Titre du document / Document title
Construction of the attainability set of a brockett integrator
Auteur(s) / Author(s)VDOVIN S. A.
TARAS'YEV A. M.
USHAKOV V. N.
Résumé / Abstract
Methods of optimal control theory [1, 2] are used to solve the problem of constructing attainability sets for a non-linear dynamical system known as the non-holonomic Brockett integrator . It is proved that the boundaries of attainability sets are characterized by points of optimal trajectories constructed for a control problem whose integral performance index defines the area of the figure bounded by a trajectory of motion of the controlled system. The problem is to maximize that area. This formulation is similar to that of Dido's problem in the calculus of variations, namely, to construct a figure of maximum area for a given perimeter. An algorithm is proposed for constructing optimal trajectories and their properties are investigated. The algorithm is based on results obtained by solving a special case of the optimal control problem with a closed trajectory of motion.The necessary optimality conditions of Pontryagin's Maximum Principle are verified for the optimal trajectories constructed. Analytical formulae are derived for the value function of the control problem and the necessary and sufficient conditions for optimally are verified using Subbotin's minimax inequalities for Hamilton-Jacobi equations.
Revue / Journal TitleJournal of applied mathematics and mechanics
Source / Source
2004, vol. 68, no
5, pp. 631-646 [16 page(s) (article)]
Langue / Language
Editeur / Publisher
Elsevier, Kidlington, ROYAUME-UNI
Localisation / Location
INIST-CNRS, Cote INIST : 1459, 35400012595758.0010
Nº notice refdoc (ud4) : 16462784


St. Anne’s Progress 8 score for 2016 is +0.66
Our Key Stage 4 Performance 2016 Progress 8 score is now +0.66. It is well above National Average and is the highest of all schools in Enfield. This means that, on average, our students achieved results that are 2/3 grade better than students of the same starting point Nationally.
Progress 8 is one of the new National Measures with regards to Secondary School Performance.
Progress 8 was introduced for all schools in 2016 (based on 2016 exam results at Key Stage 4). Progress 8 scores were published earlier this week in the provisional performance tables and the final tables will be published in January 2017. Progress 8 now replaces the 5+ A* – C including English and Maths measure.
“The Progress 8 measure is designed to encourage schools to offer a broad and balanced curriculum at KS4, and reward schools for the teaching of all their pupils. The new measure will be based on students’ progress measured across eight subjects: English; mathematics; three other English Baccalaureate (EBacc) subjects (sciences, computer science, geography, history and languages); and three further subjects, which can be from the range of EBacc subjects, or can be any other approved, high-value arts, academic, or vocational qualification.” (DfE Factsheet, Progress 8 Measure)
More information on Progress 8 is available here:
View the Enfield Secondary School Performance Tables here


But then, that’s the key to calculus: recognizing that 99.999999 effectively approaches 100. In this case, n = 1 and l = 0. Completing the CAPTCHA proves you are a human and gives you temporary access to the web property. The proton has one indivisible positive charge while the electron has one indivisible negative charge. Note that the creators of this cartoon didn’t have the wherewithall to make a ‘right’ atom, giving the nucleus four plus charges and the shell three minus… this would be a positively charged ion of Beryllium. The process of normalization is just to make certain that the value ‘under the curve’ contained by the square of the wave function, counted up across all of space in the integral, is 1. I then divide out the exponential so that I don’t have it cluttering things up. The hydrogen atom problem is a classic problem mainly because it’s one of the last exactly solvable quantum mechanics problems you ever encounter. If the savvy reader so desires, the prescriptions given here can generate any hydrogenic wave function you like… just refer back to my Ylm post where I talk some about the spherical harmonics, or by referring directly to the Ylm tables in wikipedia, which is a good, complete online source of them anyway. Hydrogen atom is simplest atomic system where Schrödinger equation can be solved analytically and compared to experimental measurements. The divergence operation uses Green’s formulas to say that a volume integral of divergence relates to a surface integral of flux wrapping across the surface of that same volume… and then you simply chase the constants. For the power series to be a solution to the given differential equation, each coefficient is related to the one previous by a consistent expression. With the new version of U, the differential equation rearranges to give a refined set of differentials. That’s part of why solving the radial equation is challenging. The modification I made allows me to write U as a portion that’s an unknown function of radius and a second portion that fits as a negative exponent. Why not, I figured; the radial solution is actually a bit more mind boggling to me than the angular parts because it requires some substitutions that are not very intuitive. Operationally, this is just another choice for spherically symmetric potential (i.e. Change ), You are commenting using your Google account. The Bohr radius ao is a relic of the old Bohr atom model that I started off talking about and it’s used as the scale length for the modern version of the atom. A small exercise I sometimes put myself through is defining the structure of del. The simplest case to consider is the hydrogen atom, with one positively charged proton in the nucleus and just one negatively charged electron orbiting around the nucleus. The value produced by divergence is a scalar quantity with no direction which could be said to reflect the ‘poofiness’ of a vector field at any given point in the space where you’re working. Here are the first few generalized Laguerre polynomials: Steven Holzner is an award-winning author of technical and science books (like Physics For Dummies and Differential Equations For Dummies). Hard to sweat the small stuff. The ‘8’ wedged in here is crazily counter intuitive at this point, but makes the quantization work in the method I’ve chosen! If you were to consider an infinitesimal volume of these perpendicular dimensions, at this locally cartesian point, it would be a volume that ‘approaches’ cubic. It’s basically just saying “What if my solution is some polynomial expression Ar^2 -Br +C,” where I can include as many ‘r’s as I want. Coulomb). The recurrence relation also gives a second very important outcome: The energy quantum number must be bigger than the angular momentum quantum number. Some of the higher energy, larger angular momentum hydrogenic wave functions start looking somewhat crazy and more beautiful, but I really just had it in mind to show the math which produces them. Calculate the Wave Function of a Hydrogen Atom Using the…, Find the Eigenfunctions of Lz in Spherical Coordinates, Find the Eigenvalues of the Raising and Lowering Angular Momentum…, How Spin Operators Resemble Angular Momentum Operators, If your quantum physics instructor asks you to find the wave function of a hydrogen atom, you can start with the radial Schrödinger equation, Rnl(r), which tells you that. In between the Sakurai problems, I decided to tackle a small problem I set for myself. ‘Quantized’ is a word invoked to mean ‘discrete quantities’ and comes back to that pesky little feature Deepak Chopra always ignores: the first thing we ever knew about quantum mechanics was Planck’s constant –and freaking hell is Planck’s constant small! The Laplace operator combines gradient with divergence as literally the divergence of a gradient, denoted as ‘double del,’ the upside-down triangle squared. Calculate the Wave Function of a Hydrogen Atom Using the Schrödinger Equation. Further, the electrons are not stacked into a decent representation for the actual structure: cyclic orbitals would be P-orbitals or above, where Beryllium has only S-orbitals for its ground state, which possess either no orbital angular momentum, or angular momentum without any defined direction. Click hereto get an answer to your question  The radial wave equation for hydrogen atom is Ψ = 116√(pi) (1a0)^3/2 [ ( x - 1 ) ( x^2 - 8x + 12 ) ] e^-x/2 where, x = 2r/a0 ; a0 = radius of first Bohr orbit.The minimum and maximum position of radial nodes from nucleus are: Also, in that last line, there’s an “= R” which fell off the side of the picture –I assure you it’s there, it just didn’t get photographed. I then perform the typical Quantum Mechanics trick of making it a probability distribution by normalizing it. The Hydrogen Atom Lecture 24 Physics 342 Quantum Mechanics I Monday, March 29th, 2010 We now begin our discussion of the Hydrogen atom. All that I do to find the divergence differential expression is to take the full integral and remove the infinite sum so that I’m basically doing algebra on the infinitesmal pieces, then literally divide across by the volume element and cancel the appropriate differentials. A general form for the radial wave equations appears at the lower right, fabricated from the back-substitutions. is a generalized Laguerre polynomial. You have to solve this by separation of variables. Further, you may not realize it yet, but something rather amazing happened with that number Q. Divergence creates a scalar from a vector which represents the intensity of ‘divergence’ at some point in a smooth function defined across all of space. The first image, where the box size was a little small, was perhaps the most striking of what I’ve seen thus far…, I knew basically that I was going to find a donut, but it’s oddly beautiful seen with the outsides peeled off. Since I was just sitting on all the necessary mathematical structures for hydrogen wave function 21-1 (no work needed, it was all in my notebook already), I simply plugged it into mathematica to see what the density plot would produce. This little bit of math is defining the geometry of the coordinate variables in spherical polar coordinates. I keep finding interesting structures here. I spent some significant effort thinking about this point as I worked the radial problem this time; for whatever reason, it has always been hazy in my head which powers of the sum are allowed and how the energy and angular momentum quantum numbers constrained them. Radius would be some complicated combination of x, y and z. So then, this framework allows you to define the calculus occurring in spherical polar space. A scalar function defines the topography of the hill… it says simply that at some pair of coordinates in a plane, the geography has an altitude. Here is how you construct a specific hydrogen atom orbital from all the gobbledigook written above. After all those turns and twists, this is a solution to the radial differential equation, but not in closed form. It isn’t exactly crippling to the field because the solutions to all the other atoms are basically variations of the hydrogen atom and all, with some adjustment, have hydrogenic geometry or are superpositions of hydrogen-like functions that are only modified to the extent necessary to make the energy levels match. There are three possible area integrals because the normal vector is in three possible directions, one each for Rho, Theta and Phi. After the hydrogen atom, the water gets deeper and the field starts to focus on tools that give insight without actually giving exact answers. Psi basically just becomes R. The first thing to do is take out the units.
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Estimating a static Phillips curve
Unemployment + boredom + Stata = this
To estimate a “classic” static Phillips curve, I analysed annual UK data for the period 1971-2010 (ONS series BCJE for inflation and series CZBH for unemployment). I estimated an equation of the form,
Where RPI is the annual year-on-year percentage change in the RPI index (i.e. the annual rate of inflation) and unemp is the rate of unemployment as a percentage of the population.
To examine the trade off between unemployment and inflation, I test,
Using the ONS data, I estimate the following model:
Since , this suggests a trade-off between unemployment and inflation. The t-statistic is approximately -1.47. The p-value against a two-sided alternative is 0.149. Therefore, we fail to reject the null at the 5% level.
Unfortunately, the Classical Linear Model assumptions that OLS relies on are violated in this case. I may address this in a future post…


https://penco.ir/referral/4933/مدل-برنامه-ریزی-غیر-خطی-عدد-صحیح-مختلط-و-راه-حل-های-ابتکاری-برای-مکان-موجودی-و-قیمت-گذاری-تصمیم-گیری-در-یک-زنجیره-تامین-حلقه-بسته

A mixed integer nonlinear programming model and heuristic solutions for location, inventory and pricing decisions in a closed loop supply chain
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت) Computers & Operations Research, Volume 65, January 2016, Pages 93–103
زنجیره تامین حلقه بسته - محل تسهیلات؛ قیمت گذاری؛ فهرست؛ عدد صحیح مختلط برنامه ریزی غیر خطی؛ Heuristics
We analyze a network design problem for a closed-loop supply chain that integrates the collection of the used products with the distribution of the new products. We present a mixed integer nonlinear facility location-inventory-pricing model to decide on the optimal locations of the facilities, inventory amounts, prices for new products and incentive values for the collection of right amount of used products in order to maximize the total supply chain profit. We develop heuristics for the solution of this model and analyze the effectiveness of these heuristics and the effects of the parameters on this system through numerical experiments.


In R. Collier’s words, “Success is the sum of small efforts, repeated day in and day out.” Now, we all know that. However… wouldn’t it be great if success is the sum of FUN efforts, repeated day in and day out?
Not really! Especially with these websites that we’ve found to aid you in building up foundational skills essential to success in the subject. Perhaps you’ve done numerous Mathematical sums as part of intensive drilling. But do you understand what you’ve practised? Here are SIX websites catering to different age groups so you can PLAY, not just practice Math!
1. XP Math
Image credits: XP Math
Practice your guess and check skills by attempting to hack a smartphone. You could even master the concept of volume with concepts from Minecraft! What’s not to love?
Sheppard software caters to a slightly younger target audience with its “Pop the Balloon” sequence identification games and various interactive methods to tackle concepts in decimals, algebra and geometry. This would likely stir up interest in those who think they are inclined to hate numbers.
Image credits: Sheppard Software
3. Manga High
As it states, “Play math, love math!”
During your first few attempts at the games on the site, you might think that it’s all easy peasy. Through the stages, the missions become progressively challenging and then you realise that the objective of the game is meant to equip you with an understanding of the said theorem or concept be it for quadratics or angles.
Image credits: Manga High
This one comes with a bonus, especially if you love science.
Image credits: Brilliant
Brilliant is meant to aid excellence in the mastery of science and math and its creator believes that learning should be interactive and bite-sized with learners having the chance to network, sharing their experiences on their attempts to understand mathematical and scientific concepts. Apart from an easily-navigable interface, Brilliant also practises what they put forth.
5. Get the Math
Get the Math gives us reasons to truly understand the subject because it can be applicable in fashion, videogames, music and … possibly almost every aspect of life! Watch videos uploaded on the site, then attempt the challenges put forth. It certainly beats assessment books doesn’t it?
Image credits: Get the Math
6. TedEd Math
Ahhhh TedEd. One of our favourite sites! If you’re really in the mood to chill and relax, just put on a TedEd video and get ready to be awed. We love this Bridge Riddle by Alex Gendler.
Image credits: Ted Ed


Math Classes to Jacobs Field
Miss Cooey's Probability and Statistics classes went to Jacobs' Field on Tuesday May 17th. The trip was in conjunction with a project in class that incorporates the slugging percentage of players. The students that attended the game were asked to record stats for an inning of the game so that the students can use the recorded statistics for comparison with their own data for their projects. The Indians made it exciting with a dramatic finish which was capped off by Home Runs by Grady Sizemore, and a game winner by Travis Hafner.


Desktop Survival Guide
by Graham Williams
ROC graphs, sensitivity/specificity curves, lift charts, and precision/recall plots are useful in illustrating specific pairs of performance measures for classifiers. The ROCR package creates 2D performance curves from any two of over 25 standard performance measures. Curves from different cross-validation or bootstrapping runs can be averaged by different methods, and standard deviations, standard errors or box plots can be used to visualize the variability across the runs. See demo(ROCR) and http://rocr.bioinf.mpi-sb.mpg.de/ for examples.


Read Time: 5 Minutes
On the last blog post I looked at the effect of recursion on functions and how we can use this to solve equations of the form f(x)=x numerically. Suspiciously, this didn't work for some functions at some starting values. The functions were unstable. Inspired by the Mandelbrot Set I decided to investigate this further.
For example, consider the function . When finding the answer to as we did last time we notice that not all starting values of x lead to a solution, and not all of the values who do lead to the same solution.
For example if we start with z=2 the value of k approaches about 1.7344, which I showed last time to be a solution to f(z)=z, but if I start at x=4, for example, the value of k blows up and diverges. I was completely bamboozled as to why this happened and so I decided to to graph this and create a Julia Set.
If a starting value of x doesn't diverge to infinity, i.e. we can use it to solve the equation , then I will colour it. The darker the colour the faster it converges, which means it is then more useful for solving the equation. If it diverges to infinity then we colour it white. Doing this with the function above we get this magnificent fractal.
This is incredibly surprising and incredibly cool. Looking closer at this image we see the water fountain-like shape seems to be infinitly self similar, with each tip holding the blob, and on each blob we can see a similar fountain. The claws that surround the entire image look like the claws on the side of the blob suggesting that if we zoom out enough we will see the same shape again. The beautiful patterns created from the lines are probably the result of many tiny bands of the water fountain interacting at the roots.
This shape, while beautiful, is very crowded. To make this easier to analyse I decided to only colour points if they approach 1.7344 . Doing this we get another fractal. While looking very different similar properties can be seen.
We see the fountains on have disappeared but now we can see the finer details of the claws, and what are on them. Inside every claw there seems to be an infinity amount of claws descending. On the sides of each claw are smaller claws that keep going. The coolest part of this fractal, however, are the blobs we can see on the claws. They are exactly the same as the massive blob. I conjecture that, although we cannot see it from this resolution, the number of blobs on each claw is infinite. Zooming into a claw we can see that it is exactly the same.
I suspect that the finer lines are due only to my algorithm, which stops after a finite number of iterations. We can see the same shape again, we can keep zooming in forever. Notice how the middle line that connects the blob to the main body can also be seen on the main body. This means if we zoom out we should find a similar shape like so:
I suspect that there should be a massive blob on the left with massive claws connect them together. If this is true then it suggests that each claw is connected on the tips, but finely. I conjecture that this shape is fully connected.
What if we try this with different functions? For example this is what looks like:
While not as cool we can still see similar patterns. The same inifinitly decscending and self repeating property can be seen.
Here is a slideshow of all the functions I tried and cool fractals I created. Click the left or right arrows to go to the next picture.
I created a web app here (that takes a while to load) to view these Julia sets since I couldn't find any other ones online that allow you to input any equation. Try playing with these functions yourself!
While I was on my fractal high I began playing a lot more with the idea of chaos creating fractals. For example, if we look at this chaos game that produces sierpinski's triangle we can generalise it in terms of complex numbers.
If we choose three sides of a triangle, and a starting number, on the complex plane and then take the arithmetic mean of the number and a random vertex of the triangle over and over we can create sierpinski's triangle.
But what if we didn't take the arithmetic mean? We can try playing with this function to get weirder fractals. For example, if we take the geometric mean we get this shape:
And a harmonic mean results in this shape:
It almost looks like serpenski's triangle was generated in non-euclidean space and projected onto the screen. I am still experimenting with different functions but haven't found anything interesting yet other than the ones listed above.
Still on my fractal high, I started looking for more geometrically analysable fractals. A simple one stood out to me. First, we draw a right angle triangle ABC. Then we can drop a perpendicular from the right angle B to the side AC. Then from the point where the new line intersects AC we can drop a perpendicular to AB, then from AB to AC and so on.
We get a zigzag pattern that, while not as beautiful as other fractals, has some intersting properties. For one, we can create a simple proof for an infinite series of trigonometric functions like so.
Notice how we can find side AC0 through both an infinite sum and pythagoras' theorem.
Cosecant can be represented using an infinite amount of cosines. We can prove another identity by realising that B0C0C1 is similar to AB0C0.
While we can prove these results with algebraic methods, I think the geometric proofs are a lot cooler.
We can construct a line of length cosine to the nth power for any n using this fractal as well. This is probably how the Ancient Greeks could have discovered Trigonometry.
Analysing these fractals gives us new ways to solve problems, interesting results, and mindblowing visuals. Awesome!


nodal planes, system of two thin lenses, chromatic and spherical aberrations.
Q 1. A thin converging lens and a thin diverging lens are placed coaxially at a distance of 5 cm. If the focal Length of each lens is 10 cm, find for the combination (i) the focal length (ii) the power (iii) the position of the principal point. [20 marks]
Q 2.Find the position of the paraxial point of a lens in the form of sphere of glass of radius 5 cm and refractive index 1.5 [10 marks]
Video Solution at 11 pm


Excel Formula To Average Non Blank Cells. In the example shown the formula in E5 is. Prepare below table.
Press the up-arrow key. G3 is the average of 2 and 2 since one cell is blank it should not be factored in 222 valid cells G4 is 3because one cell is zero one cell is blank and one cells is 3 therefore its computing 31. Function checks the cell D5.
Press the up-arrow key.
AVERAGEIFS price group where price C5C15 and group D5D15 are named ranges. Follow the following steps to use a formula to copy the value from the cell above. AVERAGEIFS Average_range range. This cell reference can be changed as you need.


On the 7th of September 2016 I started year 6. My new teacher is Mrs Sampson. I am on green table. On green table I sit with Ellie Joe, Harry, Louie and Ady. This is a list of who I sit with for my other lessons;
English:Louie, Caitlyn and Keanu.
Maths: Joe, Harry, Louie, Ellie and Ady
R.E:Joe, Harry, Louie, Ellie and Ady.
Topic:Louie, Caitlyn and Keanu.
Science:Louie, Caitlyn and Keanu.
I was scared on my first day because I didn’t know what to do or what the work was like. I found out the work was easy! I got really scared for nothing. The homework is not hard. English is fine. I struggle to do apostrophes but that is mainly it.
Maths homework is easy, it is, really! In year 5 I HATED maths homework but this year I LOVE it! The things I struggle with in maths is long division and decimals. The first maths lesson I had was SOOOOOO fun! We got to do Mathletics and it was really fun! One math lesson we got to maths and P.E in one. It was SUPER fun!!
In my other lessons I don’t struggle. My year 6 experience so far has been AMAZING! I love it! I can’t wait for my SATS. I have a feeling I will do great!
Thank you for reading my article! Comment down below what you want me to do next!


About This Website
This website is one of many websites founded and maintained by Carl Brannen. For more recent papers and articles, visit my blog index.
The purpose of www.DensityMatrix.com
is to promote the understanding of the density matrix formulation of quantum mechanics. As
quantum mechanics is usually taught, density matrices are derived functions that are mainly
useful for modeling mixed states. In this website, I show that the derivation can go both
ways, at least for the spin-1/2 fermions. Here we assume that the pure density matrices (pure
density matrices which are those which are unchanged by squaring) are
fundamental. From them, we derive the spinors. In a certain sense, the density matrix
formulation is a return to
Von Neumann's program for an algebraic foundation
for quantum mechanics. The modification is that we are now connecting
the algebra to the geometry of spacetime by way of David Hestenes'
geometric calculus or geometric algebra. In that
sense the roots of the theory date to the earliest days of quantum mechanics, and the objective of the theory is to achieve Einstein's goal of
geometrizing quantum mechanics. This is in distinction to Hestenes'
method, which is to
geometrize the spinor rather than the density matrix. The primary
advantage of choosing the density matrix formalism for geometrization
is that it avoids unphysical gauge freedom, a subject of
and or confusion.
The usual use of density matrices is well known so my website concentrates on how one
gets the spinors from pure density matrices. In doing this, we see that the U(1)
gauge symmetry appears as a geometric choice. It is the objective of the rest of these
websites to expand this geometrization to the remaining gauge symmetries.
The purpose of www.MeasurementAlgebra.com
is to promote the understanding of Julian Schwinger's "measurement algebra". The
measurement algebra is a particularly elegant method of defining the foundations of
quantum mechanics that dates to the 1950s. Schwinger was looking for a way of
defining quantum mechanics that was based on the known facts of microscopic
measurements of elementary particles. The act of making such a measurement
will typically destroy previous knowledge of the particle.
Schwinger then looks at what happens when various experiments are consecutively
conducted on an elementary particle (or on a beam of them). For example, if
the measurements are of the spin of spin-1/2 particles, then the measuring
apparatus is the Stern-Gerlach experiment. If we were to restrict our particles
to be only electrons and we only measured spin, then the measurement algebra
would represent each particle with the projection operator corresponding to
the orientation of the Stern-Gerlach apparatus that gives that spin. But we
can be more general than this and imagine an experiment that separates, for example,
muons from electrons.
If a measurement is repeated on the same particle, the result of the measurement
is unchanged. Schwinger represents this by saying that such a measurement, when
squared, gives itself. This is identical to the definition of the pure density
matrices -- therefore, we can use Schwinger's measurement algebra to extend the
density matrix formulation to more general particles. For example, instead of
working with the (single particle) density matrix for an electron, we can consider
a single particle density matrix for a lepton, a particle that is either an electron, a
muon, a tau, or one of the neutrinos. This is useful in flavor physics.
The purpose of www.CliffordAlgebra.com
is to promote the understanding of Clifford algebra, particularly in its
application to the density matrix formulation extended by Schwinger's measurement
algebra. Physicists already use two Clifford algebras in the standard model,
the Pauli algebra and the Dirac algebra. The subject is usually taught by
defining particular representations of these algebras; these are known
as the Pauli spin matrices and the Dirac gamma matrices.
The density matrix formulation of quantum mechanics is written in the Pauli or
Dirac algebra. In extending this formulation with Schwinger's measurement algebra
we need a larger algebra than even the Dirac algebra and this is where Clifford
algebra comes in.
The usual way quantum mechanics is presented has the particles represented by
vectors while the operators are represented by matrices. The equations one
solves are of the form M|m> = m|m>, where M is an operator, and |m> is an
eigenvector with eigenvalue m. These are linear equations.
In the density matrix formulation, there is no splitting of the elements into
operators and eigenvectors. Instead, all elements are operators, or matrices.
The equations one solves are of the form (|m>
But the mathematics of Clifford algebras is sufficiently advanced that it
is possible to solve these sorts of equations. While more difficult, it is
here that I hope to find the foundations of the elementary particles. To do
this, a knowledge of Clifford algebras is necessary.
There are plenty of sources of information on Clifford algebras on the web.
A good place to begin is
Wikipedia on Clifford Algebra.
These sources generally treat the "canonical basis vectors" as fundamental,
and define the rest of the algebra in terms of these. This follows the
mathematical definition of the algebras. But for the purpose of applying
Clifford algebra to Schwinger's measurement algebra, we need an analysis of
Clifford algebras from the point of view of particles. That is, we need an
analysis that concentrates on the elements of the algebra that satisfy
M M = M. These turn out to be related to the elements that square to one.
www.Snuark.com is for my preon theory
of elementary particles. It is based on the above observations. To
understand it, you will first need to learn the appropriate mathematics and
get used to my notation.
www.Brannenworks.com was originally
started so that I could sell porcelain on the web. This engrossing hobby was
driven out by a desire to better understand the foundations of physics. Since
early 2003, my website has been mostly about physics. I will continue to keep
my papers there, along with various human interest items, Java applets, etc.
What does the scientific community think?
It is very difficult to get much attention in the elementary
physics community. In particular, trying to get a busy physicist to read a
paper that will require learning new mathematical techniques is essentially
impossible for an amateur. The only paper I've written that has received
much attention was one that had all the "adult" mathematics removed from it.
is on the masses of the leptons, particularly the neutrinos. It provided
an extension of Yoshio Koide's famous empirical formula
for the masses of the charged leptons.
The way I got the paper read was by carefully eliminating all the things that
would prevent a professional physicist from reading it. First I got rid of all
the references to alternative foundations for physics. Then I got rid of any
new mathematics that anyone would find inconvenient. Then I boiled the result
down to just a few very simple equations. This got through, and as a result
my formula for the neutrino masses appears in
(hep-ph/0605074) . If your native language is Japanese, you might prefer these slides.
The MASSES2 paper is now cited in the peer reviewed literature:
Neutrino Mass and New Physics, R. N. Mohapatra and A. Y. Smirnov, Annual Review of Nuclear and Particle Science, Vol 56:569-628, (November 2006).
The primary use of my time in physics lately has been typing up a book
describing how all these things fit into the standard model. The book
is available on the web here,
and at this writing is 170 pages long.
The book gets updated as I type up new material or find corrections.
When people who are unfamiliar with mathematics and physics see the above
book they tend to be impressed by the typography, that is, by the beauty
of the typesetting. It is typeset with LaTex, a language that is used
almost universally in mathematics and physics. I used the "memoir"
class, which is particularly useful in helping control the marginal
notes, headers and footers.
People who are interested in writing papers extending this work, as
well as those who wish to write their own books, might find the source
code for the above book useful. I have made it available
At this time, I only plan on attending one more conference, the
gravitation conference in Australia in mid summer 2007. My plan
is to give a talk on mass as a quantum number in one of the
quantum gravity sections. I was thinking about going to the
cosmic ray conference in Mexico, but these things are really
very tiring to prepare for and attend and I just have too much
stuff to do right now.
Upon Julia's Clothes
Whenas in silks my Julia goes,
Then, then, methinks, how sweetly flows
That liquefaction of her clothes.
Next, when I cast mine eyes, and see
That brave vibration each way free,
Oh, how that glittering taketh me!
Robert Herrick, 1591-1674
Finally, there are a few other websites I should mention.
My old friend Al Foxx gives motivational and disability act
speeches. So I picked up the following websites and redirected
them to his website, AlFoxx.com:
Seattle Motivational . com and
Disability Act Speaker . com. While watching people
play chess at the mall, I met a sculptor, Telman Karimov,
who moved here from Turkey. He does bas reliefs, so I set
in the hopes of sending some business his way. The reason for
here is so that the robots will find them and put them into
the google search engines properly. And I should mention that
I have a blog at word
press that pretty much stays away from physics or anything else.


Which of the following refers to the proving of mathematical theorems by a computer program?
Analytical theorem proving
Automated technology proving
Automated theorem processing
Automated theorem proving
None of the choices.
Automated theorem proving (ATP) is the proving of mathematical theorems by a computer program.
Depending on the underlying logic, the problem of deciding the validity of a theorem varies from
trivial to impossible. Commercial use of automated theorem proving is mostly concentrated in
integrated circuit design and verification.


2 edition of Oxford secondary mathematics found in the catalog.
Oxford secondary mathematics
E. J. James
|Statement||E.J. James. Answer book 2.|
resources/mathematics,clickonWeblinksintheResources section and click straight through to the relevant websites. Christopher Clapham wasuntilSeniorLecturerin Mathematics at the University of Aberdeen and has also taughtatuniversitiesinNigeria,Lesotho, the author of Introduction to File Size: 6MB. Build the best foundation for success in the Cambridge Checkpoint tests, and ensure your students get the challenge and extension they need to achieve their best in the Cambridge IGCSE. This course matches the latest framework and will rigorously prepare students for the strongest achievement at Checkpoint level and be. English text book “Marigold” for class 4, CBSE, NCERT. Environmental Studies text book “Looking Around” for class 4, CBSE, NCERT. Hindi text book “Rimjhim” for class 4, CBSE, NCERT. Mathematics text book “Ganit-Ka-Jadu” Hindi Midium for class 4, CBSE, NCERT. Mathematics Illuminated is a text for adult learners and high school teachers. It explores major themes of mathematics, from humankind's earliest study of prime numbers, to the cutting-edge mathematics used to reveal the shape of the universe.
The 2000 Import and Export Market for Semi-Manufactures of Tungsten and Molybdenum in Brazil
Hail fellow well met
Governmental Evaluation Commission report on North Carolina Licensing Board for Contractors.
Secret Adversary (The Agatha Christie Mystery Collection)
impacts of an East Asia FTA on foreign trade in East Asia
Spirit of conservatism.
Symposium on R.O.C. and U.S. Relations
The training and development of young footballers in Scotland
Japanese colonization in eastern Paraguay
Cousins in the castle
A letter to an honourable gentleman of the Council-Board, for the colony of Connecticut
The moral ecology of South Africas township youth
Pastor and people: Making it happen-- together
Development of a sensitive bioassay to detect exposure to environmental estrogens
Product. Complete Mathematics for Cambridge Lower Secondary Book 3: Print and Online Student Book. Comprehensive preparation for the Cambridge Checkpoint and beyond. Junior Secondary Oxford Mathematics for the New Century is written in accordance with the Supplement to Mathematics Education Key Learning Area Curriculum Guide – Learning Content of Junior Secondary Mathematics, which commences in It consists of six volumes: 1A, 1B, 2A, 2B, 3A and 3B.
The books are designed in ‘school-based pack’ format to enable flexible teaching arrangements and. Price and stock details listed on this site are as accurate as possible, and subject to change. Occasionally, due to the nature of some contractual restrictions, we are unable to ship to some territories; for further details on shipping restrictions go to our Help section.
Welcome to Oxford's education bookshelf -- your portal to Oxford online publications. Further Resources. View all primary and secondary education resources from Oxford.
Learn about Kerboodle Online Resources – a digital learning platform that helps you engage, plan, progress and measure learning. Already use Kerboodle. Log in here. Mathematics For Secondary School - Free download Ebook, Handbook, Textbook, User Guide PDF files on the internet quickly and easily.
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These resources are. New Syllabus Mathematics (NSM) is a series of textbooks where the inclusion of valuable learning experiences, as well as the integration of real-life applications of learnt concepts serve to engage the hearts and minds of students sitting for the GCE O-level examination in Mathematics.
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Mathematicians have always been fascinated by numbers. One of the most famous problems is Fermat’s Last Theorem: if n≥3, the equation x n +y n =z n has no solutions with x, y, z all nonzero integers. An older problem is to show that one cannot construct a line of length 3 √2 with ruler and compass, starting with a unit length.
Often the solution to a problem will require you to think. 2 Aims of Mathematics Education in Schools 1 3 Mathematics Framework 2 Concepts Skills Processes Attitudes Metacognition PART B SECONDARY MATHEMATICS SYLLABUSES 4 O Level Mathematics Secondary 1 6 Secondary 2 9 Secondary 3/4 12 5 N(A) Level Mathematics Secondary 1 16 Secondary 2 19File Size: KB.
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BoxKarachi Pakistan () uan () telephoneFile Size: 1MB. This book is the second Teachers' Manual in the KLB Secondary Mathematics series. It is set to adequately guide the teacher through Form Two Secondary Mathematics as per the new curriculum. The guide should be used together with the Secondary Mathematics Students' book Two to ensure comprehensive coverage of topics at hand.5/5(2).
Oxford Forward (for Secondary School Teachers) OUP also offers newsletter resource especially for Secondary School Teachers. Oxford Forward aims to provide the up-to-date teaching and learning skills, feature stories and experience sharing from experts and teachers.
: Complete Mathematics for Cambridge Secondary 1 Student Book 1: For Cambridge Checkpoint and beyond () by Deborah Barton and a great selection of similar New, Used and Collectible Books available now at great prices/5(5). Here is an unordered list of online mathematics books, textbooks, monographs, lecture notes, and other mathematics related documents freely available on the web.
I tried to select only the works in book formats, "real" books that are mainly in PDF format, so many well-known html-based mathematics web pages and online tutorials are left out.
Oxford Mathematics Public Lecture: Alan Champneys - Why pedestrian bridges wobble: synchronisation and the wisdom of the crowd. In this lecture Alan Champneys argues that Mathematics is at its bes.
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New Enjoying Mathematics revised edition series it places emphasis on developing thinking and reasoning skills among students, by connecting the mathematics curriculum with real-life situations. Keeping CCE requirements in mind we have incorporated suggestions.
The New Syllabus Primary Mathematics (NSPM) series is designed and written based on the latest primary mathematics syllabus. In this series, the concrete to abstract approach is adopted to introduce new concepts.
Vivid and stimulating illustrations are used throughout the series to enhance learning. The knowledge base is built incrementally as the pupils progress up the levels so as to.
Mathematics Illuminated is a text for adult learners and high school teachers. It explores major themes of mathematics, from humankind's earliest study of prime numbers, to the cutting-edge mathematics used to reveal the shape of the universe.
( views) Galois Lectures by J. Douglas, P. Franklin, C.J. Keyser, L. Infeld - Morrill Press, Math Topics for Secondary School Teachers Mathematics. High-school subjects from an advanced point of view and their relation to the more advanced subjects. May be repeated once for credit.
3 Credits. Instruction Type(s) Lecture: Lecture for Math ; Lecture: Compressed Video for Math ; Lecture: Teacher Workshop for Math -Oxford International Maths for Cambridge Secondary 1 Teacher Pack 3 Stay safe and healthy.
Please practice hand-washing and social distancing, and check out our resources for adapting to these times. With a methodical and logical approach that matches the new framework, carefully developed exercises will stretch students while the sheer volume of practice will reinforce understanding.
Complete Mathematics is the new name for Oxford International Maths. Features. Matched to the latest Cambridge Lower Secondary syllabus. MPHONLINE | Complete Mathematics for Cambridge Secondary 1 Student Book 3 | | Oxford | Oxford University Press | Books | Language-and-Reference.
Junior Secondary Maths iTutor is an indispensable companion to the junior secondary New Century Mathematics coursebooks. It is specially designed to facilitate the learning and teaching of junior secondary mathematics by providing you access to Category: EDUCATION.New Syllabus Mathematics is a series of four books.
These books follow the Mathematics Syllabus for Secondary Schools, implemented from by the Ministry of Education, Singapore. The whole series covers the complete syllabus for the Singapore-Cambridge GCE O Level Mathematics.
The sixth edition of New Syllabus Mathematics retains the goals and objectives of the previous edition, but has 5/5(3).


My Thanksgiving morning was perfectly nostalgic. Up early to put the turkey on and make a nice breakfast. followed by watching the Macy's Thanksgiving parade on TV . . . updated a bit because as I watched, I cut setting triangles and assembled a Christmas quilt top from those old swap blocks.
With a large design wall, it was a lot easier to figure out what I meant by my mysteriously coded sketch and lay out the blocks.
It seems I always have to go look up setting triangle math, whenever I put blocks on point. I know that the magic number is the square root of 2–1.414–but I never remember what to do with it ... so off to the computer I go.
Here's how I will remember NEXT time:
- Since I'll need MORE side triangles, I MULTIPLY the finished block size by 1.414. Then, because I am going to cut the square into quarters, as for quarter-square-triangle units, add 1 1/4 for the seam allowances.
- For the corners, I do the opposite and DIVIDE the finished size block by 1.414. Because I am going to cut them diagonally in half, like half-square-triangle unites, add 7/8 inch.
For the corners, I used the twelve inch star block as the starting point. 12 / 1.414 + 7/8 = 9 3/8 inches. Because I inserted six inch 4-patches into the side setting triangles, I used 6 in the side triangle math. 6 * 1.414 + 1 1/4 = 9 3/4.


Philips Morris expects the sales for his clothing company to be £ 560,000 next year. Philip notes that net assets (Assets- Liabilities) will remain at 40% of sales. His clothing firm will enjoy a 8% return on total sales. He will start with £ 160,000 in the bank. What would Philips’s ending balance be?
Net assets = 40% * 560,000
Return on total Sales = Net Profit
0.08 = Net Profit
Net Profit = 560,000 * 0.08
Since net assets ratio remains the same, the closing balance will be;
=160,000 + 44,800
for more math homework help, check out AceMyHW.com


Welcome to our Mining equipment manufacturing base, Contact Us
lump size or fine material. In the calculation of belt dimensions one must take into account the minimum values of belt width as a function of the belt breaking load and the side roller inclination as shown. 5.2.2Minimum belt width: 5.2.3.Loaded volume IM: The volumetric load on the belt is given by the formula: where: Iv = load capacity of the ...
L = conveyor length (m) ε = belt elongation, elastic and permanent (%) As a rough guideline, use 1,5 % elongation for textile belts. and 0,2 % for steel cord belts. Note: For long-distance conveyors, dynamic start-up calculations. may be required, because not all elements are set in motion simultaneously,
Length related mass of the rotating parts of the idlers in a conveyor section : Length related mass of conveyor belt : 3.6 v Q l c zkd [kg/m] l m l m kd ' kg ' zkg k m [kg/m] 1000 B m t tj. v Q m j St l c 3 6 U M
Belt Widths The belt widths are as follows: 18, 24, 30, 36, 42, 48, 54, 60, 72, 84, and 96 inches. The width of the narrower belts may be governed by the size of lumps to be handled. Belts must be wide enough so that any combination of prevailing lumps and finer material does not load the lumps too close to the edge of the conveyor belt.
Jul 25, 2016· Torque input to shaft by each drive assembly (equal with torque generated by belt tension) = (BT1 – BT2)/2 x Pulley Diameter /2 = 52,341 N.m. Pulley mass = 5,286 Kg. Reaction force at Bearing A ...
Aug 15, 2008· id = inside diameter. Use consistent units and conversion factors. RE: Formula for rolled up conveyor belting. telnique (Mining) 15 Aug 08 16:45. I use this one and it works all the time. L = NS X .2618. Where L = length. N = Number of turns on belt. S = Measured inches between ends on roll of belt.
May 26, 2019· Dimensions known to calculate belt length Now, we already know the size of the pulley, either from the manufacturer's data or we can go out into the building and actually measure this. Remember Pulley 1 is always going to be the largest pulley you have, and you'll see this as we go through the calculations shortly.
the inspection and testing of belt-conveyor scale systems. Consider the diagram of a simple conveyor belt in Figure 1 below. As one would likely expect, an appropriate amount of friction must be maintained between the conveyor belt and the drive pulley to transfer the motion from the drive pulley to the belt.
Beltcomp Nov v.2007. Beltcomp is a powerful belt conveyor design software program based on ISO/DIN/IS method of calculation using metric units. Beltcomp design program is a highly dependable software to provide consistent, accurate and cost effective belt conveyor designs. Category: Science. Developer: Beltcomp.
Dec 31, 2012· Simple Torque Calculation for Belt Conveyor – bulk-online Forums. i need a simple (or estimate) formula to calculate torque (to turn)for belt conveyor application based on belt length, … Power (kW) = Lift (m) x tph x 1/367 »More detailed
Nov 20, 2013· The calculation is actually quite simple. If the speed reduction of the chain or belt drive is N:1, then the gearmotor output speed should be N times the speed calculated for the conveyor roller and the torque output should be 1/N times the …
89 Belt Tension Calculations W b =weight of belt in pounds per foot of belt length. When the exact weight of the belt is not known, use average estimated belt weight (see Table 6-1) W m =weight of material, lbs per foot of belt length: Three multiplying factors, K t, K x, and K y, are used in calculations of three of the components of the effective belt tension, T
Jun 19, 2019· The belt conveyor is used for conveying different materials from one location to another. The different components of a belt conveyor system typically are electric drives, pulleys, idlers, and a long belt. A simple conveyor system may look like below: The basics of the Calculations of Conveyor Belt Design Parameters
May 16, 2014· Belt Speed (BS): The calculator computes the belt speed (BS) in meters per second. However, this can be automatically converted to other velocity units via the pull-down menu. The Math. The formula for the speed of the belt is: BS = (D •π • R)/(2π) = ½•D•RPM. where: BS is the Belt Speed; D is the diameter of the pulley
In the case of perforated belts please note: calculate the load-bearing belt width b 0 based on the number of per-forations which decrease cross sec-tions. Staggered perforations in partic-ular can reduce the load-bearing belt width considerably. Reduce the figure for the load-bearing belt width b 0 by a further 20 % to take tolerances for per-
Excel For Conveyor Speeds. Understanding conveyor belt calculations understanding a basic conveyor belt calculation will ensure your conveyor design is accurate and is not putting too many demands on your system belt speed expressed in feet per minute fpm sd x rpm x 2618 x 1021 belt load. More Details. Formula To Calculate Motor Size For Conveyor.
Aug 18, 2021· Where can i get a simple set of formulas for this purpose? Also i need to calculate the linear speed of the conveyor? Here are some specifications about it: Overall production : 43,2 tonh/h Bags per minute : 24units Bag mass : 30kg Bag size : 0,18mx0,55mx0,8m--Regards Víctor Horn --Regards V.H.
Calculation methods – conveyor belts Siegling – total belting solutions conveyor and processing belts This brochure contains advanced equa-tions, figures and recommendations, based on our longstanding experience. Results calculated can however differ from our calculation program B_Rex (free to download from the Internet at ...
MITCalc V-Belts Calculation v.1.22. Geometric design and strength check of belt transmissions using V- belts. Application contain a database of belts, supports Imperial and Metric units, is based on ANSI, RMA, ISO, DIN and BS standards and support many 2D and 3D CAD systems. File Name:MITCalcVBelts01_64.exe.
Typical Conveyor Capacity. 1 in = 25.4 mm. 1 ft3/h = 0.028 m3/h. 1 ft/min = 5.08 x 10-3 m/s. The product cross sectional area is defined by the idler trough shape and the product pile on top of the idler trough the trapezoid shape. This section on top of the trapezoid can be described with a circle and the angle this circle makes with the belt ...
The 5th, 6th, and 7th editions of the Conveyor Equipment Manufacturers' Association Belt Conveyor Design Manual includes several methods to calculate the belt tension required to move bulk materials on a conveyor belt. They are beyond the scope of this short video. These methods include "historical", "basic", and "universal" methods.
Oct 17, 2010· Belt Conveyor Counterweight I am with the design project of fabric belt conveyor, I tried different computation of different manual available with in my access but its time I'm using *formula as stated at the manual I obtain different figure, can you help me to what formula I'm going to use. My designed involve a tripper car and 14 fly fabric conveyor belt .
side and using the resulting belt sag to compensate for the increase in length. It is important that perfect engagement between belt and sprocket is ensured. Following are several examples: a) Short conveyor (fig. 1) b) Medium length conveyors, up to a centre distance of approx. 4,000 mm (fig. 2) c) Long conveyors: centre distance > 20,000 mm and
The math is not as difficult as it appears. Here's the logic behind the center-to-center distance formula: 2C: Multiplying the center-to-center distance by 2 accounts for the belt length on the top and bottom of the pulleys Note: The pitch created by differing pulley diameters is addressed later in the equation. (D+d ÷ 2): This accounts for the belt length "wrapped around" the outer ...
formulas for the calculation for dimensions for a simple belt conveyor .. Simple Torque Calculation for Belt Conveyor - bulk-online Forums . CEMA Publiions Standards and downloads.cone crusher dimension [11-26]. fama italy equipments [11-26]. cement and concrete production line [11-22]. Read more
belts are one component of complex equipment, the loads in the belt itself are very seldom precisely predictable. This fact makes it impossible to confirm a precise belt service life. In order to opti-mize belt life of the belts, it is important to follow the catalogue technical specifications related to pulley geometry and belt sto-
Positioning operation. Step 1 : Leave the rotor inertia Jo and the gear ratio i blank if you have not selected any motor (or geared motor) yet. Then, fill in the rest of the form. The software will temporary calculate the acceleration torque with a load/rotor inertia ratio of 5:1. Step 2 :
V-Belt Length is a measure of required belt length based on the distance between the center of two pulleys and their diameters to effectively transmit the rotating force from one to another.. Formula to calculate required length of v-belt between two pulleys
Conveyor and processing belts Calculation methods – conveyor belts Content Terminology 2 Unit goods conveying systems 3 Take-up range for load-dependent take-up systems 8 Bulk goods conveying systems 9 Calculation example Unit goods conveying systems 12 The formulae, figures and recommenda- These differences are a result of the tions in this brochure are state …
Pulley Calculator. RPM, Belt Length, Speed, Animated Diagrams. If you know any 3 values (Pulley sizes or RPM) and need to calculate the 4th, enter the 3 known values and hit Calculate to find the missing value. For example, if your small pulley is 80mm diameter, and spins at 1000 RPM, and you need to find the second pulley size to spin it at ...
May 10, 2015· belt conveyor design calculations pdf Image Gallery. belt conveyor design calculations pdf both co and co2 and if needed for reaction 5 the natural gas with | File Size: 400 x 341 · 66 kB · jpeg Download. belt conveyor design calculations pdf TITLE_IMG2 | File Size: IMG_SIZE2 Download.
Motor Sizing Calculations This section describes certain items that must be calculated to find the optimum motor for a particular application. Selection procedures and examples are given. Selection Procedure First, determine certain features of the design, such as drive mechanism, rough dimensions, distances moved, and positioning period.


Mathematics is the language of science, and with the explosive development of computer applications to virtually every facet of business and industry, it is rapidly becoming the language of society. Throughout history, mathematics has been studied for its beauty as well as its utility. Mathematics has often been considered more as a "way of thinking" than as a collection of facts, formulas and procedures. The very nature of mathematics requires the development and constant use of a wide variety of analytical skills and approaches to problem solving which impact the student's very existence and are highly prized by prospective employers. The study of mathematics prepares a student for life, as well as for a career.
The demand for quality graduate mathematics students is such that truly excellent opportunities exist for graduate study. Graduates of programs in mathematics also have an excellent background for further study and/or employment in the related sciences, as well as many areas of business and law. The Society of Actuaries is constantly seeking graduates to pursue a career in the insurance field.
Check out the website of our newest Mathematics faculty member, Dr. Charles Samuels.
Strengths of the DEPARTMENT OF MATHEMATICS and the DEPARTMENT OF PHYSICS
Pre-engineering classes offered
During the past several years, 7 out of 8 Physics majors have continued their studies at graduate school
Excellent and friendly student-faculty relations, even after graduation of the students
Faculty consists of both young/energetic and experienced mathematicians and physicists
Students in upper divisions are willing to help and support freshmen
Students have easy and direct access to faculty
Students are encouraged to do independent work, also in the physics labs


Illinois Valley Community College Ottawa Center is hosting “Express Registration” from 4-7 p.m. Tuesday, May 14.
The summer enrollment opportunity will feature on-the-spot counseling, financial aid information and admissions representatives. Main campus summer A begins Monday, May 20, Ottawa Center Summer begins Monday June 3 and main campus Summer B begins Wednesday, June 12.
Ottawa Center summer courses include basic and intermediate algebra, basic geometry, technical mathematics, music appreciation, general psychology, strategies for college and speech.
RSVP at www.ivcc.edu/events; call (815) 224-0800 for information.


How to Beat the odds with a Lottery Group
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Numerosity: Play with Addition!
Addition + Play = Making Math Fun
This educational math game is aimed at children 6 to 8 years old. They’ll learn math, review concepts and improve their numerical skills whilst having fun!
Did you know that addition is commutative, or that if you move one number from one side of the equal sign to the other, its sign changes?
Learn Addition by playing with the numbers and discovering all these rules by yourself, at your own pace.
Create your profile to challenge your friends! Win coins, unlock all the 20 levels, try to beat your own record and win the most challenging achievements to become a master of addition!
And, at the end of the game…SURPRISE! A fabulous certificate made especially for you to send to your parents and hang on the wall!
Come and check it out! I’d love to play and learn from you!
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ThoughtBox is an educational software provider that delivers learning experiences in specific subject areas centered around Gameful Learning. ‘At ThoughtBox we believe in researching and creating software that gives kids the best educational value and encourages them to discover and learn the rules of math on their own. We believe in quality content and educational apps that give kids more than just a few minutes of play’.
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If you wish to calculate BMI yourself, below are the BMI formulas for both English units and metric units:
|Metric Units: BMI = Weight (kg) / (Height (m) x Height (m))|
|English Units: BMI = [Weight (lb) / (Height (in) x Height (in))] x 703|
Example : Someone who is 5'6" (5 * 12 + 6" = 66") and weights 160 lb has a BMI of BMI Calculation = [160 / (66 x 66)] x 703 = 25.8 <== This person is Overweight.
o A BMI of less than 18 means you are under weight.
o A BMI of less than 18.5 indicates you are thin for your height.
o A BMI between 18.6 and 24.9 indicates you are healthy.
o A BMI between 25 and 29.9 suggests you are overweight.
o A BMI of 30 or greater indicates obesity.


Post Follow-up: Working the New ACT Math Probability Items
In the previous post, we divided the probability items found in the last two Preparing-for-the-ACT Guides into three categories. In this post, we work those items. If you have questions or comments, shoot me an email at email@example.com.
These items are provided to give you examples of the ways you can expect ACT to test probability. These are screenshots from the ACT’s booklets, not the property of 36 University.
Item Type 1: Basic Probability Items
These items require you to apply the basic probability formula:
P(A) = (# of events corresponding to A/ total # of possible events)
Step 1) Recognize there are now 755 pieces.
Step 2) Of those 775 pieces, 5 are the new “extra” pieces.
Step 3) Use probability formula: P(extra piece) = 5/755
Step 1) Current probability of red marble: 12/32
Step 2) Recognize we need a fraction that will reduce to 3/5, so the denominator has to reduce to 5.
Step 3) Begin adding red marbles in increments so that the total number of red marbles is divisible by 3.
Current Probability of red: 12/32 –> 3/8
Add 3 red marbles. Updated probability of drawing red marble: 15/35 –> 3/7
Add 8 red marbles. Updated probability of drawing red marble: 20/40 –> 1/2
Add 13 red marbles. Updated probability of drawing red marble: 25/45 –> 5/9
Add 18 red marbles. Updated probability of drawing red marble: 30/50 –> 3/5. (I should have known!)
Item Type 2: Probability from Graphs
These items require you to utilize your graph reading skills and basic probability concepts.
Step 1) They provide formula for odds. Odds = in the age range:not in the age range.
Step 2) Percentage of persons in 25-35 years range: 42% or 42 out of 100.
Step 3) If 42 out of 100 are in the age range, the other 58 must not be in the age range.
Step 4) Set up the odds. 42:58 –> 21:29
Step 1: P(Type A or Type AB blood) = (# of Type A + # of Type AB)/ (Total # of possibilities)
Step 2: P(Type A or Type AB blood) = (67 + 6)/150 –> 73/150
Item Type 3: Probability of Multiple Events
Multiple events probability items ask you take one additional step. Often, that means you’ll just need to multiply the probabilities of each event. Here are examples:
Step 1: 80% pass written test. Of 1,000, we expect 800 to pass written test. (80% • 1000)
Step 2: Of those that pass written test, 60% pass driving test. 60% • 800 that passed written –> 480 expected to pass both
Step 1: Chances of guessing a particular item correctly is 1/3, since there are three answer choices.
Step 2: Chances of guessing all 4 items correctly? Multiply the probabilities: (1/3) • (1/3) • (1/3) • (1/3) –> 1/81
Wrapping It Up
We hope these solutions helped you work these items more efficiently! If you have an alternative, quicker method to solving any of these items, we’d love to see it.
Recent & Related Posts:


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A student whose jingle helped her memorize more than 125 digits of the infinitely long number that begins with “3.14” was allowed to smear a real pie in the face of her math teacher during a competition that was part of the March 14 Pi Day festival at Bedford-Stuyvesant Collegiate school on Gates Avenue. Even she was surprised by the feat.
“It is exciting to know that I was able to memorize a larger amount of pi,” said 14-year-old Yolanda Dunbar. “I am impressed with myself.”
As a reward, Dunbar got to throw a pie — the edible kind — in the face of her math teacher. The second- through fourth-place winners were awarded the opportunity to challenge the teacher of their choice to a pie-eating contest.
Dunbar said she learned half the digits of pi by listening to a song she found on Youtube and half by rote memorization.
This is the second year Dunbar won. Back in the sixth grade, she beat out her classmates and creamed then-math-teacher Caitlin Webster, who says the annual party is an excuse to inject some fun into the sometimes-dry subject.
“We celebrate Pi Day to create some joy and excitement around math,” said Webster. “It is something that is fun and not strictly challenging.”
The school hosts a handful of other wacky math events. For example, they celebrate a Fun Facts Friday, where teachers dressed as ninjas randomly storm classrooms and students have to correctly multiply to help free their space-traveling tiger mascot, Cosmo, whom the ninjas have supposedly kidnapped.


|2017 STAR SAT Conversion Instructions|
Instructions for PAGE STAR 2017 SAT Scores Conversion
Changes for 2017 STAR only*:
The PAGE STAR program will accept scores from two versions of the SAT, the "old" three-part and the "new" two-part SAT. However, the old three-part SAT scores must be converted to the College Board new two-part SAT "section scores" in order to be accepted for the 2017 PAGE STAR Program. Please see conversion instructions below.
*(NOTE: Please alert your sophomores and juniors that the "old" three-part SAT will not be accepted for 2018 STAR. Thank you.)
To qualify for nomination:
The student with the highest totaled "section scores" in a single sitting should be nominated to be the PAGE STAR Student for your school. If, by chance, you have two or more students with the same score, the school is responsible to break the tie and determine the STAR nominee using GPA (the grade average numerically computed by utilizing the system normally utilized by the school.) The "tied" student with the highest GPA is to be nominated for STAR. NO TIES at the high school level will be allowed for STAR 2017.
If all of your seniors took only the "new" SAT, simply determine which student had the highest score on a single sitting/administration of the test and enter that student's scores on the "Evidence-Based Reading and Writing" section and the "Math" section on the PAGE STAR nomination website.
Minimum scores for both "section scores" are Evidence-Based Reading and Writing 530 and Math 530. The nomination website will be "open/live" after October 17, 2016; the deadline to enter nominations is December 15, 2016. The last acceptable SAT test date for STAR 2017 will be November 5, 2016.
Conversion of old SAT scores & determination of nominee:
To convert the old three-part SAT score to the new two-part "section scores" to determine the total SAT "new" test equivalent score and nominate a student, follow these instructions:
Use the College Board Concordance Tables links below:
EXAMPLE: (Assume a student had scores on the "old" three-part SAT test of: Critical Reading 700; Writing 690; and Math 740.)
STEP ONE: Add the old SAT Critical Reading score and the old SAT Writing Score together and then, using the "Old SAT Writing plus Critical Reading Sections to New SAT Evidence-Based Reading and Writing Section" equivalent score on the new SAT.
(In our example, this would mean adding 700 to 690, for a total of 1390; and using the Concordance Table, the 1390 would convert to 730.)
STEP TWO: To determine the new SAT equivalent Math score, use the "Old SAT Math Section to New SAT Math Section Concordance Table." Based on the Concordance Table, the 740 in math would convert to 760 on the new test.
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STEP FOUR: When entering the student's test scores on the PAGE STAR nomination website, the scores must be entered in "section scores" equivalent to the new SAT's two parts:
In our example, the scores reported on the PAGE STAR nomination website would be Math Section: 760; Evidence Based Reading and Writing Section: 730. (The total score of 1490 will automatically be calculated on the nomination website.)
If you have any questions, please call the PAGE STAR office at 770-216-8555 or email us at STAR@pageinc.org.


Next Generation Cryptography now available with Azure Web Sites
Securing your site with SSL has never been more important, but even though encryption isn’t new, cryptographers keep looking for ways to be more secure and we in Azure Web Sites are always looking for ways to support the latest and greatest. Today, the greatest is Elliptic Curve Cryptography (ECC) certificates. Elliptic curve cryptography is an encryption technology based on the algebraic structure of elliptic curves over finite fields. If that sounds complicated, don’t fret…not a lot of people get it. Elliptic curves are graphs drawn based on the y2 = x3 + ax + b family of algebraic functions. When you plot the X and Y values of such a function, the curve looks elliptic and symmetric. For example, the graph for the function y2=4x3-4x+4 would look like this: Without going too deep into the math behind this, the symmetry and computational complexity in this sort of function allows us to efficiently create a public and private key set that are much harder to break. We generate the private key, then use a selected elliptic function to derive the public key from it. Reversing this (as in, an attacker calculating the private key from the public key) is a monumental computational task that would be unrealistic with today’s technology and should remain so for many more years. Compared the classic private/public key generation, this is harder by a factor of 10, approximately (read this if you want all the gory details). This means that a 256 bit long key set generated using ECC is equivalent to a key over 2600 bits long in RSA. The standard in today’s market is 2048 bits, which would still take a VERY long time to crack with today’s computing power, so cracking an ECC key set would be virtually impossible even for someone with access to supercomputers. What all this means in the real world is that instead of buying a regular SSL Certificate to secure your site, you can choose to purchase an ECC certificate instead, thus having better security. ECC certificates are relatively new to the market, and so not many certificate providers offer them. One such provider is Symantec, and another is Entrust, and other providers will soon jump on the wagon as well. If this is interesting to you, then you will be glad to know Azure Web Sites has been tested and fully supports ECC certificates! To use one, work with your certificate provider of choice to buy one, and then simply upload it to Azure as a PFX file like you would upload a classic RSA certificate and assign it to your site. This is all there’s to it! Keep in mind that not all clients support ECC certificates, but if you’re running Windows Vista or later, you should be able to browse to your site over SSL regularly without any configuration or changes to the client. Stay safe!


Introduction to Coding Theory
Instructor: Vitaly Skachek
Lecture: Tue. 10:15-12:00, J. Liivi 2-206
Practice: Fri. 12:15-14:00, J. Liivi 2-206
Office hours: Fri. 10:15-11:15, J. Liivi 2-216, or by appointment
Contact: Vitaly Skachek
The final exam will take place on Tuesday, June 10th, in room 511. The starting time is 15:00. The length of the exam is three hours.
It is allowed to use any printed or hand-written material during the exam. No electronic devices (computers, tablets, mobile phones) are allowed during the exam.
About the course
- How is a compact disc protected from scratches?
- How polynomials can help to keep a secret?
- How to send more bits over the network link that link can carry?
We will answer these and other questions. The course is dealing with mathematical methods and algorithms for reliable transmission and storage of information. The main object under consideration is an error-correcting code, which is typically a set of vectors equipped with certain properties. The discussed methods make use of linear algebra and finite fields. Only knowledge of linear algebra (introductory course into linear algebra) is assumed. All necessary mathematics will be explained in the course.
- Linear algebra or equivalent course
- Interest in application of mathematics to computer science and engineering
The course is suitable for all levels: Bachelor, Master and Ph.D. The basic knowledge of linear algebra is assumed (linear transformations, vectors spaces, solving systems of linear equations). Beyond that, all necessary mathematical background will be explained in the course. However, knowledge of basics in probability theory, discrete mathematics and finite fields can be helpful.
- Lecture 1: communications model; BSC and BEC channels; code and its parameters.
- Lecture 2: ML and nearest-neighbor decoding; examples of simple codes; Shannon theorems.
- Lecture 3: correction and detection of errors; correction of erasures.
- Lecture 4: linear codes; generator matrix; parity-check matrix.
- Lecture 5: construction of finite fields; primitive elements.
- Lecture 6: parity-check matrix; dual code; Hamming code.
- Lecture 7: extended Hamming code; concatenated code; syndrome decoding.
- Lecture 8: Singleton bound; sphere-packing bound; Gilbert-Varshamov bound.
- Lecture 9: asymptotic bounds; Reed-Solomon codes; Vandermonde matrix.
- Lecture 10: generalized Reed-Solomon codes; GRS codes as cyclic codes.
- Lecture 11: decoding of GRS codes; key equation; Peterson-Gorenstein-Zierler decoding algorithm.
- Lecture 12: solving key equation by using extended Euclid's algorithm.
- Lecture 13: finding error values by using Forney's algorithm; summary of decoding of GRS codes; example.
- Lecture 14: NP-hardness of nearest-neighbor decoding; LDPC codes.
R.M. Roth, Introduction to Coding Theory, Cambridge University Press, 2008
F.J. MacWilliams, N.J.A. Sloane, The Theory of Error-Correcting Codes, North-Holland Publishing Company, 1977
J.H. van Lint, Introduction to Coding Theory, Springer 1999
Final grade structure
- Homeworks: 60%
- Final exam: 40%


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Discover the magic of 34 possible symbol combinations. This game is no mathematical mystery – it’s just an amazing fruit game with exciting win multipliers.
The MAGIC 81 (JOKER) symbol substitutes for all symbols and appears on at most 3 reels at the same time – but never on the 1st, 2nd and 3rd at once. Every winning combination involving a MAGIC 81 symbol doubles the total win multiplier: x2, x4, x8.


Donald T. Non-Linear Elastic Deformations. Quantum Field Theory. Claude Itzykson.
Richard G. Applications of Group Theory in Quantum Mechanics. First Steps in Differential Geometry. Andrew McInerney. Mathematical Methods for Physicists and Engineers. Royal Eugene Collins. Methods of Applied Mathematics.
Francis B. Lie Groups, Physics, and Geometry. Robert Gilmore. Geometric Algebra for Physicists. Chris Doran. Guide to Essential Math. From Spinors to Quantum Mechanics. Gerrit Coddens.
The Geometry of Physics. Theodore Frankel. Alberto Roberts. William C. Fiber Bragg Gratings. Raman Kashyap. Classical Optics and its Applications. Masud Mansuripur. A Course in Modern Mathematical Physics. Peter Szekeres. Fundamentals of Electro-Optic Systems Design. Sherman Karp. Fiber Optic Data Communication. Casimer DeCusatis. Ordinary Differential Equations. Mark G. Organic Electronics in Sensors and Biotechnology. Ruth Shinar.
Structured Light and Its Applications. David L.
Luther Pfahler Eisenhart. Applied Group Theory. George H. Principles of Nano-Optics.
Lukas Novotny. Plasmonic Nanoelectronics and Sensing. Er-Ping Li. Some Mathematical Methods of Physics. Gerald Goertzel.
Cambridge Illustrated Handbook of Optoelectronics and Photonics. Safa Kasap. Fundamentals of Scientific Mathematics. George E.
Scattering Theory. John R. Introduction to Quantum Optics. Gilbert Grynberg. Curvature in Mathematics and Physics. Shlomo Sternberg. Advances in Imaging and Electron Physics. Peter W. Finite Quantum Electrodynamics.
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This morning’s Washington Post has a story that says Maryland math teachers are gathering today to consider a another new way to teach math to students. It’s called Curriculum Focal Points and it’s being pushed by the National Council of Teachers of Mathematics.
The Post story says of the Curriculum Focal Points report:
“The report urges teachers to focus on three broad concepts in each grade and on a few key subjects — including the base-10 number system, fractions, decimals, geometry and algebra — that form the core of math education in higher-achieving nations. Some are calling Focal Points the most significant publication in the field since the 1980s.”
I thought the Everyday Math program that my son is learning at Forest Lakes Elementary School was the new math. As a matter of fact, this program from the University of Chicago School Mathematics Project was just adopted county wide in the Harford County Public Schools this year. We parents are just grappling with how to get used to this program that uses a method of “spiralling” where students first get introduced to new math topics and then get more intimately involved as they run into them again later. (Here’s a link to my son’s school’s math website) Now I learn that even the state math leaders already suspect this might not be the way to go. I thought my third-grader was a bit lucky to have been in a class that actually started with the Everyday Math program in first grade. I figured he would have the benefit of not having to switch methods in mid-stream. But with today’s math teachers summit it looks like that might not be the case. The story says Maryland’s math curriculum is up for revision in 2009 — the year my daughter will start first grade. The Washington Post story says that American students fall far behind Singapore and Japan and a dozen other nations in math. Perhaps we should simply invite some of their teachers over here to tackle the job — or at least to give us some tips.


The UW-BSC high school calculus competition
the University of Wisconsin- Baraboo /Sauk County is proud to announce a unique calculus competition for the benefit of high school students in Sauk County Wisconsin.
In April, a panel of UW-faculty from across the state will prepare a contest which will contain challenging problems from material covered in in the AP Calculus (A-B) syllabi.
A high school can form a team up to five members.
Here is an example of a sample Test.