After adding about 5 lines of code, the frame rate (per second) went up from 7 to 2700. This is a little bit too fast, but at least now there exists processing time for complicated shading algorithms. So I made a few different shading algorithms. I think I should stick with the original one (from Chromomancy Update #1) for now.
Weight assigned to each of the 4 vertexes based on taxicab distance. At least the shapes are easily visible here….
The first weighting algorithm I used in this project. It’s not working any better. Weights are assigned to each vertex based on the “real” distance (not taxicab) to the 4 square vertexes.
My favorite one. You can actually see part of the jetstream here (the darkblue thing poointing right, inside of the aquamarine colored part).
The problem here is that the slopes at the corners for the shading approach infinity, so discontinuities are abound. So I decided to try two different interpolation methods, to make the derivative a smaller value, say 0.
Utter failure. I feel like I did something wrong coding this, but I’d rather put the blame on quadratic interpolation. It’s not even the right color. I have no idea where all the yellow came from. And the top left corner just looks ugly.
Another failure. Squares are easy to see. Logistic interpolation failed. The growth functions learned in calculus are not useful. Better than the Quadratic one though. And at least the jetstream is visible (the darkblue hook thingy).
So today’s progress…. well all that was really done was increasing the frame rate over 300-fold.


March 1st is World Maths Day. What is that, you ask? World Maths Day is an online mental arithmetic game.
From the World Maths Day website:
Students play at home and at school against other students around the world in live games of mental arithmetic. Each game lasts for 60 seconds and students can play up to 100 games, earning points for their personal tally. There are 5 levels of play, 20 games on each level.
We welcome school aged children and homeschoolers to register and participate. It’s a great way to improve numeracy and mental arithmetic skills and have fun in the process.
… and it’s absolutely free of charge!
World Maths Day was originally created for students aged 4 – 18 years, but this year and adult’s age category (19 – 119 years) has been added, although the adults are not eligible for prizes.
Read more at the World Maths Day website and register before March 1. The site also provides practice games which can be accessed before March 1.
By registering, you are automatically registered for World Spelling Day on March 3. Have fun!


We recognise that increasing the number of science and mathematics teachers, particularly in some parts of the country, given the career choices available to graduates of these subjects is a challenge. We are taking a number of steps to increase their numbers further.
We are implementing a package of up to £67 million to transform mathematics and physics teaching in England. This will provide subject knowledge training to 15,000 non-specialist serving teachers and recruit up to 2,500 additional mathematics and physics teachers. The package includes programmes to encourage the brightest A level students and undergraduates into teaching; salaried part-time and abridged courses for career changers; a salaried route for post-doctoral maths and physics researchers; and support for qualified teachers wishing to return to the profession.
We have increased bursaries for science and mathematics trainee teachers; including £30,000 for physics trainees with first-class degrees. We are also offering prestigious scholarships, worth up to £30,000 for physics, and £25,000 for mathematics, chemistry and computing trainees, in partnership with the professional bodies for these subjects.
Through the School Direct route, which is specifically targeted at career changers and allows them to earn a salary whilst they train to teach, we are providing enhanced grant funding of £25,000 (up to £29,900 in inner London) to schools that pay the trainee an enhanced salary of at least £21,000 (£25,000 in inner London).
Our marketing campaign, Your Future | Their Future, includes targeted subject specific science and mathematics advertising through a range of media. Those who wish to teach secondary science or mathematics are eligible for our enhanced Premier Plus service, which provides support from a dedicated adviser to guide them through the application process. Those applicants who would benefit from it can also access funded courses to boost or refresh their subject knowledge to a level that will allow them to teach the subject.
To ensure that these teachers work in the schools where they are most needed, we have expanded school-led initial teacher training (ITT) by introducing School Direct and accrediting more school-centred initial teacher training providers. School-led ITT gives schools the leading role in responding to recruitment needs in their local area, including for science and mathematics teachers. We have also supported the growth of Teach First, a prestigious teacher training route which places trainees in some of the most deprived and challenging areas of the country. As a result of these reforms, 2015/16 is the first year in which more than half of postgraduate ITT is school-led, with 51% of trainees on a school-led route.
The National College for Teaching and Leadership has also recently changed its approach to allocating ITT places, giving individual schools and universities the freedom to recruit as many science and mathematics trainees as they need, up to the national target for each subject.
We have also recently launched the National Teaching Service (NTS). This will help schools that are finding it difficult to retain and recruit the teachers they need, such as in rural, coastal or deprived areas. We will first test aspects of the model through a pilot of 100 NTS teachers/middle leaders starting in secondary and primary schools in the North West from September 2016. Thereafter the national programme will be rolled out to other parts of the country so that by 2020 there will be 1,500 outstanding NTS teachers and middle leaders in schools that need them.


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Parents, educators and policy makers are increasingly concerned about how children learn math.
We are earnestly updating ourselves in our knowledge of mathematics and developing the skills and disposition essential to be effective Math Teachers. Our teaching instructions are largely guided by recommendations set forth by NCTM (www.nctm.org) to upkeep a high-quality mathematics education through research-based studies not only on curriculum related standards but also on teaching standards. It shares the six principles fundamental and the five content standards where a focal point of significant concepts and skills are set developmentally appropriate for each grade level
As teachers, we are taking a journey together with the children as we go through the same processes in exploring and discovering mathematics through problem solving, reasoning and proof, communication, connections and representation as part of the daily classroom learning and teaching. As a result, it is our hope that children can take away with them a life skill of this math knowledge into the real world to becoming self-confident and academically and socially adept. It is no longer the teacher-directed approach where children sit and wait for their teacher to give them the “one right answer”.
Parents often see their children struggle with comprehending abstract Math concepts and sometimes they do not know how to help them. They also know that their own fear of Math will have a negative influence on their children.
Kidsgo123 is created to address these concerns. It offers a platform for parents to share their ideas and challenges, to receive tips and advice on what it means to know and do mathematics with young children. Parents can:
1. Determine the theory that children learn by
– constructing their own knowledge by connecting new information to the existing ones.
– interacting with supportive peers and adults and
– manipulating with materials
2. Help children thrive in an environment by providing them with basic concepts and understandings which they actively use for making sense and meaning in various experiences that help them build a strong foundation for future learning.
3. To create positive learning environment that provides them with appropriate challenges and expectations to think critically and creatively.


Another batch of last quarter's transactions is coming, and Giverny Capital is the first to be presented here.
Giverny Capital has made small buys here and there. But here's the most significant transactions of the fund:
Carmax: +5%, now represents 9,1% of the total US portfolio
GOOG + 5%, now represents 4,1% of the total US portfolio
Disney + 6%, now represents 3,8% of the total US portfolio
Edwards Lifescience + 5%, now represents 3,2% of the total US portfolio
Credit Acceptance Corp + 7% now represents 2,8% of the total US portfolio
What whalewisdom doesn't show is the canadian positions of Giverny Capital. I know that about 20% of the fund is occupied by three canadian stocks which are MTY Food Group, Dollarama and Constellation Software. However, I don't know the exact percentage of each stock.
So, if we do the math, we could reduce each US position by 20% to know the real percentage of a specific stock in the fund. For instance, Carmax would represent about 7,2% of the fund (9,1% X 80%).
I really like Giverny because they know how to combine the most important metrics in a big performant portfolio. You learn a lot when you study the metrics of the stocks bought by your favorite investors.


I am learning WebGL and I've drawn a full screen quad with colors for each vertex. No lighting or normals or perspective matrix or depth buffer; I'm just drawing a gradient background. This is what I get:
It looks good but I cannot help noticing the diagonal smear from the bottom right to the top left. I feel this is an artifact of linear interpolating the far opposite vertices. I'm drawing two triangles: the bottom left, and the top right. I think I would get similar results using OpenGL instead of WebGL.
Given the same four colors and the same size rectangle, is there a way to render this so the edge between the two triangles isn't so apparent? Maybe more vertices, or a different blending function? I'm not sure exactly what the colors should be at each pixel; I just want to know how to get rid of the diagonal smear.
The issue is the top right triangle has no knowledge of the bottom left corner so the top right triangle is not including any of the blue from the bottom left (and visa versa)
A couple of ways to fix that.
One is to use a 2x2 texture with linear sampling. You have to do some extra math to get the interpolation correct because a texture only interpolates between pixels
+-------+-------+ | | | | +-------+ | | | | | | +---|---+---|---+ | | | | | | +-------+ | | | | +-------+-------+
Above is a 4 pixel texture stretched to 14 by 6. Sampling happens between pixels so only this center area will get the gradient. Outside that area would be sampled with pixels outside the texture so using CLAMP_TO_EDGE or on the opposite side of the texture using REPEAT.
Note: to see what I mean about the extra math needed for the texture coordinates here is the same example without the extra math
Another way is to do the interpolation yourself based on those corners (which is effectively doing what the texture sampler is doing in the previous example, bi-linear interpolation of the 4 colors).


This week, grades 5, 6, 7 and 8 took the French version of the Beaver Computing Challenge (BCC), under the supervision of Christelle Beaujon and Colin Cavarroc.
The BCC is a problem solving contest with a focus on computational and logical thinking. Questions are inspired by topics in computer science but only require comfort with concepts found in mathematics curriculum.
Congratulations to all the students for their kind participation!
Results will be given in January. Depending on their results, students can participate to the Algorea contest : http://www.france-ioi.org/concours/algorea


The K’NEX Education product range has been designed to maximize pupil engagement in today’s busy classroom. It is uniquely designed to aid in the teaching of science, technology, engineering and maths topics. Sets have been designed for school use and teach today’s young scientists and engineers key science, technology, engineering and maths concepts by constructing real world models, reflecting the changing world they live in.
Each product in the K’NEX Education line come with a comprehensive teacher’s guide, with lesson plan and follow up work suggestions. The easy to follow colour coded students instructions allow teachers to direct pupils to work independently or in groups.
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Φ (Phi) is the 21st letter of the Greek alphabet.
In mathematics, it is used to represent a number known as the Golden Mean, which is the ratio of two sides of a rectangle called the Golden Section that has very special properties.
The schematic image on the right side of this site represents how the Golden Section is constructed geometrically. Mathematically, the number Φ is equal to (1 + √5) / 2. It is related to the famous Fibonacci Series of numbers [0, 1, 1, 2, 3, 5, 8, 13, 21, …] and has many wonderful properties that connect it to nature, art, and design.
|The 1959 Disney animated short film entitled “Donald in Mathmagic Land,” where Donald Duck gets an education in the beauty of mathematics, is wonderful. Among other things, Donald learns about the Golden Section.|
|This very beautiful, and much more modern, video, “Nature by Numbers,” illustrates the Golden Section and other examples of math in nature.|


Calculate Julian Date. (don't press return.) in auto mode, civil calendar changes from julian to gregorian between october 4/15, 1582. Formulas for computing the julian date from year, month, and day in the julian and gregorian calendars are given below.
In astronomy, a jd (julian date) is defined as the contiguous count of days from january 1, 4713 b.c., greenwich mean noon (equal to zero hours utc). Without some other references to crosscheck you'd never notice it and take it as the gregorian date as granted. And have updated your code to reflect as var jd = time/86400000 + 2440587.5;
The Result Is The Number Of Days To Add To The Julian Date To Get Its Equivalent Gregorian Value.
Likewise, it converts any date to a julian day number. To calculate a julian date from a modern calendar date, you simply figure out how many days have passed since 4713 bce, then work out any fractions for a time other than noon. However technically, a julian date can mean different things.
For Example, This Would Create A Date From A Yyyyddd Julian Date Like 1999143.
Aavso produced jd calendars give the last four digits of the julian day for each day of every month for a year. Add up the day of the month, c, e, and f. Add the day fraction to the julian day number year = now.year month = now.month day = now.day day_fraction = now.hour + now.minute / 60.0 + now.second / 3600.0 / 24.0 # the value 'march_on' will be 1 for january and february, and 0 for other months.
Astronomers Refer To A Julian Date As The Number Of Days Since The Beginning Of The Julian Period (January 1, 4713.
After changing a text box, click outside of the calculator, or press tab, to update all other data. So i feel your calculator is far more. The julian day calculation formula is used.
Note That This Always Gives You A Half Day Extra.
So June 15, 2015, In Julian Date Will Be 15166, September 27, 2008, 8271, And So On.
Formulas for computing the julian date from year, month, and day in the julian and gregorian calendars are given below. For example, october 2, 1216, has the calculation 12x. In astronomy, a jd (julian date) is defined as the contiguous count of days from january 1, 4713 b.c., greenwich mean noon (equal to zero hours utc).


Theoretically, numerically and empirically the range is not only a highly efficient volatility proxy, but also that it is approximately Gaussian and robust to microstructure noise. Two factor models - one persistent and other mean reverting - do a better job describing simultaneously the high and low frequency dynamics of volatility - to explain both autocorrelation of volatility and the volatility of volatility.
Volatility is not constant. It is both time-varying and predictable. Gaussian quasi-maximum likelihood estimation (QMLE) for estimating stochastic volatility falls wayside because the volatility models are non-Gaussian - log absolute or squared returns. Range - difference of highest and lowest log security prices is a much more efficient estimator - due to its near normality.


Mathematics N3: Course description
The Mathematics N3 course covers the syllabi as prescribed by Department of Higher Education and Training. It is one of the subjects that are required when registering as an Installation Electrician (Wireman’s License) at Department of Labour. The syllabi of the N1 and N2 mathematics will be revised at the start of the Mathematics N3 course.
Topics covered in the Mathematics N3 course:
- Exponents and Logarithms
- Equations, Word Problems & Manipulation
- Algebraic Graphs
- Co-ordinate Geometry
The learner will be provided with:
- Renkalec Training Centre will enroll the learner at a FET college for the examination of this subject. Department of Higher Education and Training (DoHET, Umalusi) will issue a certificate once the learner has passed the examination.
- All books, additional study material and some past exam papers will be provided.
- Individual mid-term assignments will be marked and results submitted to the department for year marks.
- Pre-exam revision is also provided for final preparation for the examination.
We only offer N3 via correspondence.
Correspondence: R1950 per subject all study material and exam enrollment included (excluding) postage.
- Correspondence: R1 950 per candidate


پنجشنبه 8 فروردین 1398
نویسنده: Antoinette Mckay
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The Fibonacci sequence betting has gained popularity since it is associated with the famous mathematical Fibonacci system. The strategy revolves around the principle that under fixed or slowly changing odds, a progressive form of betting is based on the bet amount. However, as the bet progresses, the Fibonacci sequence can get more and more complicated. Despite its popularity, the Fibonacci sequence betting system does come with its fair share of pros and cons. For a novice, a look into the Fibonacci Sequence of betting is a must to understand the world of betting better.
A Brief History of the Fibonacci Sequence
The Fibonacci betting sequence is broadly based upon the Fibonacci series developed by Leonardo Pisano. Ancient Indian mathematics used the Fibonacci sequence. However, it was Pisano who was instrumental in introducing the series to the West. The sequence starts from zero, and is followed by a one, and subsequently goes on to infinity. Here’s the starting of the sequence.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377…
If you notice carefully, you’ll see that each successive digit is a sum of the previous two numbers. In the Fibonacci sequence betting system, we mostly tend to stay till the 11th term.
Fibonacci Sequence Betting
Fibonacci numbers betting is based upon a negative progression betting. This means that the bets placed depend directly upon the results of the stakes-placed previously. So, let’s consider a Fibonacci sequence betting example:
It is important to note in this regard that one of the most efficient ways to place bets is to consider each bet as a unit bet of INR 10 or INR 100.
So, suppose a game offers odds in the range of 2.0, you should ideally start betting from 1.
Thus, considering your unit bet is INR 100, your bets should follow the following progression in terms of stakes placed.
1st bet = 1 x 100 = INR 100
2nd bet = 1 x 100 = INR 100
3rd bet = 2 x 100 = INR 200
4th bet = 3 x 100 = INR 300
5th bet = 5 x 100 = INR 500
6th bet = 8 x 100 = INR 800
7th bet = 13 x 100 = INR 1300
8th bet = 21 x 100 = INR 2100
9th bet = 34 x 100 = INR 3400
10th bet = 55 x 100 = INR 5500
11th bet = 89 x 100 = INR 8900
It is recommended to not bet beyond the 11th term. However, this is subject to the stakes you are putting up. If your unit bet is high and you have a greater amount of money at your disposal, then you can bet beyond the stipulated term.
Now, while indulging in Fibonacci sequence sports betting, you have already lost the first five bets as per the list given above. The 6th bet that you place can result in a win. Accordingly, you should move two places down on the number line and place your bet at the value as per the 4th bet. Suppose you win that bet again. Then you should further move down two places and place the next bet as per the 2nd bet.
However, if you lose the bets at any point in time, you should just move onto the next number in the sequence. So, supposing you lost the 4th bet stake after going down from 6th bet, your next bet should be as per 5th bet value.
But the rule to move two places lower on the list after every win has two exceptions:
- If you win a bet in the sequence before you have moved at least two places prior to that win, then you should start from the beginning of the sequence.
- If you are betting in a cycle to make for efficient bankroll management, after the cycle ends, start again at the beginning of the sequence.
Pros and Cons of Fibonacci Sequence Sports Betting
- No loss: Given the way the stakes of the bet are distributing, following the Fibonacci sequence betting will ensure that when you do win, the previous investments you have made are covered in due time. Subsequently, with each successive win, your losses are covered.
- Consistency: The longer cycles you play, the greater are your chances to make profits
- You could lose all your money if the losing streak is consistent enough.
So the question remains: Is the Fibonacci sequence betting a strategy that ensures a sure win? Betting is not based on certainty. You win some, and you lose some, and in the long term, the house never loses. Thus, while the sequence is grounded in mathematics, and the progression is sound, it is not foolproof.


Average month calculation 03-10-2022 01:11 PM I want to calculate the average units per month. The formula I have is Measure = AVERAGEX (VALUES ... established in 1959. The average historical performance of the DAX index in September since 1959. . Steps to use an Average function in Power BI are as follows. Upload the above data table to the. SUM (Column Name). e.g. to create the sum of sales, follow the steps given below. Step 1: Click on New Measure under the Modeling tab. Type SalesSum and type SUM formula on the right side of the equal sign. Type Table1 (Sales) inside SUM () as shown below. Step 2: To check, use Card visualization and drag SalesSum on the canvas. In such a case, you can use the SUMPRODUCT function to get the weighted average of the score. Here is the formula that will give you the weighted average in Excel: =SUMPRODUCT (B2:B8,C2:C8) Here is how this formula works: Excel SUMPRODUCT function multiplies the first element of the first array with the first element of the second array. Then. . Most expensive month to stay with an average 72% rise in price. Average Sun - Thu price over the last 2 weeks. Average Fri & Sat price over the last 2 weeks. Best Dax hotels. ... The average price of a double room in Dax is $154 per night. In the last 3 days, KAYAK found great deals as cheap as $65 per night. Daimler Aktie Prognose. FTSE Forecast 2022, 2023, 2024. DAX index predictions for August 2023. The forecast for beginning of August 13013. Maximum value 13741, while minimum 12185. Averaged DAX value for month 12976. Value at the end 12963, change for August -0.38%. DAX predictions for September 2023. The DATESINPERIOD function allows you to create calculations at different granularities by just changing the first argument of AVERAGEX. For example, you can obtain the moving daily average thus working at the day granularity by using Date [Date] instead of Date [Calendar Year Month]: 1 2 3 4 5 6 7 8 VAR Result = CALCULATE ( AVERAGEX (.


Some maths online tutor offer software with lessons included, others are one on one lessons. Additionally the tutor may offer shorter lessons at a lower price. A tutor is not only helping you with maths they are helping your over all confidence and should teach you skills such as exam and assignment skills. How Much Help Are You Requiring?
Most math online tutors will offer both; however the other decision you will need to make is that of the level of tutor contact. By contact I mean 1 on 1, face to face lessons, or will instant messenger suffice?
Some math online tutors conduct lessons via Skype or other video calling technology. If you require a quick fix than maybe a lesson with an automated tutor will work. Chris is school teacher who was looking for another way to help students achieve their desires at school.
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I sometimes get inspired to write about things I learn. When I do,
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A topological proof.
With examples from general relativity.
A nice application of linear and abstract algebra.
An explanation that doesn’t require a semester’s worth of abstract algebra.
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That is, using a constant number of word operations.
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Christmas activity sheets for grade 5
Christmas Picture Addition - Add the Christmas pictures to find 5 sums to 10. Great online learning resource for children looking to improve math social studies , language christmas arts skills through hands on games , science activities. Then click the add selected questions to a test button before moving to another page. The grade leveled and core aligned sheets can grade all be found below. Here you will find a range of free Christmas Math Activities 5 including Christmas Maths sheets Christmas Math games. hide the show to save images bellow, right click on shown image then save as. Christmas Math Worksheets.
from kindergarten to grade 5 and beyond. These sheets are great to have in December. Christmas Spelling Unit ( Grade 5) The 5th grade spelling unit has a word list , alphabetical order worksheets, puzzles a test form. To view the video on TpT click hereStudents have to use their math skills to eliminate suspects so they can find out who committed the crime ( a robbery). Some of the worksheets displayed are Trace the activity dotted lines then activity activity color the A christmas carol, Making reindeer names, A christmas carol photocopiable, Christmas math work first grade, Christmas vocabulary words, christmas Lesson christmas lesson 1 Christmas matching work. activity Three Kings Day activity Activity Sheets. We are always writing new sheets for this section activity every October - December. Showing activity top 8 worksheets in the category - Christmas for First Grade Activity. Save hours christmas of activity prep time with our online treasure trove of ready- to- go lessons activity printables, , activities for christmas every grade, , subject skill 5 level. Students read the passages and answer the questions 5 that follow. 5 Christmas First Grade Activity. A series of Reading Comprehension Worksheets for second grade ( 2nd Grade). Select one or more questions using the checkboxes above each question. Four clues are given to. Christmas Counting Numbers 1- 5 Worksheet.
Showing top 8 worksheets in the christmas category - Three Kings Day Activity Sheets. The most wonderful time of activity year is just a few days away and most of us plan to celebrate it in a special way. Some of the worksheets displayed are Wise men Celebra la navidad y el d reyes magos lesson plan for grades, 9 for 10 lesson 3, Celebrate christmas , The three kings, three kings day lesson plan for grades, Celebra la navidad y el d reyes magos lesson plan for grades k The feast of the. Scholastic Teachables - browse all worksheets printables, , resources more for the classroom! Children can also learn easy fun cooking recipes many other fun crafts.
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Alphabetize Third Grade Dolch Words - Four worksheets for practicing alphabetizing third grade Dolch words. Christmas activity sheets for grade 5. Winter christmas Alphabetical Order Activity - Easy. Select a activity Grade 5 Level. Christmas Math Activity: Christmas CSI Math for - Who Stole Santa' s Sleigh? Christmas Worksheets.
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Jingle Bell Rock Lyrics. Have you wanted to introduce simple computer- free coding ideas to your kids? Have activity you ever checked out grade the binary alphabet? Christmas Division Practice # 2 - Divide a 2- digit number by a 1- digit number and find the christmas remainder. It' s pretty cool especially if you have kids into coding games. christmas comprehension worksheets for 5th grade generated on lbartman.
Merry Christmas from Math- Drills. Alphabetizing Worksheets.
Animal Eyes ( A Dolch sight word site - Levels include primer and grade one words). 5 out of 5 ( 1 Vote) A Christmas Carol Students who receive early instruction in monitoring their comprehension and strategies to fix comprehension problems are aware of what they understand and can identify what they do not. Christmas Math Activity: ADVANCED EDITION. Christmas CSI Math - Who Stole Santa' s Sleigh? This product now comes with an engaging video hook! To view the video on TpT click hereStudents have to use their math skills to eliminate suspects so they can find.
christmas activity sheets for grade 5
Christmas Activities and Lesson Plans. The Christmas seasonal pages will provide you with great resources for the Christmas holiday season. Ideas within this section include: journal activities, ornaments, craft ideas, lesson plans, and more.


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• There are 3 main types of transitions: • Transitions between activities within a. Here, we will see how to find the last two digits of a large number. Get transitions between first digits of power of 2 ideas for your own presentations.
Exponents, or powers, are a way of indicating that a quantity is to be multiplied by itself some number of times. New York: Random House. All that we needed to do is click on a transition thumbnail and PowerPoint transitions between first digits of power of 2 will play a preview for us. . (Values increase in 0.
024 · p10n+3, which means four powers of two will occur in that range. However, it is clear that differential industrialization has created vast differences in the digits power of nations since the industrial revolution. In the previous post we tried to understand calculating the units digits of large numbers like $^$, 53^71$ etc. Using this table you can see that the unit digit can be 1, 3, 9, 7 and the sequence repeats in this order for higher powers of 3. We first need to find the number of digits of ^n$, which can be done using logarithms: we need to solve (approximately) ^n transitions between first digits of power of 2 = 10^d$.
What are the last 2 digits of an integer? At any given time the transitions between first digits of power of 2 nations of the world tend to be organized into an “international transitions between first digits of power of 2 ord. Phase transitions between liquid and solid phase. Powers of 2 Table,870,912 1,073,741,823 3FFF FFFF,073,741,824 2,147,483,647 7FFF FFFF,147,483,648 4,294,967,295 FFFF FFFFThis is the 32-bit machine addressing.
transitions between first digits of power of 2 How to find the last digits of a positive power? Speaker Notes: • Definetransition. Bellow is a table with the power and the unit digit of 3 to that power. · The Biden-Harris transition team is considering pursuing legal action if the head of the federal agency overseeing the mechanics of a transfer of power doesn&39;t move in the coming days to free up. On the Transitions tab, in the Timing group, under Advance Slide, do one of the following: To make the slide advance to the next slide when you click the mouse, select the On Mouse Click check box. Presidential Transitions: Issues Involving Outgoing and Incoming Administrations Congressional Research Service 1 Introduction At its heart, a presidential transition is the transfer of executive power from the incumbent President to his or her successor.
25 · p10n; three powers of two appear when p2m > 1. The declining hegemon preemptively attacks transitions the rising great power to get rid of the challenger transitions between first digits of power of 2 early. 2 Select slide 1 transitions and then, on the Transitions tab, select the Push effect. 25 · p10n; multiplying it by 8 would make it a power of two and power of ten). However, the industrial revolution, which began in England two hundred years ago and spread transitions between first digits of power of 2 slowly through the West, has only recently swept into eastern Europe and Asia and has still to reach the majority of nations in the world. Chapters 2 and 3 are theory-based. . Assume the worst case start for the first power of two in a three power of two range, just below 2 · p10n 2.
Or in other words: We have proven that the units digits for 1,3,7 and 9 will repeat after at most four consecutive powers. Thus, shown in long form, a power of 10 is the number 1 followed by n zeros, transitions between first digits of power of 2 where n is the exponent and is greater than 0; for example, 10 6 is written 1,000,0. Between transitions between first digits of power of 2 10, since 294 ≈ 1.
This option opens up all of the possible transitions in PowerPoint ranging first from subtle, exciting. Between 10, since 297 ≈ 1. Notice that the exponent tells us how many bases to multiply, not how many multiplications to perform. In reality it is a rectangle fit to the size of the slide.
Last Two Digits of Large Number. · Given three numbers a, b and k, find k-th digit in a b from transitions between first digits of power of 2 right side. Here’s an example where this occurs 1. Finding the last 2 digits of an integer amounts to computing it mod &92;&92;bmod~10^ n mod 10n. Powers of 2 TableFFFF 11 more rows. Let&39;s multiply the nine and the negative two first and then we can multiply the 10 to the ninth and 10 to the negative third power. Anyone can earn credit-by-exam regardless of age.
· Powers of 2 Table. For the transition between second and third slide, I used another motion path to shift the transitions between first digits of power of 2 toy where I wanted it to be. transitions between first digits of power of 2 Positive powers of ten end in 0; positive powers of two end in 2, 4, 6, or 8. That inequality can be rewritten as 1. To make the slide advance automatically, select the After check box, and then enter the number of minutes or seconds that you want. Thus, the fractional notation is actually preferred in higher mathematics, although the root symbol is still used occasionally, especially for square roots. For example, there are four powers of two betw. ) Choose to advance to the next slide manually (by mouse) or after.
Share yours transitions between first digits of power of 2 for free! Many are downloadable. Using this logic you can find that the unit digit of (3 power ) is 7.
The type of transition words or phrases you use depends on the category of transition you need, as explained below. 1 7 4 ≡ 9 2 ≡ 1 ( m o d 10). 4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. - The table goes up to the 64th power of two.
The major limitation of the concept of power transition is that it refers to a period extending roughly transitions between first digits of power of 2 from 1750 to a time in the future (one may guess transitions between first digits of power of 2 transitions between first digits of power of 2 about ) when transitions between first digits of power of 2 world-wide industrialization has. Starting with 5, the last digit repeats in a cycle transitions between first digits of power of 2 of period one: 5. The first power of two, p2m, transitions between first digits of power of 2 satisfies the inequality p10n < p2m < 1.
transitions Presidential Transition Act. The interleaving of powers explains some properties of decimal to binary and binary to transitions between first digits of power of 2 decimal conversions. View in Landscape mode on Smartphones.
Had the entire world industrialized at the same time and at the same speed, there would transitions between first digits of power of 2 have been transitions between first digits of power of 2 great changes in international relations but no necessary major transitions shifts in the distribution of power among nations. · Transition words and phrases can help your paper move along, smoothly gliding from one topic to the next. at 1:41pm. The result has been that first one nation and then another has experienced a sudden spurt in power, transitions between first digits of power of 2 as in a race where one runner after another goes into a brief sprint.
1 2 3 The theory was first published in 1958 by its creator, A. In general, the last digit of a power in base n n. If you have trouble thinking of a way to connect your paragraphs, consider a few of these 100 top transitions as inspiration.
In my diagram above, you can see there are four transitions between first digits of power of 2 powers of two between 1. by Vaughn Aubuchon: Here is a brief summary chart illustrating the mathematical powers of two, shown in binary, decimal, and hexadecimal notation. That inequality says that p2m+4 starts after 1. Powers of 2 begin with 1 about 30% of the time.
What are the powers of 2 tables? Negative powers of ten end in 1; negative transitions between first digits of power of 2 powers of two end in 5. This is the 32-bit machine addressing. Four powers of two appear between p10n and p10n+1 when p2m < transitions between first digits of power of 2 1. The theory of the balance of power, on the other hand, may be more applicable to the preindustrial “dynastic” transitions between first digits of power of 2 period, when there were many nations of roughly equivalent power, when nations were kings who could and did switch sides freely, and when nations increased their power primarily through clever diplomacy, alliances, and military conquests. So if I were to change the order, we could write this as nine times, nine times, nine times negative two.
, its ability to influence the behavior of other nations. Thus, each nation’s increase in power could be counterbalanced by similar international action on the part of transitions between first digits of power of 2 its rivals. The first power of two in the next power of ten interval, p2m+4, satisfies the inequality 16 · p10n < p2m+4 < 20 · p10n (I multiplied everything by 24= 16) transitions between first digits of power of 2 3. Open transitions between first digits of power of 2 Up More PowerPoint Slide Transition Options. The Presidential Transition Act of 1963 (Pub. For example: starting with 5, their last digit is always 5; starting with 25, transitions their last two digits are always 25; starting with 125, their last three digits alternate between 125.
View Adding Two Digit Numbers PPTs online, safely and virus-free! START ON THE RIGHTTHINKTHINKNow do some on your own! Given the above relationship, you’ll see that there will be three or four powers of two between every consecutive pair of powers of ten. 9 of the way to the next power of ten.
An industrializing nation undergoes a number transitions between first digits of power of 2 of changes as it modernizes its economy. In this phase diagram the mole fractions x 1 and x 2 are displayed for increasing temperatures. The unit fraction notation used for roots previously may have given you the idea that roots are really the same as powers, only with a unit transitions between first digits of power of 2 fraction (one over some number) instead of an integer as the exponent. In the expression 25, 2 is called the base and 5 transitions between first digits of power of 2 is called the exponent, or power. Powers of 2 Table. So φ(10) = 4 and this proves that a^ is congruent to 1 for a equal to 1,3,7 or 9. Does anyone know how to make a second digit of a two digit number the power transitions between first digits of power of 2 of transitions between first digits of power of 2 the number&39;s first digit. Power transition, from one dominant state to another, is a familiar historical event, but power diffusion is a more novel process and more difficult to manage.
) A span of four powers of two represents a factor of 8 (the first one is not a factor; it’s just the starting point). Power of 10, in mathematics, any of the whole-valued exponents of the transitions between first digits of power of 2 number 10. 100–398), the Presidential Transition Act of (Pub. 25 is shorthand for &92;&92;"multiply five twos together&92;&92;": 25 = 2×2×2×2×2 = 32. We’ll prove this below. This is because powers of 2 follow Benford’s law. 27 · 1030 The three powers of two run stops there because 2103 ≈ 1.
Organski, in his textbook, World Politics (1958). The probability of war will increase transitions between first digits of power of 2 during the power transition, the shaded area, and conflict will result from one of two circumstances: The rising great power attacks the declining hegemon because it is dissatisfied with the current world order. So as not to bog transitions you (or me) down in symbols, let’s prove this less formally: 1. (There are four powers transitions between first digits of power of 2 of two in the interval 100, 101), but since 100 = 20, I won’t count that as “between”. seconds. A single step—taking the oath of the office of President— accomplishes this transfer. 6 · p10n+1, which means that there can’t be four powers of two between p10n+1 and p10n+2.
25 · p10n transitions between first digits of power of 2 (p2m can never be equal to 1. The Push effect is selected and is previewed on the slide. 32 · d2 or d2 = log10(2) · d10 ≈ 0. The power of a toric lens can be specified by describing how the cylinder (the meridian that is most different from the spherical power) differs from the spherical power. Mixtures which composition lies in the yellow region spontaneously separate into two phases with molar fractions x 1 and x 2. It goes through a “power transition.
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Welcome to the Saint Joseph High School Mathletes club!
The club participates in three math competitions each year: Huntington University in October, Trine University in January and St. Mary's College in May. At each event, the top individuals and teams are recognized.
In addition, the math department hosts mathematic competitions for Saint Joe students: the Indiana Math League (IML, 6 per year) and the American Mathematics Competition (AMC in February). The IML and AMC are not club events but the mathletes do practice and prepare for them.
The club also competes in online math competitions hosted by Interstellar Inc weekly throughout the fall. With this competition, the team is paired against a specific school. Saint Joe and the competing school take the same online math quiz and the scores are compared. Ideally, both schools take the online math quiz at the same exact time, but school schedules don't always allow.
For more information contact moderator Mr. Brett Goodrich at firstname.lastname@example.org.


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Here is a fun-damental theorem that I think most people take for granted:
Any integer greater than 1 can be uniquely written (up to reordering) as a product of primes.
Some of you may know this as the Fundamental Theorem of Arithmetic. It’s pretty embarrassing that I didn’t know this was a theorem, or even that it was true, until my discrete math class in college. It’s also pretty embarrassing that I haven’t posted a blog entry on here for like a week or two, so I decided to make up for my incompetence by proving this theorem on my blog.
There are two parts to this proof: existence (every number has such a prime decomposition) and uniqueness (every number has only one prime decomposition). Before we begin the actual proof, though, we need the following piece of information:
Well-Ordering Principle: Every non-empty set of positive integers contains a smallest element.
That’s not hard to believe, right? I’ll give you time to convince yourself of this fact. Good? Good.
Let’s get started. How do you know this decomposition exists?
We’re going to prove this by contradiction. Let’s assume that this prime decomposition does not exist for every integer, and say we take all those nasty counterexamples and put them in a set C. Since this set of counterexamples is comprised of mere positive integers and thus a nonempty subset of the natural numbers, we know by the well-ordering principle that C has a minimal element. Let’s call this minimal element k.
We have two cases now: either k is prime or it is composite.
Case 1: k is prime. Then this already contradicts the fact that k is a counterexample, because it can indeed be written as a product of primes (itself). So let’s go to the next, more interesting case.
Case 2: k is composite. Then that means k = ab, for some positive integers a and b. Since we’re working with all positive integers, this implies that a and b are both less than k. Ah, but remember what this means: a and b can both be written as a product of primes. Why? Because k was the smallest integer that couldn’t be written as a product of primes, so the claim must hold for anything smaller than it.
Okay, let’s write a and b as a product of primes, shall we?
Let a = p1p2p3…pn and b = q1q2q3…qm, where the pi’s and qj’s are prime numbers (i = 1, …, n and j = 1, …, m). That means k = p1p2p3…pnq1q2q3…qm, thus contradicting again that k ∈ C.
But that means C doesn’t have a minimal element, because if it did, it can’t be an element of C. This can only mean that C is empty, so every element can be written as a product of primes, proving the existence of such a decomposition for all integers greater than 1!
Okay, fine; this decomposition exists. How do you know each number only has one?
I’m going to spit out some statements that need some proving, so I’ve left them as exercises to the reader. (Okay, fine, I proved them for you.)
First, let p be a prime, and a, b be integers. Then if p divides ab and p doesn’t divide a, then p divides b.
Using this fact and induction, we can show the following: let a1, a2, …, an be integers. Then if p divides the product a1a2…an, then p must divide aj for some j between 1 and n (inclusive).
Now we can actually prove that if a number has a prime decomposition, it can only have at most one. Again we will do this by contradiction. Assume that a number s has more than one distinct prime decomposition, say
s = p1p2…pn and s = q1q2…qm.
Then p1p2…pn = q1q2…qm. We can cancel out all the common prime numbers from both sides to get another equation where no one prime appears on both sides. So:
pi1pi2…pik = qj1qj2…qjl
Clearly pi1 divides the left hand side. Then since these two quantities are equal, pi1 must also divide the right hand side. So by our earlier statement, pi1 must divide qjx for some x between 1 and l. But this is impossible, as all of these numbers are distinct primes—a contradiction. Thus, every number can only have at most one prime decomposition! ■
And there you have it: the Fundamental Theorem of Arithmetic, a fact about numbers that most people probably already knew anyway.


All the different types of casino games explained, along with a look at how some games are pure chance and others involve an element of skill. Games available in most casinos are commonly called casino games. In a casino game, the Random number games may be played at a table, such as roulette, or through the purchase of paper tickets or cards, such as keno or bingo. Here is a list of the top 10 Casino games. Everyone then looks at their cards and tries to make the best 5-card and 2-card poker hands. Blackjack Baccarat Craps Roulette The house edge is defined as the ratio of the average loss a player makes to the initial bet amount. Of course, the casino may not win exactly 53 cents of a unit; this figure is the average casino profit from each player if it had millions of players each betting for 10 spins at 1 unit per spin. There is a place on the table to bet for each of these situations, and you can place multiple bets during each play. A 5 card hand totaling 21, for example, pays off at 3 to 1. In a casino poker game, the house is banking all the action. In certain games the house only has a small house edge, so you could simply stick to playing those games. Live Roulette online only European Roulette French Roulette. We examined what casino managers and the pro gamblers have divulged about casino games with the best odds of winning, and here is what we found. The casino has an edge of less than 1 percent in most cases. This article looks at the best games based on any specific preferences you may have. Some people strategize to keep betting on the same number to win the big payoff. With slots, the more money you put in per bet, the higher your chance of winning. Everyone then looks at their cards and tries to make the best 5-card and 2-card poker hands. The Experts Agree Professor of Analytics Michael Magazine has crunched the numbers, and agreed that blackjack is the best way to go home with money in your pockets. We are certain you will find something to suit. Spanish 21 also has several bonuses for various hands. Contests Community Calendar Academic Challenge Mark's Garden Student Athlete Grit TV 5. This would expand to cover licensed movie, video game, celebrity and board game slots. The hands are then compared against the dealers. For example, if a game is played by wagering on the number that would result from the roll of one die, true odds would be 5 times the amount wagered since there is a 1 in 6 chance of any single number appearing, assuming that you get the original amount wagered back. It plays the same as the Pass line. The cards 2 wo spielt ihr book of ra online 9 are worth face value. Each casino will https://www.fachklinik-fredeburg.de/Therapie-fuer-Frauen.aspx their games differently. Lists Home Search Listverse Our Books About Listverse. Retrieved 13 October A hand equaled http://www.lokalkompass.de/luenen/leute/psychotherapeut-luedke-hilft-bald-im-fernsehen-d223916.html 10 becomes a 0 or baccarat. Remember you can try all of our pya pal casino games for ovo casino kundendienst, with play money.


Maths is at centre of the Tregony School curriculum. We embrace the richness of the subject, the opportunities for exploration and the interconnectedness between mathematics and the wider school curriculum.
- We believe that mathematics teaches us how to make sense of the world around us through developing a child's ability to calculate, to reason and to solve problems.
- We want to help children to understand and appreciate number, statistics, measures and geometry.
- We support children to develop these key and fundamental skills through a teaching for mastery approach.
- The children are expected to explore and deepen their understanding of mathematics in progressive, small step lessons.
- The children build upon previous knowledge and known facts to reason, make connections and develop their understanding of the curriculum.
- The National Curriculum states ‘Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas.’ Therefore, the intention for mathematics is to ensure that all pupils become fluent, reason mathematically and solve problems.
- We seek to equip our children with key mathematical skills and knowledge that will prepare them for the next stage in their learning and provide them with the necessary numerical foundations to be successful in adult life.
We use White Rose as the basis for the delivery of the National Curriculum for mathematics. This scheme is an exciting class mastery approach based upon the concentre, pictorial and abstract approach. All lessons incorporate opportunities for whole-class, group and individual exploration and learning. Problem-solving is at the heart of every lesson and there are opportunities to build mathematical fluency built in.
White Rose provides the planning documentation and in-lesson resources that we use however we have created our own bespoke lesson structure. This lesson structure meets the needs of the learners in our school and incorporates opportunities to: engage with real-life mathematics, broaden mathematical vocabulary, work collaboratively, identify and address mathematical misconceptions while developing both fluency and problem-solving and reasoning skill and understanding.


Res 341 Individual Assignment: Exercises From the E-Text
• Resources: Ch. 8 Applied Statistics in Business and Economics• Prepare answers to the following exercises in Ch. 8 of Applied Statistics in Business and Economics:
• Chapter Review questions 5 and 6• Chapter Exercises 8.46 and 8.62
Note. Methods of computation could include the usage of Microsoft® Excel®, SPSS, Lotus, SAS®, Minitab®, or by hand computation.


|Mirror [#1]||Statistical Analysis of fMRI Data.pdf||48,889 KB/Sec|
|Mirror [#2]||Statistical Analysis of fMRI Data.pdf||37,259 KB/Sec|
|Mirror [#3]||Statistical Analysis of fMRI Data.pdf||38,244 KB/Sec|
This book is designed be used for the course titled “Statistical Analysis of fMRI Data”, offered by the Department of Biostatistics at The Johns Hopkins University. The course explores the intersection of statistics and functional Magnetic Resonance Imaging (fMRI). The book contains the key video lectures from the course (but does not contain any assessments).


Computing the singular values and singular vectors of a large matrix is a basic task in high dimensional data analysis with many applications in computer science and statistics. In practice, however, data is often perturbed by noise. A natural question is the following. How much does a small perturbation to the matrix change the singular values and vectors? Classical (deterministic) theorems, such as those by Davis-Kahan, Wedin, and Weyl, give tight estimates for the worst-case scenario. In this talk, I will consider the case when the perturbation is random. In this setting, better estimates can be achieved when our matrix has low rank. I will also discuss several applications of these results including locating hidden structure in a random graph and the matrix completion problem. This talk is based on joint work with Van Vu and Ke Wang.
Jacobs Hall, Room 2512, Jacobs School of Engineering, 9500 Gilman Dr, La Jolla, San Diego, California 92093
University of Colorado
Department of Mathematics
Seminar Speaker Bio
Sean O’Rourke is an Assistant Professor at the University of Colorado Boulder. Before joining the University of Colorado, he was a postdoctoral research associate at Yale University. Sean received his Ph.D. from the University of California, Davis in 2011 under the supervision of Alexander Soshnikov. His research interests include Probability Theory and Mathematical Physics, and he routinely studies random matrices and random polynomials.
Wyn Hughes (firstname.lastname@example.org)


I am a first-year PhD student at the Computational Privacy Group at Imperial College London. I study the intersection of machine learning and privacy with a focus on machine learning-based attacks against query-based systems.
Before my PhD, I obtained an MSc in Data Science from the University of Ljubljana and a BSc in Computer Science at the Ss. Cyril and Methodius University in Skopje. I did both my Bachelor’s and Master’s thesis with the Department of Knowledge Technologies at Jožef Stefan Institute, where I researched change detection and adaptation in multi-target regression on data streams. During my higher education and high school, I have participated in mathematical and algorithmic competitions, such as Google HashCode (finalist) and International Mathematical Olympiad (medalist).


Dividing Large Numbers is fun with Power Puzzle worksheets! Bundled set of 3. Find the surprise answers inside!
Students are encouraged to simplify as a first step, to help keep the numbers small. Improper fractions can be converted into mixed numbers, and the integer part can be removed from the division process. This also helps to make the long division step easier. After solving, students look for their answers in a Number Search grid.
Students love Word Search and Number Search puzzles, and this follow-up activity tells students whether or not their answers are correct. If you can find your answer then you know you are right. (Positive reinforcement!) And if your answer is not in the grid then it is probably incorrect. This acts as a SELF-CHECK, and you will immediately know if you are right or not. No need to wait for a teacher or parent to grade your work!
This is more than just finding words in a list - you have some thinking to do!
3 worksheets in this set. Answer keys are provided.
Power Search is Word Search with a twist!
We give the clues - You find the answers!
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18 inches in cm an inch is a commonly used unit of length in the US Common and Imperial measurement systems. An inch is equal to 1/12 foot or 2.54 centimeters.
The inch is primarily used in the UK or United States as the rest of the world has adopted the International System of Units, the modern version of the metric system.
Many product imports and exports are reported in customs, which requires limited use of the standard US system.
Table of Contents
Use Of Customs
Inches are abbreviated but are often denoted by a double prime symbol ″. Usually, a double quote ” is used instead of a double dash for simplicity.
Also, parts of an inch are often represented in decimal or fractional form. Inches are commonly dividing into fractions
However, varying precision, including halves (1/2), quarters (1/4), eighths (1/8), sixteenths (1/16), thirty seconds (1/32), and sixty.
Equivalent Length Size or Measurements
The basic or current length of an inch was defined in the Pound and Yard Convention of July 1, 1959, which redefined the inch in terms of metric units.
However, he convention defined a yard as precisely equal to 0.9144 meters, which allows us to derive the length of an inch as equal to 2.54 centimetres.
Adoption Around the Globe
An inch is most commonly used for shorter measurements in many fields, including mathematics, construction, and engineering in the US.
However, many scientific fields have switched to using SI units of length. Tenths, hundredths, and thousandths are used for tiny measurements, often in areas like machines
Although UK or Canada has adopted the metric system, inches are primarily used due to proximity and trade with the United States.
The customs gauge is also in limited use in the UK, mainly in the public sector for signaling purposes.
These are known as dyadic fractions.
Convert 18 x 18 inches to centimetres
To convert length x width measurements from inches to centimetres. One inch equals 2.54 centimetres.
Also, to convert 18 x 18 inches to centimetres, we need to multiply each number of inches by 2.54 to get the length and width in centimetres.
Definition Of Customs
An inch (letter: in) is a unit of length. It is defined as 1⁄12 feet but is also 1⁄36 yards. Although traditional standards for the exact size of an inch vary, it is exactly 25.4mm.
In the United States, Gulf, Dubai Canada, and the United Kingdom, the inch is a widely used unit of length.
Origin and History of Customs
One of the first definitions of the customs says that the length is equal to three grains of barley. An inch is now the division of 1/12 foot.
Despite this, the actual length of the inch has changed with the variation in the actual size of the foot.
It wasn’t until the 1959 Yard and Pound Agreement when the world agreed that the exact length of the national yard was 3/4 yards, that the definition of the inch was 1 inch.
In fact, before the 1959 agreement, there were multiple definitions of the obligation, and the precise duration varied around the world.
Definition of Centimetre
The centimetre is a basic unit of length or size in the metric system.
It is also the base unit in the centimetre-gram-second system of units. The functional unit of length is in centimetres for many measurements in everyday life. One centimeter is equal to 0.01 (or 1E-2) meter.
Centimetres to Inches Conversion Factor
To convert a value in inches to the equivalent value in centimeters.
Also, simply multiply the size in inches by 2.54 (the conversion factor).
Formulas from inches to centimetres
Centimeters = inches * 2.54
To convert 18 inches in cm or 18 x 18 inches to centimetres, we need to bear the span of 18 by 2.54 and the width of 18 by 2.54.
The US used an 1893 standard that defined the yard as equal to 3,600/3,937 meters or 0.914401828803658 meters.
On the other hand, Britain used an 1824 definition where the yard is the length of a physical artefact.
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These workshops and accompanying resources are intended to support teachers in developing mental maths strategies in their classrooms. The Mental Maths Handbooks explore the key properties of number and number relationships, outlining practical approaches to developing an understanding of these. It also explores background knowledge for teachers and fundamental facts in relation to mental maths. A range of concrete, practical activities that will support pupils in their development of addition and subtraction mental maths strategies are also outlined. Finally, a selection of engaging and enjoyable activities to consolidate learning and provide opportunities for pupils to master addition and subtraction facts are included.


Progress in modeling dynamics has always been closely associated with advances in computing. It is used to scrutinise the impact of risk and uncertainty in financial and other forecasting models. It is very useful when complex financial instruments need to be priced. Most listed exotic options are marked-to-model and the JSE needs accurate values at the end of every day.
Monte Carlo methods in a local volatility framework are implemented. This paper discusses how Monte Carlo MC simulation is implemented when exotic options like Barriers are valued. We further summarise the historical development in modern computing and the development of the Monte Carlo method.
Introduction Why is simulation or modeling an important component of analysis for scientists? Simulation is the imitation of a real-world process or system. Simulation games are fun too and one gains valuable experience at the same time. Experience and insight are gained by simulating the valuation of financial products, constructing portfolios and testing trading rules McLeish, Through simulation work is transferred to a computer.
Models can be handled that involve greater com- plexity and fewer assumptions, and a more faithful representation of the real world is possible. Morrison states that modeling is neither science nor mathematics; it is the craft that builds bridges between the two. Modeling is important because scientists investigate the world around us by build- ing models that simulate real-world problems. Our insight in a physical system, com- bined with numerical mathematics, gives us the rules for setting up an algorithm the model , or a set of rules for solving a particular problem Steinhauser, These models usually take the form of differential equations that have to be solved to obtain physical answers.
Researchers usually start with a very simplistic model and try to solve it analytically or algebraically. Such models are mostly easier to analyse and scrutinise.
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This inevitably means they have to make a lot of simplifying assumptions. This means that modeling practitioners need to be familiar with a wide variety of mathematical specialities, computer science and one or more disciplines which provide data. This is exactly the route the evolution of the Black-Scholes option pricing model took. Black, Scholes and Merton made some simplifying assumptions that enabled them to devise a backward parabolic partial differential equation PDE. They solved this PDE analytically using Fourier series methods. It is now well-known that this model is far from the real world and stock prices behave in a much more complex manner.
Since most of the original simplifying assumptions have been relaxed. When some of these assump- tions are relaxed, one finds that the model cannot be solved analytically anymore. Most problems where there is significant uncertainty, can be solved using Monte Carlo techniques. Monte Carlo methods are techniques utilising random numbers and probability to solve problems. The analysis is based on artificially recreating a chance process, running it many times and directly observing the results.
Monte Carlo methods are attractive in evaluating integrals in high dimensions Glassermann, What does this have to do with financial engineering? The foundation of the theory of derivative pricing is the random walk of asset prices. According to the Feynman-Kac theorem, the solution to this PDE can be represented by an expected value — valuing derivatives is reduced to computing expectations.
Monte Carlo simulation is widely used in statistics in calculating an expected value of a particular function. Boyle showed that all financial options are always the expected value of certain functions. If we were to write the relevant expectation as an integral, we would find that its dimension is large or infinite. This is precisely the setting in which Monte Carlo methods become attractive Glassermann, Weber stated that the Monte Carlo method is widely used in the financial markets as a valuation tool.
It is used with path-dependent options and in models with more than one state variable. It is sometimes preferred to finite difference or tree methods, even in situations where these methods could work well — simply because its generality and its robustness in contexts where a portfolio of options is being valued. In this paper, we consider the Monte Carlo approach to value exotic options. However, it is also known that these formulas do not lead to market related and realistic prices and hedge ratios. This is due to the assumption of a fixed volatility. However, such option are path-dependent meaning that the actual path the stock takes to get to the expiry value on the expiry date does matter.
To price them correctly one should either use stochastic volatility models or local volatility models. The choice here is to use either finite difference techniques or Monte Carlo simulation. This note will focus on Monte Carlo techniques. Section 3 gives a brief overview of exotic options.
In section 4 we bring local volatility into the Black-Scholes framework and we discretise the Black-Scholes stochastic differential equation. Section 5 is crucial where we show how to use Monte Carlo simulation when pricing options. We conclude in section 8. Note that there are three Appendices where we elaborate on some of the theory described in this paper. Appendix A shows why Monte Carlo simulation can be used when pricing options and we show how to discretise the Black-Scholes stochastic differential equation.
In Appendix B we discuss the generation of random numbers and in Appendix C we elaborate on convergence issues when simulating stock price paths and option values. A Lesson in History Progress in modeling dynamics2 has always been associated with advances in computing Morrison, As such dynamics has reached maturity with the devel- opment of digital computers, both as concept and technological product. But, why is reading the history of science important? Donald Knuth motivates, why, as a computer scientist he reads the history of science. First, reading history helped him to understand the process of discovery.
Sixth, history teaches how human experience has changed over time. As humans we should care about that Haigh, A bit of Computing History The modern history of computing is quite short Copeland, In Wil- helm Schickard , constructed a machine for his mathematician friend Jo- hannes Kepler which was able to perform addition, subtraction, multi- plication and division Steinhauser, Charles Babbage is generally credited with originating the concept of a programmable computer Dasgupta, Babbage built a small working model in but he never completed a full-scale machine.
The punch card was developed by Hermann Hollerith during It was developed for a population census. Dynamical is what concerns change. This computer was not programmable but a full-scale machine was built in Turing , at Cambridge University, invented the principle of the modern computer.
He described an abstract digital computing machine consisting of a limit- less memory and a scanner that moves back and forth through the memory, symbol by symbol, reading what it finds and writing further symbols. He further stated that the actions of the scanner are dictated by a program of instructions that is stored in the memory in the form of symbols. Alan Turing designed the Bombe. It was built in and was an electro-mechanical special purpose computing device. The second world war brought much needed progress though.
Both the British and Americans developed electronic computing machines. The first fully function- ing electronic digital computer was Colossus, used by the Bletchley Park and British cryptanalysts from February The Colossus computer was built on the theoretical framework set by Turing Colossus had two problems: First, it had no internally stored programs.
Second, Colossus was not a general-purpose ma- chine, being designed for a specific cryptanalytic task involving counting and Boolean operations. The primary function for which ENIAC was designed was the calculation of tables used in aiming artillery. These earliest large-scale electronic digital computers, the Colossus and the ENIAC, did not store programs in memory. These machines were massive which led the IBM chairman, Thomas Watson, to state in that there might be a world market for five computers and no more Steinhauser, The main character was Stanilaw Ulam Ulam and Edward Teller developed the first thermonuclear weapon also known as the hydrogen bomb or H-bomb.
Ulam was intensely interested in random processes. He relaxed by playing solitaire and poker. His extensive mathematical background made him aware that statistical sampling techniques had fallen into desuetude because of the length and tediousness of the calculations. Due to the computational issues, this method did not really take off. This triggered the spark that led to the Monte Carlo method. One of the first problems solved on the ENIAC in was a computational model of a thermonuclear reaction6. Los Alamos got its own computer early in A signif- icant advance in the use of the Monte Carlo method came out of the collaboration between Nicholas Metropolis and Edward Teller.
Together they introduced the idea of what is today known as importance sampling, also referred to as the Metropolis algorithm7. Monte Carlo Methods and the Pricing of Options Boyle was the first to relate the pricing of options to the simulation of random asset paths. This reaction is responsible for the energy produced in the sun. The future important role of Monte Carlo simulations in finance was assured. Boyle et al. We can narrow this definition down slightly, by stating that exotic options are options for which payoffs at maturity cannot be replicated by a set of standard options de Weert, Further to this, a structured derivative product is a bespoke instrument that enables an investor to pursue strategies tailored to his or her market view Tan, Such a product allows an investor more control over the yield-risk tradeoff in his investment.
Exotic options and structured notes have traditionally been traded over-the-counter OTC. The JSE was the first exchange in the world to list such products. Since , the types of exotic listed on the JSE have grown tremendously. Most exotic options are European in nature — this means they can only be exercised on the expiry date.
If an instrument is liquid, a full mark-to-market MtM process can be run be- cause on-screen traded prices or bid-ask spreads are available. However, all exotic instruments are very illiquid, and a mark-to-model process is used. This means mod- els are used in estimating the end of day levels.http://checkout.midtrans.com/ligar-chicas-palencia.php
In this note, we will describe how these exotic instruments can be evaluated using Monte Carlo simulation. Deterministic Local Volatility One of the original assumptions made by Black, Scholes and Merton was that volatility is constant. In Equation 4. The local volatility is the instantaneous volatility for each point in space and time i. In this case, local volatility is a scaler field Boas, ; Reif, These concepts come from mean field theory MFT where the Ising model is a standard many-body system discussed in solid state physics textbooks Harras, ; McCauley, ; Sornette, It is clear that W , and consequently its infinitesimal increment dWt , still represents the only source of uncertainty in the price history of the security.
Black, Scholes and Merton made some assumptions in order to facilitate a better understanding of the dynamics of the security price St. One of the main assumptions is that of risk neutrality. In its simplest form, this infers that all risk-free portfolios can be assumed to earn the same risk-free rate.
This equation is a backward parabolic partial differential equation also known as the back- ward Kolmogorov equation Rebonato, ; Duffie, Discretising the Black-Scholes Equation Fourier solved his simplistic heat conduction equation analytically by introducing Fourier transforms. The extended version is not solved that easily. However, we will understand the SDE in Equation 4. See Appendix A for the derivation. Equation 4. This, together with equations 5. Equations 4. So the question is how do we sample from the continuous distribution for the variable ST? In order to start the simulation we need a starting asset value S t0.
Such a price path is shown in Figure 1 where we have 25 time steps. In that case we can take larger time steps and get by with a smaller number of time steps N.
The general solution to the Black-Scholes backward parabolic partial differential equation in Equation 4. Note that the expectation is taken under the risk-neutral probability measure Q where the stochastic term in Equation 4. Using the mathematical law of expectation, the expectation for a call option in Equation 5. We thus need to integrate over all possible S-values that is larger than the strike K at expiry.
We can use either Equation 4. Note: N is the number of time steps and M the number of simulations. By scrutinising equations 5. It is evident that such an analysis is based on artificially recreating a chance process, running it many times and directly observing the results. Figure 2 shows 5 price paths generated with Equation 4. If we have a call option with a strike price of , Equation 5. This is shown in Table 1. However, crucial to obtaining the correct terminal values ST is that the volatilities we use in equations 4. This shows we first of all need the stock price at each time step, i.
We have given some examples in Table 1. But, further to this, we also need the instantaneous volatility at each time step for each stock price. We can obtain all of this from a three dimensional local volatility surface. We will discuss this in section 6 below. Whereas stochastic volatility and jump-diffusion models introduce new risks into the modeling process, local volatility models stay close to the Black-Scholes theoretical framework and only introduce more flexibility to the volatility.
This is one of the main reasons of fierce criticism of local volatility models Ayache et al. Thus, it is a mistake to interpret local volatility as a complete representation of the true stochastic process driving the underlying asset price. Local volatility is merely a simplification that is practically useful for describing a price process with non-constant volatility.
A local volatility model is a special case of the more general stochastic volatility models. So there is still just one source of randomness, ensuring that the completeness of the Black-Scholes model is preserved. Completeness is important, because it guarantees unique prices, thus arbitrage pricing and hedging Dupire, Note that Equation 6. The main problem is that the implied or traded volatilities are only known at discrete strikes K and expiries T.
This is why the parameterisation chosen for the implied volatility surface is very important. If implied volatilities are used directly from the market, the derivatives in Equation 6. This can still lead to an unsta- ble local volatility surface. Furthermore we will have to interpolate and extrapolate the given data points unto a surface. Since obtaining the local volatility from the data involves taking derivatives, the extrapolated implied volatility surface cannot be too uneven. If it is, this unevenness will be exacerbated in the local volatility surface showing that it is not arbitrage free in these areas.
This function is quadratic across strike and exponential across time. This three dimensional function is fitted to traded data. They further showed that all derivatives in Equation 6. There are no functional forms available and all derivatives in Equation 6. The local volatility surfaces are used when exotic options are evaluated. However, we also see from the local volatility surface that it has more curvature. This shows that the local volatility skew is twice that of the implied volatility skew.
Here we also show the local volatility surface with steeper sides. Continuing with our example: in section 5 and Table 1 we tabulated some price paths. We now want to calculate the Dupire local volatility for each stock price at each time step. This is the local volatility that should then be used in equations 4. On a practical note: in equations 4.
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To apply Equation 6. In our example, the price paths were shown for a one year time period. We thus cannot generate the same price paths under a local volatility regime. So we run this experiment and generate 5 price paths under the ALSI local volatility surface. The newly generated price paths are shown in Figure 5. The actual numbers are listed in Table 2 and the corresponding local volatilities are listed in Table 3. Comparing graphs 5 and 2 and Tables 2 and 1 reveal that the stock prices are not that much different.
This is the way it should be because the local volatility does not differ that much from the implied volatility. However, even these slight differences, can lead to vastly different exotic option prices and especially, Greeks. We price this option using Monte Carlo simulation under a local volatility surface and using the closed-form solutions.
To explain the differences between the MC and closed-form solutions, we look at an example of a one month down-and-out put. Monte Carlo simulation is implemented by using Equation 5. We can further use either Equation 4. Having calculated the stock price at each time step ti , makes it quite easy to implement the boundary conditions. At each time step one needs to check if the stock price S ti is above or below the barrier H.
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If we want to implement the closed-form solution, we need to understand that we can do it in two different ways: we first price it using a fixed volatility of The price dynamics of this option is shown in Figure 6 where closed-form is ab- breviated by CF. More information about this seller Contact this seller 7. Ex-library, so some stamps and wear, but in good overall condition. Seller Inventory Z1-C More information about this seller Contact this seller 8.
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: Adaptive Markov Control Processes Applied Mathematical Sciences 9780387969664: Hernandez-Lerma, Onesimo: Books. This book is concerned with a class of discrete-time stochastic control processes known as controlled Markov processes CMP's, also known as Markov decision processes or Markov dynamic programs. Starting in the mid-1950swith Richard Bellman, many contributions to CMP's have been made, and. Free 2-day shipping. Buy Applied Mathematical Sciences: Adaptive Markov Control Processes Hardcover at. Adaptive Markov Control Processes O. Hernández-Lerma auth. This book is concerned with a class of discrete-time stochastic control processes known as controlled Markov processes CMP's, also known as Markov decision processes or Markov dynamic programs. SIAM J. on Applied Dynamical Systems. Browse SIADS; SIAM J. on Applied Mathematics. Browse SIAP; SIAM J. on Computing. Browse SICOMP; SIAM J. on Control and Optimization. Browse SICON; SIAM J. on Discrete Mathematics. Browse SIDMA; SIAM J. on Financial Mathematics. Browse SIFIN; SIAM J. on Imaging Sciences. Browse SIIMS; SIAM J. on Mathematical.
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This paper presents finite-state discretization procedures for discrete-time, infinite horizon, adaptive Markov control processes which depend on unknown parameters. The discretizations are combined with a consistent parameter estimation scheme to obtain uniform approximations to the optimal value function and asymptotically optimal adaptive. Buy Adaptive Markov Control Processes Applied Mathematical Sciences 1989 by Onesimo Hernandez-Lerma ISBN: 9780387969664 from Amazon's Book Store. Everyday low prices and free delivery on eligible orders.
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Adaptive Markov Control Processes Applied Mathematical Sciences by Onesimo Hernandez-Lerma. Springer, 2012-10-29. Softcover reprint of the origina. Paperback. Good.
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Recently, I have started learning Python. I'd like to make a cosine distribution simulation."Index Error:list index out of range" is shown on my display. but I think I define a length of list, and I write0 < key < len(thickness). why the Error is shown on my display??import mathdef main():height = 20 thickness = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] with open('output/output.csv', 'w', encoding = 'utf-8' ) as f:f.write('x,thikcness\n')for t in range(90):deg = trad = math.radians(deg)x = height * math.tan(rad)key = round(x)if 0 < key <= len(thickness):thickness[key] += 1for t in len(thickness):f.write(str(thickness[t]) + '\n')if __name__ == "__main__":main()
Because you wrote key <= len(thickness) instead of key < len(thickness)
To elaborate, the indices of thickness begin at 0 in python, not 1.