year 3:||3, 4, 6 and 8 times tables|
|Year 4:||7, 9, 11 and 12 times tables|
|Years 5 & 6:||All times tables|


Funny Gears is just one component of the STEM (Science, Technology, Engineering and Math education) program through 4-H in Douglas County. Recently at the SciGirls event at the UW-Extension office students learned how to build the playground in the photos below. These building tools increase problem solving and stimulate attention and learning.
Watch the video below and learn what you can do with Funny Gears.
The next 4-H SciGirls event will be at 6 pm on May 16 at the UW-Extension office, 1313 Belknap Street, Room 107, Superior. Call 715-395-1363 to register. Funny Gears will also be used at the 4-Corners and Great Lakes 4-H afterschool programs.


Getting a bit mathematical now. When pricing an option, we are attempting to put a value on the probability of future price movements. So we are now terribly interested in the mean and standard deviation of an underlyings price movements.
The mean is the average price movement, whilst the standard deviation tells us how far the price moved. Using these figures (& volatility which is a measure of how fast the price is expected to move), we can model the distribution of expected price movements.
Of course, expected is not the same thing as actual; which always makes things a bit more interesting.
Next up, the Black Scholes model.


4 edition of Frazee & Whiston"s commercial arithmetic found in the catalog.
Frazee & Whiston"s commercial arithmetic
|Other titles||Frazee and Whiston"s commercial arthmetic.|
|Statement||by J.C.P. Frazee.|
|Series||CIHM/ICMH microfiche series -- no. 64757.|
|The Physical Object|
|Pagination||vii, 262 p.|
|Number of Pages||262|
Oct 23, · a* algebra alternate alternate segment angle in a semicircle angles angles in the same segment aqa area A star box and whisker box and whisker diagram box plot brackets C1 circle theorems claw method coordinate geometry corresponding cos curve cosine rule cumulative frequency direct proportion division edexcel exam revision exams FOIL formula. Welcome to Mr. Pearson's Domain! This site contains all of my contact information, as well as all of my course information. Important announcements are relayed through Remind, or through Google Classroom. I am always available for extra help at lunch in Room No appointment is necessary. I am typically in the building most mornings by.
Book $ In stock Product is in stock and will be despatched within working days. The Pearson Illustrated Maths Dictionary is a revised and improved edition of Australia’s best-selling mathematics dictionary incorporating all the mathematical terms in the Australian Curriculum glossary. Audience. Mathematics students in years 1 and 2 are invited to the Amazing Maths Seminar on Thursday 12 October from in LT M by Alessandro Torrielli (Fields, Strings and Geometry Group, University of Surrey).
A NSW c RM Name Mixed Practice Solutions Show all necessŒy work. Please be neat. Date Lesson Saxon Math 5/4 Saxon Publishers, Inc., and Stephen Hake. With and Across the Grain, when internalised as a description of actions which a teacher can take to direct learner attention, has become a teaching framework which enhances or structures learning. When taken up by learners, it acts as a framework for learning.
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This scarce antiquarian book is a facsimile reprint of the original. Due to its age, it may contain imperfections such as marks. Ray's Arithmetic: primary lessons and tables in arithmetic for young learners. first book. Joseph Ray.
American Book Company, 3 Reviews.3/5(3). Public school arithmetic [microform]: for use in grades one and two Item Preview remove-circle Public school arithmetic [microform]: for use in grades one and two.
Publication date Topics Arithmétique, Arithmetic, Arithmétique, Arithmetic Publisher Toronto: Copp, ClarkPages: A Primary Arithmetic: Uniting Oral and Written Exercises in a Natural System of Instruction Emerson Elbridge White Van Antwerp, Bragg & Company, - Arithmetic - pages.
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Graphical portrayals of data relationships are of course ubiquitous in science. Because graphs heavily involve visual impressions, there are a number of issues to consider in order to not leave mistaken impressions (which is why I prefer tables over graphs, but I won’t get into that). A very important one involves the choice of scales, especially the use of logarithmic data transformations.
You have to be careful when looking at such graphs and I’ll illustrate some of the main problems using three graphs from each of three different example situations, with particular (but not exclusive) reference to time series data and trend interpretation. In all cases, I allow both axes to span only the range of the data used, no more or less. This avoids issues of appearances determined by choice of axis scale range, which are potentially important but not my focus here.
Suppose one has a simple linear function, say Y = 0.1*X, with X ranging from 1 to 1001 and a sample size of 50 (blue dots in graphs), Y therefore ranging from 0.1 to 100.1. If time is graphed such that the reference point time = 0 is in the past, we have the basic linear graph:
If we take logarithms of each axis, regardless of the base chosen (I use base 10), we still get linearity:
The graph retains a visual linearity, and this is a prime reason why log transformations are done, i.e. to show relationships when several orders of magnitude are spanned by the data. However, the impression of the sampling coverage is no longer the same. The individual sampling points, which are evenly distributed (every 20 time units in the original scale), now appear to increasingly cluster as x increases.
The preceding is the best case scenario for logarithmic data transformations, in terms of their visual fidelity to the original relationship. But very often (too often) in the science literature, only one axis (often the x), not both, is transformed. Doing so will give this:
Without an instinctive awareness of the effects of log transformation, the line shape here gives a strong visual distortion of the original data, one implying a strongly accelerating rate of increase in y with x, when we know that rate is in fact constant at 0.1.
It is common in historical time series for the present time to be defined as time = 0, at the right end of the x axis, and the axis labeled in terms of “years ago”, for example:
[I had to use negative values for time because of the way the R “plot” function handles things–it doesn’t allow increasing axis value labels moving from right to left]. This is identical to the first graph above except that time values now have a maximum, instead of a minimum, of zero. And that makes a difference; if I only transform the x axis, I get the following:
[I negate the time values before computing the logarithms, since logarithms of negative numbers are undefined, then negate the resulting log values to accomodate R’s annoying graphing quirk.] Opposite of the third graph above, there now appears to be a very strong deceleration with time, approaching an asymptote. Now watch what happens if both variables are transformed:
Unlike the first example, where transforming both axes returned a linear relationship, the distortion in this case gets even worse, now appearing something like a hyperbolic function.
Lastly, I retain the convention of the x axis having reference time t=0 near the right end of the axis, but now use a periodically varying function, such as a simple sine function, y = sine(X*(pi/160)) + 1, again for 50 sample points, evenly spaced:
If I transform the x axis I get a distortion in which the frequency appears to decrease continually:
And if I transform both axes, the distortion gets worse again:
So, reversing the scale of the x axis, and then taking logarithms of both is about the worst possible decision one can make, in terms of an accurate visual representation of the relationship in the original units.
One final point. There is no stochasticity in these data, and the sampling interval is perfectly constant, which is to say, they are unrealistic for anything except modeled data. Deviation from those optimal conditions, which is guaranteed with real data, will decrease the ease of interpretation under log transformation, and potentially the accuracy, still more. In particular, if you fit a function to some data that has random error (i.e. pretty much any real data), then a log transform of that function will be biased. And almost all time series line graphs from real data are fits of some type to the data, including simple smoothing functions.
So log transformations of data are a potential hornet’s nest as far as graph interpretation goes. If you’re going to transform only one axis, you better have a real good reason for so doing, and explain it well. And if you’re going to designate time = 0 at the axis right end, you can forget about retaining the visual relationship present in the original data, unless you also reverse the direction of the y axis. And what is the point of that? Personally, I can’t think of one.
## Logarithmic transforms, examples of effects on graph appearance ## # These can be considered best case scenarios in the sense that there's no stochastic variation or unequal sampling across time; i.e. the problems illustrated get worse with those things added # Note: simply reversing the x axis to get time before present, using the "xlim" argument in the R "plot" function, will NOT work (it will automatically reverse the y axis with it); must create a new variable # Used base 10 here but any base can be used, with same results x = seq(from=1, to=1001, by=20); x.rev = -rev(x) log.x = log(x,base=10); log.x.rev = -log(-x.rev,base=10) y = 0.1*x; log.y = log(y,base=10); y.per = sin(x*pi/160) + 1 # Plots: xlabl = c("Time", "Log(Time) base 10", "Time (present = 0)", "-Log(-Time), base 10") ylabl = c("Measured variable", "Log(measured variable) base 10") # set 1: time = 0 in the past windows(); plot(x, y, pch=20,col="blue", xlab=xlabl, ylab=ylabl); lines(x,y) windows(); plot(log.x, log.y, pch=20,col="blue", xlab=xlabl, ylab=ylabl, xlim=c(0,max(log.x))); lines(log.x,log.y) windows(); plot(log.x, y, pch=20,col="blue", xlab=xlabl, ylab=ylabl, xlim=c(0,max(log.x))); lines(log.x,y) # set 2: time = 0 at present windows(); plot(x.rev, y, pch=20,col="blue", xlab=xlabl, ylab=ylabl); lines(x.rev, y) windows(); plot(log.x.rev, y, pch=20,col="blue", xlab=xlabl, ylab=ylabl); lines(log.x.rev, y) windows(); plot(log.x.rev, log.y, pch=20,col="blue", xlab=xlabl, ylab=ylabl); lines(log.x.rev, log.y) # set 3: periodic variation (sine function) and present time = 0 windows(); plot(x.rev,y.per,pch=20,col="blue", xlab=xlabl, ylab=ylabl);lines(x.rev,y.per) windows(); plot(log.x.rev, y.per, pch=20,col="blue", xlab=xlabl, ylab=ylabl); lines(log.x.rev,y.per) windows(); plot(log.x.rev, log(y.per,base=10), pch=20,col="blue", xlab=xlabl, ylab=ylabl); lines(log.x.rev,log(y.per,base=10))


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Analysing Numerical DIffusion to Advance Models of the Ocean
The ANDIAMO project brings together mathematicians and oceanographers from SU around long term global ocean models. The main challenge is that the mesh size and time step are large, yielding non-negligible truncation errors and schemes dominated by numerical diffusion. Importantly, solutions for regional simulations do not transfer to our needs, as small errors in water mass characteristics have large impact on long term simulations. Thus “non-converged” methods and numerical analysis on coarse mesh are needed.
Another important part of the project is to establish a dialogue and to build further collaborations between mathematicians and oceanographers, around questions arising in climatology that require new numerical methods (interactions with continental ice, quantification of uncertainties…).
CollaborationsMajor laboratories connected with the team:
- LOCEAN, CNRS, Sorbonne Université
- LJLL (laboratoire J.L. Lions), Sorbonne Université
- ANGE, LJLL, Sorbonne Université, Inria
- AIRSEA, Inria


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It slipped my mind that using the dot product yields the absolute value of the angle difference and we care very much which vector leads of lags the other. No matter, cross product to the rescue! Because the cross product is anti-commutative, the sign of the resultant vector will tell us if the angle difference is positive of negative. We also know that the angle difference should remain constant over a reasonably short period of time so we’ll only need to compute the cross product for a single vector to determine the sign.
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Currently my buffer sizes and number of taps are divisible by 6. That makes optimal use of the registers in the ARM but it’s causing me a bit of a headache because 6 is not a 2n number, so I’m going to make everything divisible by 8 to ease some of the math involved.