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Reflecting on the Physics of Cliff Diving
What are the key physics principles involved in calculating the speed of a cliff diver just before hitting the water? The key physics principles involved in calculating the speed of a cliff diver
just before hitting the water include kinematics, gravity, velocity, acceleration, and displacement.
Cliff diving is not just an adrenaline-pumping sport, but also a captivating showcase of physics principles in action. When a cliff diver takes a leap off a high cliff, several key physics concepts
come into play to determine the speed at which the diver will be traveling just before hitting the water.
Kinematics is the branch of physics that deals with the motion of objects without considering the forces causing the motion. In the case of a cliff diver, kinematics helps us understand the diver's
motion in terms of velocity, displacement, and acceleration.
Gravity and Acceleration
One of the fundamental forces at work during a cliff dive is gravity. Gravity pulls the diver downward, causing the diver to accelerate as they fall towards the water. The acceleration due to gravity
is constant at 9.8 m/s^2 on Earth, and it plays a crucial role in determining the diver's speed.
Velocity and Displacement
Velocity is a vector quantity that describes the rate of change of an object's position. In the case of a cliff diver, their initial velocity is zero as they start from rest on the cliff. The final
velocity, just before hitting the water, is what we aim to calculate using the principles of kinematics.
The displacement of the diver, in this case, is the vertical distance from the cliff's edge to the water. By understanding the diver's displacement, we can apply the kinematic equations to determine
the final speed at impact.
In Conclusion
By combining the principles of kinematics, gravity, velocity, acceleration, and displacement, we can calculate the speed at which a cliff diver will be traveling just before hitting the water.
Understanding the physics behind cliff diving not only adds depth to the sport but also highlights the intricate relationship between science and extreme sports.
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Ergodicity of the Liouville system implies the Chowla conjecture | Published in Discrete Analysis
Dynamical Systems
December 12, 2017 BST
Ergodicity of the Liouville system implies the Chowla conjecture
Ergodicity of the Liouville system implies the Chowla conjecture, Discrete Analysis 2017:19, 41 pp.
The Liouville function $\lambda:\mathbb N\to\{-1,1\}$ takes a product $p_1p_2\dots p_k$ of (not necessarily distinct) primes $p_1,\dots,p_k$ to $(-1)^k$. That is, $\lambda(n)$ is the parity of the
number of primes in the prime decomposition of $n$. It is a completely multiplicative function (that is, $\lambda(mn)=\lambda(m)\lambda(n)$ for any two positive integers $m,n$, and like various other
multiplicative functions it plays an important role in number theory. In particular, it appears to behave like a random $\pm 1$ sequence in various ways, and if this could be proved rigorously it
would have major consequences: the Riemann hypothesis, for instance, is equivalent to the statement that the sums $\lambda(1)+\lambda(2)+\dots+\lambda(n)$ grow more slowly than $n^\alpha$ whenever $\
alpha>1/2$. (Note that this would be the expected behaviour for a random sequence.) It is known at least that $\lambda(1)+\dots+\lambda(n)=o(n)$, and in fact this statement is equivalent to the prime
number theorem.
Of great interest recently has been the study of more detailed statistical properties of the Liouville function, where one is interested not just in individual values but in correlations between
nearby values. For example, it is believed that $\lambda(x)$ and $\lambda(x+1)$ should be independent, in the sense that $\lambda(1)\lambda(2)+\dots+\lambda(n)\lambda(n+1)=o(n)$. More generally, the
Chowla conjecture asserts that for any set $\{k_1,\dots,k_r\}$ of distinct positive integers we have that $\sum_{m\leq n}\lambda(m+k_1)\dots\lambda(m+k_r)=o(n)$. This conjecture is still wide open,
though weakenings of it, which have been proved in the last few years by Matomäki, Radziwiłł, Tao and Teräväinen (in various combinations), turn out to be very useful for applications. For example,
Tao, building on work by Matomäki and Radziwiłł, established a logarithmically averaged version of the conjecture for two-point correlations, and used it in his solution of the Erdõs discrepancy
problem. Also, Tao and Teräväinen have proved a logarithmically averaged version for all correlations of an odd number of points, which, slightly surprisingly, turns out to be an easier problem. (One
might at first think that this would imply the same for all correlations. However, the statement that $\lambda(m+k_1)\dots\lambda(m+k_r)$ averages zero is not the same as the statement that the
values $\lambda(m+k_1),\dots,\lambda(m+k_r)$ are independent, and it does not imply independence even if one assumes the same statement for all subsets of $\{k_1,\dots,k_r\}$ of odd size, or indeed
for all subsets of $\mathbb N$ of odd size.)
It turns out to be rather fruitful to reformulate questions of this type as questions about dynamical systems. A standard construction in symbolic dynamics is to take an infinite sequence of letters
in a finite alphabet and take the closure of all its shifts (in the product topology). The shift acts on this closure, turning it into a dynamical system. Thanks to the Furstenberg correspondence
principle, it comes with a natural measure that makes it into a measure-preserving system. The properties of this system relate to various features of the sequence, and methods from ergodic theory
and topological dynamics can be used to prove interesting theorems that do not involve dynamics in their statements.
The main result of this paper is that the general logarithmically averaged Chowla conjecture (that is, the statement for all correlations and not just correlations between pairs) follows from a
dynamical statement that looks significantly weaker. In dynamical terms, the Chowla conjecture states that the dynamical system one obtains from the Liouville sequence has the Bernoulli property,
which means that it is isomorphic to the system one gets from all $\pm 1$ sequences. (This implication holds because if every finite string occurs with the right frequency, then shifts of the
Liouville sequence land in a basic open neighbourhood with the right frequency, so all the basic open neighbourhoods have the right measure and the system becomes the same as what one would get with
the shift acting on the space of all $\pm 1$ sequences with the product measure.) The paper shows that to prove the Bernoulli property, it is enough to establish that the system is ergodic, which
means that there are no invariant subsets of measure strictly between 0 and 1. In general, an implication like this is far from true: there are a number of properties that say that a dynamical system
is “somewhat random”: the property of being ergodic is one of the weakest, and the Bernoulli property is the strongest. So the result is telling us something interesting about the Liouville sequence.
Several powerful tools from analytic number theory, additive combinatorics, and ergodic theory are used in the proof.
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MikeWelland.com - Mesoscale models
Mesoscale ('Latin: intermediate') models capture phenomena that are right on the edge between where matter is considered a collection of atoms, and where it can be considered a smooth, continuous
medium. An important example of this are interfaces between phases, and the associated energy and effects.
These models are typically derived from considering the total energy of the system, and can naturally incorporate thermodynamic (CALPHAD-type) potentials. By applying the theory of irreversible
processes, a robust mathematical approach, a thermodynamically consistent model of the system's evolution can be derived in such a way to capture multiphysics effects.
Integrating thermodynamics with phase-field and transport models
Phase changes and transport processes like heat balance and diffusion are driven by thermodynamic forces. In this work models are developed which integrate equilibrium thermodynamic data into
phase-field and transport models. A central issue is how to understand and control the interfacial energy contributions.
The image below to the left is a typical free energy diagram for a binary two-phase system. The green line shows how the components are distributed between phases at equilibrium. The images to the
right are different ways to extend the curves to the left into a continuous free energy surface with a trough along the equilibrium.
A commonly encountered situation is a phase on sitting on the boundary between two other phases, like water beading on the hood of a car. This new model simplifies this 3D problem into a 2D one by
projecting the 'included' phase onto the boundary, resulting in substantial computational efficiency.
Lithium-oxygen electrodes reactions for a advanced battery type
The Lithium-oxygen reaction is interesting for advanced batteries since oxygen is available in the air, which could mean weight and size reduction. This work looks at couple reaction-diffusion and
growth of particles on the cathode surface.
The image to the right is the schematic for the reaction, and below is the predicted chemistry in the electrolyte as particles nucleate and grow.
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Besides ATP, H2O, and NADH, another important final product… | GradePack
Besides ATP, H2O, and NADH, another important final product…
Besides ATP, H2O, аnd NADH, аnоther impоrtаnt final prоduct of the glycolysis pathway is ________.
Recоrd the wоrk fоr this problem on lined pаper for uploаd аt the conclusion of the quiz. 8. a) List the row operations that will transform matrix 1 into matrix 2 with the
indicated first column. b) Write the completed Matrix 2 immediately after the the first column is completed. Matrix 1 Matrix 2 Use the WIRIS Editor to enter your answers for
parts a) and b) in the space provided with correct mathematical notation. Be sure to record the work for this problem on lined paper for upload at the conclusion of the quiz.
Interpersоnаl Smаrtness аnd Intrapersоnal Smartness are the same accоrding to Howard Gardner and research on Multiple Intelligences.
Which religiоn hаs less structure аnd guidаnce?
Africаn аnd Nаtive American religiоn has a fоcus оn ancestors.
Vаriаtiоns in the shаpe оf the earth's оrbit:
The fоur thermаl lаyers оf the аtmоsphere in order beginning from the surface are:
The pаtient will demоnstrаte diet upgrаde trials withоut signs and/оr symptoms of aspiration with 10/10 trials.
Jаvier will demоnstrаte the аbility tо reduce the number оf disfluencies in his speech by using easy starts 85% of the time in a structured conversation.
Sаndy will fоrmulаte 3-wоrd utterаnces tо communicate daily needs with 75% accuracy with minimal cues.
Jаmie will аct upоn nаmed/described elements in 2-part оral directiоns with no more than one repetition of directions, in 8 of 10 opportunities.
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Printable Math Puzzles For 2Nd Grade - Printable Crossword Puzzles
Printable Math Puzzles For 2Nd Grade – free printable math worksheets for 2nd grade measurement, free printable math worksheets for 2nd grade regrouping, fun math puzzles for second grade, That does
not learn about Printable Math Puzzles For 2Nd Grade? This mass media is popular to instruct expression. In virtually any point about this world, this multimedia will need to have been very
acquainted for many people. At least, people might have ever seen it in class. Some other individuals might have ever seen it from another provider.
Regarding students, this will not be a whole new factor any more. This media is incredibly common for use in teaching and understanding actions. There are actually points you may want to know
relevant to the crossword puzzle. Are you currently thinking about understanding more? Now, let us look into the data beneath.
What you ought to Understand about Printable Math Puzzles For 2Nd Grade
Let us recall the memory where you can find this press. College can be a location where kids probably will see it. For instance, when youngsters are studying a terminology, that they need various
entertaining pursuits. Effectively, Printable Math Puzzles For 2Nd Grade may be one of your actions. Here is the method that you remedy the puzzles.
In a crossword puzzle, you will realize plenty of letters that happen to be put into extended distance. They might not appear to be so as. In fact, you will definately get to see a number of words.
Yet, you will always find recommendations of the things words that you must see in the puzzle. Their list might have a lot more than 5 terms to find. It depends in the puzzle producer, however.
When you are the one who make it, you can choose how many words how the youngsters need to find. Individuals words and phrases may be published earlier mentioned, adjacent to, or underneath the
puzzle. Moreover, Printable Math Puzzles For 2Nd Grade are generally in square condition. Square is most popular design to be utilized. You need experienced no less than one, do not you?
Around this second, you need to have at any time recalled plenty of remembrances about this puzzle, correct? Related to the application of this puzzle in teaching and discovering actions, terminology
discovering is not the sole one that utilizes this press. It is rather probable to be used in other topics.
Yet another example is, you can use it in science topic for teaching about planets in galaxy. The title of planets might be written down to assist youngsters discovering them in puzzle. It is really
an interesting action on their behalf.
Additionally, it is far from too hard being a job. Indeed, individuals can use it for another use beyond the schooling industry. To make Printable Math Puzzles For 2Nd Grade, very first option is to
make it all on your own. It is not hard by any means to prepare it alone.
The next solution is to try using crossword puzzle machine. There are numerous cost-free web sites and totally free application that will help work less difficult. It will also help you arrange the
puzzle just by typing down words and phrases you want, and bam !! Your crossword puzzle is able to use.
It is quite simple to make your Printable Math Puzzles For 2Nd Grade, proper? You do not have to spend lots of your time and efforts making it by using a assistance of the appliance manufacturer.
Printable Math Puzzles For 2Nd Grade
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Crypto and new computing strategies
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Crypto and new computing strategies
British physicist David Deutsch has been writing for several years on
the theoretical properties of computers which would exploit quantum
mechanics. Here is the abstract from his paper in Proc. R. Soc. Lond. A,
v 400, p97-117, 1985:
Quantum Theory, the Church-Turing Principle and the Universal Quantum
"It is argued that underlying the Church-Turing hypothesis there is an
implicit physical assertion. Here, this assertion is presented explicitly
as a physical principle: 'every finitely realizable physical system can be
perfectly simulated by a universal model computing machine operating by
finite means.' Classical physics and the universal Turing machine, because
the former is continuous and the latter discrete, do not obey the principle,
at least in the strong form above. A class of model computing machines that
is the quantum generalization of the class of Turing machines is described,
and it is shown that quantum theory and the 'universal quantum computer'
are compatible with the principle. Computing machines resembling the
universal quantum computer could, in principle, be built and would have many
remarkable properties not reproducible by any Turing machine. These do
not include the computation of non-recursive functions, but they do include
'quantum parallelism,' a method by which certain probabilistic tasks can
be performed faster by a universal quantum computer than by any classical
restriction of it. The intuitive explanation of these properties places
an intolerable strain on all interpretations of quantum theory other than
Everett's. Some of the numerous connections between the quantum theory of
computation and the rest of physics are explored. Quantum complexity theory
allows a physically more reasonable definition of the 'complexity' or
'knowledge' in a physical system than does classical complexity theory."
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Calculate Loan Discounts Easily with a Loan Discount Calculator
Calculate Loan Discounts Easily with a Loan Discount Calculator
Are you considering taking out a loan? Before making any decisions, it’s important to have a clear understanding of how much you’ll be paying in interest and what your monthly payments will be.
That’s where a loan calculator comes in. With this powerful tool, you can easily determine the total cost of your loan, including the interest you’ll be paying over its duration.
A loan calculator allows you to input the loan amount, interest rate, and loan term, and it will provide you with a detailed breakdown of your monthly payments. This information can be incredibly
valuable when comparing different loans or trying to negotiate a better interest rate. With the ability to quickly and accurately calculate your repayment schedule, you can make informed decisions
about your financial future.
What sets a loan calculator apart from other financial tools is its ability to factor in discounts. Many lenders offer incentives, such as loyalty or autopay discounts, that can significantly reduce
your interest rate. By using a loan discount calculator, you can easily see how these discounts will impact your monthly payments and overall savings. With just a few clicks, you can find out if it’s
financially beneficial to take advantage of these offers and maximize your savings.
Calculate Your Savings with a Loan Discount Calculator
Are you curious to know how much you can save on your loan payments? With a loan discount calculator, you can easily and accurately calculate your potential savings.
Calculating your savings can be a complex task, especially if you have multiple loans with different interest rates and terms. However, with a loan discount calculator, you can input the necessary
information and instantly see how much you could potentially save on your loan payments.
The calculator takes into account the principal amount, interest rate, and loan term to determine your monthly payment. It also calculates the total interest paid over the life of the loan. By
applying a discount to your interest rate, you can quickly see how your payment amount and total interest paid will change.
Whether you’re considering refinancing your loan or simply want to see how a potential discount could affect your monthly payments, a loan discount calculator can help. It allows you to compare
different scenarios and make an informed decision about your finances.
Using a loan discount calculator is easy. Simply enter the loan details, including the principal amount, interest rate, and loan term. Then, input the discount rate you want to apply. The calculator
will instantly show you how your monthly payment and total interest paid will change with the discount.
Calculating your savings with a loan discount calculator can help you make wise financial decisions. It allows you to see the impact of a discount on your loan payments and determine if it’s worth
pursuing. So why wait? Start calculating your savings today and take control of your finances.
Why Use a Loan Discount Calculator?
Calculating your loan interest, discount rate, and monthly payment can be a complex task. Not only does it require you to have a good understanding of financial calculations, but it also takes time
and effort to manually crunch the numbers.
That’s where a loan discount calculator comes in handy. With just a few clicks, you can quickly and accurately calculate the savings that a loan discount can offer you. Whether you’re considering
refinancing your mortgage or taking out a personal loan, using a loan discount calculator can help you make informed financial decisions.
Accurate Calculations
A loan discount calculator takes into account various factors, such as the loan amount, interest rate, discount rate, and term, to provide you with accurate calculations. You don’t have to worry
about making mathematical errors or miscalculating your savings. The calculator does all the work for you, ensuring precision and reliability.
By using a loan discount calculator, you save a significant amount of time. Instead of manually calculating different loan scenarios, you can input the relevant information into the calculator and
get immediate results. This allows you to compare different loan options and determine which one offers the most savings in the shortest amount of time.
Overall, a loan discount calculator is a valuable tool that can simplify the loan calculation process and help you make informed financial decisions. It provides accurate calculations and saves you
time, making it an essential resource for anyone considering taking out a loan or refinancing their existing loan.
How Does a Loan Discount Calculator Work?
A loan discount calculator is a tool that helps you calculate the amount of money you can save on your loan payments by applying a discount to the loan interest rate. This calculator takes into
account the principal amount of the loan, the interest rate, and the repayment term to provide an estimate of the savings you can make.
The calculator works by taking the loan amount, interest rate, and repayment term as inputs. It then uses these inputs to calculate the monthly payment for the loan without the discount. Next, it
applies the discount to the interest rate and recalculates the monthly payment. The difference between the two monthly payments represents the savings you can expect by applying the discount.
For example, let’s say you have a $10,000 loan with an interest rate of 5% and a repayment term of 5 years. Without applying a discount, the monthly payment would be calculated to be $188.71.
However, if you apply a discount of 1%, the interest rate would be reduced to 4%, resulting in a new monthly payment of $184.17. The difference between the two monthly payments is $4.54, which
represents your savings each month.
By using a loan discount calculator, you can quickly and accurately determine the potential savings you can achieve by applying a discount to the interest rate of your loan. This can help you make
informed decisions about your borrowing options and find the best loan terms for your needs.
Benefits of Using a Loan Discount Calculator
Using a loan discount calculator can provide numerous benefits when you are considering applying for a loan. It allows you to easily and accurately calculate your savings, giving you a better
understanding of the financial impact of different interest rates and discount options. Here are some key benefits of using a loan discount calculator:
1. Accurate Calculation of Savings
A loan discount calculator helps you accurately calculate the amount of money you can save on a loan. By entering the loan amount, interest rate, and any available discount options, the calculator
can provide you with an estimate of your total savings. This allows you to make an informed decision and choose the best loan option for your financial situation.
2. Quick and Easy Comparison
With a loan discount calculator, you can quickly compare different loan options. By inputting the details of each loan, including the interest rate and discount options, you can easily compare the
savings offered by each loan. This allows you to determine which loan provides the most favorable terms and the greatest potential for savings.
3. Understanding the Impact of Interest Rates
The interest rate on a loan has a significant impact on the total amount you will repay over the loan term. By using a loan discount calculator, you can see how different interest rates affect your
total repayment amount. This helps you understand the importance of obtaining a lower interest rate and the potential savings that can be achieved.
4. Budgeting and Planning
A loan discount calculator also helps with budgeting and planning. By calculating your loan payments with different interest rates and discount options, you can better understand how these factors
will affect your monthly payments. This allows you to plan your budget accordingly and ensure that you can comfortably afford your loan payments.
5. Easy to Use
Most loan discount calculators are user-friendly and require minimal input to provide accurate results. They are designed to be easy to use, even for those who are not familiar with complex financial
calculations. With just a few simple steps, you can quickly calculate your potential savings and make an informed decision about your loan options.
In conclusion, using a loan discount calculator can offer numerous benefits, including accurate calculations, quick comparisons, a better understanding of interest rates, help with budgeting and
planning, and ease of use. By taking advantage of a loan discount calculator, you can make informed financial decisions and potentially save a significant amount of money on your loan.
Loan Interest Calculator
When applying for a loan, it is vital to understand the interest that will be charged on your loan. The loan interest calculator is a useful tool that can help you determine the amount of interest
you will be paying over the course of your loan repayment.
With the loan interest calculator, you can input the loan amount, the interest rate, and the loan term to calculate the total interest you will pay. This information can be valuable for budgeting
purposes and understanding the cost of borrowing.
By using the loan interest calculator, you can also compare different loan options to find the most affordable option for your needs. It allows you to adjust the loan term and interest rate to see
how they affect your monthly payment and the total interest paid.
The calculator takes into account the discount offered by the lender, if applicable. This discount could be in the form of lower interest rates for specific qualifying individuals or entities. By
entering the discount into the calculator, you can calculate the savings you will make on your loan.
Understanding the interest on your loan is crucial for financial planning. The loan interest calculator provides an easy and accurate way to calculate the interest and savings associated with your
loan. Take advantage of this tool to make informed decisions and save money on your loan payments.
Remember, it is always a good idea to consult with a financial advisor or loan specialist before making any decisions regarding loans or borrowing.
Understanding Loan Interest
When you take out a loan, one of the most important factors to consider is the interest rate. The interest rate determines how much extra money you will need to pay back on top of the loan amount. It
is crucial to understand how interest is calculated so you can make informed decisions about borrowing.
Interest is essentially the cost of borrowing money. Lenders charge interest to compensate for the risk they take in lending money and to make a profit. The interest rate is usually expressed as a
percentage and can vary depending on factors such as your credit score, the type of loan, and market conditions.
The amount of interest you will pay over the life of a loan can have a significant impact on your finances. To understand the total cost of a loan, you can use a loan payment calculator. This handy
tool allows you to input the loan amount, interest rate, and term to calculate your monthly payment, as well as the total amount of interest you will pay over the life of the loan.
Loan Amount Interest Rate Loan Term Monthly Payment Total Interest Paid
$10,000 5% 5 years $188.71 $3,322.92
$20,000 7% 10 years $233.79 $8,455.06
$50,000 4.5% 15 years $369.85 $20,573.44
As you can see from the above examples, even a small difference in the interest rate can result in a significant difference in the total amount you will pay in interest. That’s why it’s essential to
shop around for the best loan terms and interest rates before making a decision.
By understanding how interest is calculated and using a loan calculator, you can make informed decisions about borrowing and ensure that you are getting the best possible terms for your loan.
How to Use a Loan Interest Calculator
A loan interest calculator is a useful tool that can help you determine the cost of a loan. By inputting the loan amount, interest rate, and term, the calculator can calculate your monthly payment
and total interest paid over the life of the loan. Here’s a step-by-step guide on how to use a loan interest calculator:
Step 1: Gather the necessary information
Before you can start using the loan interest calculator, you’ll need to gather some information. This includes the loan amount, interest rate, and loan term. The loan amount is the total amount you
intend to borrow, while the interest rate is the percentage you’ll be charged for the loan. The loan term is the length of time you have to repay the loan.
Step 2: Enter the information into the calculator
Once you have the necessary information, enter it into the loan interest calculator. The calculator will typically have input fields for the loan amount, interest rate, and loan term. Fill in these
fields with the corresponding information.
Step 3: Calculate your monthly payment
After you’ve entered all the necessary information, the loan interest calculator will calculate your monthly payment. This is the amount you’ll need to pay each month to repay the loan over the loan
term. The calculator takes into account the loan amount, interest rate, and loan term to provide an accurate monthly payment amount.
Step 4: Calculate the total interest paid
In addition to calculating your monthly payment, the loan interest calculator can also determine the total interest paid over the life of the loan. This is the amount of interest you’ll end up paying
in addition to the loan amount. It’s important to consider the total interest paid when deciding if a loan is affordable.
Using a loan interest calculator can give you a clear understanding of the cost of a loan and help you make informed financial decisions. By knowing your monthly payment and total interest paid, you
can budget accordingly and determine if the loan is the right choice for your financial goals.
Advantages of Using a Loan Interest Calculator
When it comes to managing your finances and planning for the future, a loan interest calculator can be an invaluable tool. Here are some advantages of using a loan interest calculator:
Accurate Calculation of Interest Rates
Calculating interest rates manually can be complex and time-consuming. A loan interest calculator allows you to input the necessary information, such as the loan amount and the interest rate, and it
will quickly calculate the total interest you will pay over the life of the loan. This accuracy can help you make informed decisions and avoid any surprises.
Saves Time and Effort
Using a loan interest calculator saves you the hassle of manually performing the calculations yourself. It eliminates the need for complicated formulas and ensures that your calculations are
error-free. This saves you time and effort, allowing you to focus on other important aspects of your financial planning.
Helps You Compare Different Loan Options
A loan interest calculator allows you to calculate the interest rates for different loan options. By inputting the loan amount, interest rates, and loan terms, you can quickly compare the total
interest paid for each option. This enables you to choose the most affordable loan option and make an informed decision.
Financial Planning and Budgeting
Using a loan interest calculator can also be beneficial for financial planning and budgeting purposes. By calculating the interest rates for different loan scenarios, you can determine the impact on
your monthly budget. This helps you plan your expenses and allocate funds accordingly, ensuring that you can comfortably afford the loan payments.
In conclusion, using a loan interest calculator provides several advantages. It offers accurate calculations, saves time and effort, helps you compare loan options, and aids in financial planning and
budgeting. By utilizing this helpful tool, you can make informed decisions and ensure that you are getting the best loan deal possible.
Loan Rate Calculator
If you’re in need of a loan and want to know how it will impact your finances, a loan rate calculator is a valuable tool. This calculator allows you to determine the amount of your monthly payment
and the interest rate you can afford. By entering the necessary information, such as the loan amount and term, the calculator will calculate the total cost of the loan and give you a clear
understanding of your financial obligations.
Using a loan rate calculator is simple and straightforward. You just need to input the required details, such as the loan amount, interest rate, and term, and the calculator will do the rest. It will
provide you with an accurate calculation of your monthly payments, including both the principal and interest. This information is crucial for understanding how much you can afford to borrow and what
your financial responsibilities will be.
Benefits of Using a Loan Rate Calculator
• Accuracy: A loan rate calculator provides accurate calculations, ensuring that you know the exact amount of your monthly payment and the total cost of the loan.
• Time-saving: By using the calculator, you can quickly determine whether a loan is affordable for you or not. It saves you time by giving you instant results.
• Easy comparison: If you’re considering multiple loan options, the calculator makes it easy to compare different rates and terms to find the best one for your needs.
• Financial planning: With the help of a loan rate calculator, you can plan your finances better by understanding the impact of the loan on your monthly budget.
Whether you’re looking to buy a new car, invest in a home, or pay for higher education, a loan rate calculator is an essential tool to help you make informed decisions. By accurately calculating your
monthly payments and considering the interest rate and term, you can determine what loan options are feasible and choose the one that best fits your financial situation and goals.
What is a Loan Rate?
A loan rate refers to the interest rate that a borrower pays on a loan. It is the cost of borrowing money and is usually expressed as a percentage of the loan amount. The rate is calculated based on
various factors such as the borrower’s credit score, the term of the loan, and the market conditions.
When you take out a loan, you will be required to make regular payments to repay the borrowed amount and the interest. The loan rate determines the amount of interest that you will have to pay over
the course of the loan.
Calculating the loan payment with the loan rate is an important step in managing your finances. A loan discount calculator can help you determine the monthly payment and the total amount you will pay
over the loan term.
Loan Amount Loan Rate Loan Term Monthly Payment Total Payment
$10,000 5% 5 years $188.71 $11,322.60
$20,000 3.5% 10 years $193.33 $23,199.60
$30,000 4.25% 15 years $221.60 $39,888.60
As you can see from the table above, the loan rate directly affects the monthly payment and the total payment. A higher loan rate translates to higher monthly payments and a larger total payment over
the loan term.
Using a loan discount calculator can help you compare different loan rates and terms, allowing you to make an informed decision when it comes to borrowing money. It is a valuable tool for budgeting
and planning your finances.
How to Calculate Loan Rate
Calculating the loan rate is an important step in understanding the financial implications of taking out a loan. By determining the interest rate, you can determine how much you will ultimately pay
back and how much you will save with any applicable discounts. Here are the steps to calculate loan rate:
1. Determine the Loan Amount
Before calculating the loan rate, you need to know the loan amount. This is the total amount of money that you are borrowing. It can be a fixed amount or a range depending on your needs.
2. Find out the Interest Rate
The interest rate is the percentage charged by the lender for borrowing the money. It is the cost of borrowing the funds and is typically expressed as an annual percentage rate (APR). The interest
rate can vary depending on factors such as your creditworthiness and the type of loan you are applying for.
3. Consider any Applicable Discounts
In some cases, lenders may offer discounts on the interest rate. These discounts can be based on factors such as your relationship with the lender, automatic payment setups, or special promotions.
It’s important to consider these discounts as they can significantly reduce the overall cost of the loan.
4. Use a Loan Rate Calculator
To calculate the loan rate accurately, it’s recommended to use a loan rate calculator. These online tools take into account the loan amount, interest rate, and any applicable discounts to determine
the final loan rate. They provide you with an accurate estimate, saving you time and effort in manual calculations.
By following these steps and using a loan rate calculator, you can accurately calculate the loan rate and make an informed decision about your borrowing options. Knowing the loan rate will help you
understand the total cost of the loan, including any discounts that can help you save money.
Advantages of Using a Loan Rate Calculator
A loan rate calculator is a powerful tool that can provide numerous advantages when it comes to managing your finances. Here are some of the key benefits of using a loan rate calculator:
Accurate Calculations Easy to Use
A loan rate calculator uses mathematical formulas to accurately calculate your loan interest rate. A loan rate calculator is designed to be user-friendly, making it easy for anyone to navigate and
This ensures that you have access to reliable and precise information about your potential loan input their loan details. Whether you are a financial expert or a beginner, you can easily use
payment. the calculator to determine your loan payment.
Quick Results Compare Different Loan Options
A loan rate calculator provides instant results, eliminating the need for manual calculations. You The calculator allows you to input different loan rates, terms, and amounts, making it easy to
can obtain your loan payment amount within seconds, saving you time and effort. compare your options. You can see how different factors affect your loan payment, helping you
make an informed decision.
Plan for the Future Save Money
By using a loan rate calculator, you can plan your financial future more effectively. You can examine By calculating your loan payment accurately, you can avoid unnecessary expenses and potentially
different scenarios and determine how your loan payment will change based on factors such as interest save money. Knowing the exact amount you need to pay each month enables you to budget accordingly
rate fluctuations and loan term adjustments. and avoid overpaying on interest.
Overall, a loan rate calculator is a valuable tool that empowers you to make informed financial decisions. It provides accurate calculations, ease of use, quick results, the ability to compare
different loan options, and helps you plan for the future while potentially saving money. Incorporating a loan rate calculator into your financial management strategy can greatly benefit your
financial well-being.
Loan Payment Calculator
If you are considering taking out a loan, it’s important to understand how much your monthly payments will be. With the Loan Payment Calculator, you can easily calculate your monthly payment amount
and determine the total interest paid over the life of the loan.
The calculator takes into account the loan amount, interest rate, and any applicable discounts or rate reductions. Simply enter the required information, and the calculator will provide you with an
accurate estimate of your monthly payment.
By entering different loan terms and interest rates, you can not only calculate your monthly payment, but also compare different loan options to find the best fit for your needs and budget.
Additionally, if you are eligible for any discounts or rate reductions, the calculator will factor those in to give you a more precise estimate of your payment amount. This can help you understand
the potential savings you could enjoy by taking advantage of these offers.
It’s important to note that the Loan Payment Calculator provides an estimate and should be used for informational purposes only. The actual payment amount may vary depending on additional fees,
taxes, and other factors.
Using the Loan Payment Calculator can give you a clear understanding of what to expect when it comes to your monthly payments. It empowers you to make informed decisions and plan your finances
accordingly. Whether you are looking to buy a new car, finance a home improvement project, or consolidate debt, this calculator is a valuable tool to help you calculate your loan payment accurately.
What are Loan Payments?
When you take out a loan, you are typically required to make regular payments to repay the amount you borrowed plus any interest that has accrued. Loan payments are the amounts you pay back to the
lender according to an agreed-upon schedule.
Calculating loan payments can be complex, especially when considering interest rates and repayment terms. Luckily, there are loan payment calculators available to simplify the process.
An interest rate is a significant factor in determining the loan payment amount. This rate represents the cost of borrowing the money and is typically expressed as a percentage. The interest rate can
vary depending on factors such as creditworthiness, loan type, and market conditions.
A loan payment calculator takes into account the loan amount, interest rate, and repayment term to calculate the amount you need to pay each period. By inputting these values, you can instantly know
your monthly, bi-weekly, or weekly payment amounts.
Using a loan payment calculator can help you explore different scenarios and determine the best repayment plan for your financial situation. It’s especially useful when comparing loans with different
interest rates or repayment terms. By adjusting the rate or term inputs, you can see how it impacts the loan payment amount and total interest paid.
Loan payment calculators are also handy when considering loan discounts. Some lenders offer discounts on the interest rate if certain conditions are met, such as making automatic payments or having a
good credit score. With a calculator, you can easily see how these discounts would affect your payment amount and savings over time.
In conclusion, loan payments are the amounts you must repay to the lender when borrowing money. To calculate these payments accurately, you can utilize a loan payment calculator, which considers
factors such as loan amount, interest rate, and repayment term. By using this tool, you can explore different scenarios, compare loan options, and determine the most suitable repayment plan for your
financial needs.
How to Calculate Loan Payments
Calculating loan payments is an essential step in managing your finances and understanding the true cost of borrowing. By knowing how to calculate your loan payments, you can determine the amount you
need to pay each month or at a specific interval.
To calculate your loan payments, you will need to know the loan amount, interest rate, and the loan term. The loan amount refers to the total amount you borrowed, while the interest rate is the
percentage charged by the lender for borrowing the money. The loan term is the length of time over which you will repay the loan.
Once you have these three pieces of information, you can use a loan payment formula to calculate your monthly payments. The formula takes into account the loan amount, interest rate, and loan term to
provide an accurate payment amount.
The formula for calculating loan payments involves multiplying the loan amount by the monthly interest rate, then dividing it by 1 minus the discount factor. The discount factor is calculated using
the interest rate and the number of payments made each year. This formula can be complex, so it’s recommended to use a loan payment calculator or spreadsheet to simplify the process.
Here is an example of how to calculate loan payments:
1. Determine the loan amount, for example, $10,000.
2. Find the interest rate, for example, 5%, and convert it to a decimal (0.05).
3. Decide on the loan term, for example, 3 years.
4. Calculate the monthly interest rate by dividing the annual interest rate by the number of payments per year. For example, if the loan has monthly payments, divide 0.05 by 12.
5. Use the loan payment formula or a calculator to determine the monthly payment amount.
Calculating loan payments allows you to understand the financial commitment you are making and plan your budget accordingly. By determining the monthly payment amount, you can assess whether it fits
within your financial means and make necessary adjustments if needed.
In conclusion, understanding how to calculate loan payments is crucial for making informed financial decisions. By considering the loan amount, interest rate, and loan term, you can accurately
calculate your monthly payments and plan your finances effectively. Utilizing a loan payment calculator or spreadsheet can simplify the calculations and provide you with accurate results.
Advantages of Using a Loan Payment Calculator
When it comes to managing your finances, it’s important to have a clear understanding of your loan payment options. This is where a loan payment calculator can be extremely helpful. Here are some
advantages of using a loan payment calculator:
1. Accurate Payments:
A loan payment calculator allows you to calculate your monthly payment with great accuracy. By simply entering the loan amount, interest rate, and loan term, you can quickly obtain the exact amount
you will need to pay each month.
2. Comparison Shopping:
Using a loan payment calculator gives you the freedom to compare different loan options. By adjusting the loan amount, interest rate, and loan term, you can see how different loans will affect your
monthly payments. This allows you to make informed decisions and choose the loan that best fits your financial situation.
3. Planning for the Future:
By using a loan payment calculator, you can plan for the future. You can see how additional payments will affect your loan balance and the amount of interest you will pay over time. This knowledge
can help you create a payment plan that will allow you to pay off your loan faster and save money on interest.
4. Understanding the True Cost of a Loan:
With a loan payment calculator, you can easily see the total cost of your loan. This includes the principal amount borrowed, the interest paid over the life of the loan, and the overall cost of
borrowing. This information can help you make more informed decisions and avoid taking on loans with high costs.
Using a loan payment calculator can make a big difference in managing your finances. It provides you with accurate payment information, allows you to compare different loan options, helps you plan
for the future, and gives you a better understanding of the true cost of a loan. With all these advantages, it’s clear why a loan payment calculator is an essential tool for anyone considering
borrowing money.
Question and answer:
How can I calculate my savings using a loan discount calculator?
To calculate your savings using a loan discount calculator, you need to enter the loan amount, interest rate, term, and any other relevant information into the calculator. The calculator will then
provide you with an estimate of your monthly payments and savings over the life of the loan.
What is a loan payment calculator?
A loan payment calculator is a tool that helps you estimate your monthly loan payments based on factors such as loan amount, interest rate, and term. By using a loan payment calculator, you can
determine how much you will need to pay each month and plan your budget accordingly.
How does a loan rate calculator work?
A loan rate calculator works by taking into account factors such as loan amount, term, and interest rate to calculate the interest you will pay over the life of the loan. It can also help you compare
different loan rates to find the best option for your financial needs.
What is a loan interest calculator?
A loan interest calculator is a tool that helps you calculate the amount of interest you will pay over the course of a loan. By entering the loan amount, interest rate, and term, the calculator can
provide you with an estimate of the total interest you will owe, allowing you to plan your repayment strategy and calculate potential savings by paying off the loan early.
Are loan discount calculators accurate?
Loan discount calculators are designed to provide accurate estimates based on the information you input. However, it’s important to note that these calculators are only tools and the actual terms and
conditions of a loan may vary. It’s always a good idea to consult with a financial expert or loan provider for a more precise calculation based on your specific circumstances.
How can I calculate my savings using a loan discount calculator?
You can calculate your savings using a loan discount calculator by entering the loan amount, interest rate, and loan term into the calculator. The calculator will then calculate your monthly payments
and total savings over the life of the loan.
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Mathematics Grade 6 Printable Version (pdf)
Course Introduction
Core Standards of the Course
Strand: MATHEMATICAL PRACTICES (6.MP)
The Standards for Mathematical Practice in Sixth Grade describe mathematical habits of mind that teachers should seek to develop in their students. Students become mathematically proficient in
engaging with mathematical content and concepts as they learn, experience, and apply these skills and attitudes (Standards 6.MP.1-8).
Standard 6.MP.1
Make sense of problems and persevere in solving them. Explain the meaning of a problem and look for entry points to its solution. Analyze givens, constraints, relationships, and goals. Make
conjectures about the form and meaning of the solution, plan a solution pathway, and continually monitor progress asking, "Does this make sense?" Consider analogous problems, make connections
between multiple representations, identify the correspondence between different approaches, look for trends, and transform algebraic expressions to highlight meaningful mathematics. Check answers
to problems using a different method.
Standard 6.MP.2
Reason abstractly and quantitatively. Make sense of the quantities and their relationships in problem situations. Translate between context and algebraic representations by contextualizing and
decontextualizing quantitative relationships. This includes the ability to decontextualize a given situation, representing it algebraically and manipulating symbols fluently as well as the
ability to contextualize algebraic representations to make sense of the problem.
Standard 6.MP.3
Construct viable arguments and critique the reasoning of others. Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Make conjectures
and build a logical progression of statements to explore the truth of their conjectures. Justify conclusions and communicate them to others. Respond to the arguments of others by listening,
asking clarifying questions, and critiquing the reasoning of others.
Standard 6.MP.4
Model with mathematics. Apply mathematics to solve problems arising in everyday life, society, and the workplace. Make assumptions and approximations, identifying important quantities to
construct a mathematical model. Routinely interpret mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not
served its purpose.
Standard 6.MP.5
Use appropriate tools strategically. Consider the available tools and be sufficiently familiar with them to make sound decisions about when each tool might be helpful, recognizing both the
insight to be gained as well as the limitations. Identify relevant external mathematical resources and use them to pose or solve problems. Use tools to explore and deepen their understanding of
Standard 6.MP.6
Attend to precision. Communicate precisely to others. Use explicit definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose. Specify
units of measure and label axes to clarify the correspondence with quantities in a problem. Calculate accurately and efficiently, and express numerical answers with a degree of precision
appropriate for the problem context.
Standard 6.MP.7
Look for and make use of structure. Look closely at mathematical relationships to identify the underlying structure by recognizing a simple structure within a more complicated structure. See
complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, see 5 - 3(x - y)2 as 5 minus a positive number times a square and
use that to realize that its value cannot be more than 5 for any real numbers x and y.
Standard 6.MP.8
Look for and express regularity in repeated reasoning. Notice if reasoning is repeated, and look for both generalizations and shortcuts. Evaluate the reasonableness of intermediate results by
maintaining oversight of the process while attending to the details.
Strand: RATIOS AND PROPORTIONAL RELATIONSHIPS (6.RP)
Understand ratio concepts and use ratio reasoning to solve problems (Standards 6.RP.1-3).
Standard 6.RP.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. The following are examples of ratio language: “The ratio of wings to beaks in the
bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
Standard 6.RP.2
Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. The following are examples of rate language: "This
recipe has a ratio of four cups of flour to two cups of sugar, so the rate is two cups of flour for each cup of sugar." “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." (In
sixth grade, unit rates are limited to non-complex fractions.)
Standard 6.RP.3
Use ratio and rate reasoning to solve real-world (with a context) and mathematical (void of context) problems, using strategies such as reasoning about tables of equivalent ratios, tape diagrams,
double number line diagrams, or equations involving unit rate problems.
1. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to
compare ratios.
2. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took four hours to mow eight lawns, how many lawns could be mowed in 32 hours? What is
the hourly rate at which lawns were being mowed?
3. Find a percent of a quantity as a rate per 100. Solve problems involving finding the whole, given a part and the percent. (For example, 30% of a quantity means 30/100 times the quantity.)
4. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
Strand: THE NUMBER SYSTEM (6.NS)
Apply and extend previous understandings of multiplication and division of whole numbers to divide fractions by fractions (Standard 6.NS.1). Compute (add, subtract, multiply and divide) fluently with
multi-digit numbers and decimals and find common factors and multiples (Standards 6.NS.2-4). Apply and extend previous understandings of numbers to the system of rational numbers (Standards 6.NS.5-8)
Standard 6.NS.1
Interpret and compute quotients of fractions.
1. Compute quotients of fractions by fractions, for example, by applying strategies such as visual fraction models, equations, and the relationship between multiplication and division, to
represent problems.
2. Solve real-world problems involving division of fractions by fractions. For example, how much chocolate will each person get if three people share 1/2 pound of chocolate equally? How many 3/
4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mile and area 1/2 square mile?
3. Explain the meaning of quotients in fraction division problems. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient. Use the
relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.)
Standard 6.NS.2
Fluently divide multi-digit numbers using the standard algorithm.
Standard 6.NS.3
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
1. Fluently divide multi-digit decimals using the standard algorithm, limited to a whole number dividend with a decimal divisor or a decimal dividend with a whole number divisor.
2. Solve division problems in which both the dividend and the divisor are multi-digit decimals; develop the standard algorithm by using models, the meaning of division, and place value
Standard 6.NS.4
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to
express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
Standard 6.NS.5
Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (for example, temperature above/below zero, elevation above/below sea
level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of zero in each situation.
Standard 6.NS.6
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with
negative number coordinates.
1. Recognize opposite signs of numbers as indicating locations on opposite sides of zero on the number line; recognize that the opposite of the opposite of a number is the number itself. For
example, -(-3) = 3, and zero is its own opposite.
2. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the
points are related by reflections across one or both axes.
3. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
Standard 6.NS.7
Understand ordering and absolute value of rational numbers.
1. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the
right of –7 on a number line oriented from left to right.
2. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 °C > –7 °C to express the fact that –3 °C is warmer than –7 °C.
3. Understand the absolute value of a rational number as its distance from zero on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world
context. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.
4. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.
Standard 6.NS.8
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with
the same x-coordinate or the same y-coordinate.
Strand: EXPRESSIONS AND EQUATIONS (6.EE)
Apply and extend previous understandings of arithmetic to algebraic expressions involving exponents and variables (Standards 6.EE.1-4). They reason about and solve one-variable equations and
inequalities (Standards 6.EE.5-8). Represent and analyze quantitative relationships between dependent and independent variables in a real-world context (Standard 6.EE.9).
Standard 6.EE.1
Write and evaluate numerical expressions involving whole-number exponents.
Standard 6.EE.2
Write, read, and evaluate expressions in which letters stand for numbers.
1. Write expressions that record operations with numbers and with letters representing numbers. For example, express the calculation "Subtract y from 5" as 5 - y and express "Jane had $105.00 in
her bank account. One year later, she had x dollars more. Write an expression that shows her new balance" as $105.00 + x.
2. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe
the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.
3. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving
whole-number exponents, applying the Order of Operations when there are no parentheses to specify a particular order. For example, use the formulas V = s^3 and A = 6s^2 to find the volume and
surface area of a cube with sides of length s = 1/2.
Standard 6.EE.3
Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply
the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
Standard 6.EE.4
Identify when two expressions are equivalent. For example, the expressions y + y + y and 3y are equivalent because they name the same number, regardless of which number y represents.
Standard 6.EE.5
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine
whether a given number in a specified set makes an equation or inequality true.
Standard 6.EE.6
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the
purpose at hand, any number in a specified set.
Standard 6.EE.7
Solve real-world and mathematical problems by writing and solving equations of the form x + a = b and ax = b for cases in which a, b and x are all non-negative rational numbers.
Standard 6.EE.8
Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have
infinitely many solutions; represent solutions of such inequalities on number line diagrams.
Standard 6.EE.9
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in
terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the
equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between
distance and time.
Strand: GEOMETRY (6.G)
Solve real-world and mathematical problems involving area, surface area, and volume (Standards 6.G.1-4).
Standard 6.G.1
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the
context of solving real-world and mathematical problems.
Standard 6.G.2
Find the volume of a right rectangular prism with appropriate unit fraction edge lengths by packing it with cubes of the appropriate unit fraction edge lengths (for example, 3½ x 2 x 6), and show
that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = kWh and V = bh to find volumes of right rectangular prisms with fractional edge
lengths in the context of solving real-world and mathematical problems. (Note: Model the packing using drawings and diagrams.)
Standard 6.G.3
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate.
Apply these techniques in the context of solving real-world and mathematical problems.
Standard 6.G.4
Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving
real-world and mathematical problems.
Strand: STATISTICS AND PROBABILITY (6.SP)
Develop understanding of statistical variability of data (Standards 6.SP.1-3). Summarize and describe distributions (Standards 6.SP.4-5).
Standard 6.SP.1
Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical
question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.
Standard 6.SP.2
Understand that a set of data collected to answer a statistical question has a distribution that can be described by its center, spread/range and overall shape.
Standard 6.SP.3
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
Standard 6.SP.4
Display numerical data in plots on a number line, including dot plots, histograms, and box plots. Choose the most appropriate graph/plot for the data collected.
Standard 6.SP.5
Summarize numerical data sets in relation to their context, such as by:
1. Reporting the number of observations.
2. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
3. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking
deviations from the overall pattern with reference to the context in which the data were gathered.
4. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE). Send questions or comments to USBE Specialist - Jennifer Throndsen and see
the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer Throndsen. These materials have been produced by and for the teachers of the
State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These
materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah
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Functional Analysis Topics
1. Classical Linear Spaces
2. Completeness, Linear Functionals, Linear Operators, and Compactness of the Closed Unit Ball
3. The Open Mapping Theorem, Closed Graph Theorem, Uniform Boundedness Principle, and Hahn-Banach Theorem
4. The Weak Topology and Weak* Topology
5. Inner Product Spaces
6. Normed Algebras
Submit an Error: Do you think that you see an error in any of the pages? Click the link and let us know so that we can fix it as soon as possible! All help is greatly appreciated with there being so
many possible errors that can be overlooked.
• 1. Real Analysis (3rd Edition) by Halsey Royden.
• 2. Real Analysis (4th Edition) by Halsey Royden and Patrick Fitzpatrick.
• 3. Complete Normed Algebras by Frank F. Bonsall and John Duncan.
• 4. Introduction to Tensor Products of Banach Spaces by Raymond A. Ryan.
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Stored Random Voltages
A-149-1 Quantized/Stored Random Voltages
This module features four different analog random control voltages that are generated in different ways.
• Module A-149-1 is the first module of the A-149-x range. In this group Doepfer presents by popular request several functions of Don Buchla's "Source of Uncertainty 265/266" (SOU) modules that
cannot be realized with existing A-100 modules.
The "Quantized Random Voltages" section has available 2 CV outputs: "N+1 states" and "2N states". N is an integer number in the range 1...6 that can be adjusted with the manual control (Man N)
and an external control voltage CVN with attenuator. Whenever the rising edge of the input clock signal (Clk In) appears a new random voltage is generated at the N+1 resp. 2N output. The N+1
output is capable to generate N+1 different voltage levels (or states), the 2N output up to 2N different states. If for example N is set to 4 the N+1 output generates up to 5, the 2N output 16
different states. The voltage steps of the 2N output are adjusted to 1/12 V in the factory. Consequently exact semitones can be obtained in combination with a VCO. The voltage steps of the n+1
output are adjusted to 1.0 V in the factory corresponding to octave intervals in combination with a VCO. For each output a trimming potentiometer is available on the pc board that enables the
user to select other voltage steps for the output in question.
Even the "Stored Random Voltages" section has 2 stepped CV outputs available: one with even voltage distribution of the max. 256 output states and second one with adjustable voltage distribution
probability. The distribution probability is adjusted by a manual control (Man D) and an external control voltage CVD with attenuator. With the control set fully counterclockwise most of the
random voltages will be low magnitude but even medium and high magnitude voltages may appear but with smaller probability. As the control is turned to the right (or a positive control voltage
appears at the CVD input) the distribution moves through medium to high magnitude voltage probability. The symbol at the lower jack socket shows this coherence graphically.
The voltage range is 0...+5V for both outputs of the "Stored Random Voltages" section. For each output a trimming potentiometer is available on the pc board that enables the user to select
another voltage range for the output in question.
The A-149-1 can be extended by 8 random digital voltages with the A-149-2 Digital Random Voltages module.
• Technical details: If you are interested in technical details here is some information. All random voltages are derived from digital pseudo random generators that work with shift registers and
digital feedback via exor gates. The digital output voltages of the shift registers are added up with resistors to obtain variable stepped analog voltages. For the N+1 output all resistors have
the same value, the 2N output uses resistors in ratios of 1:2:4:8:16:32. Consequently the N+1 output has less different states available than the 2N output. In addition the digital shift register
outputs are gated dependent on the current N voltage (sum of manual control + external CV) by which the number of possible states can be reduced. In contrast to the A-117 the shift registers are
not clocked by an internal oscillator but by the external clock input Clk In. The generation of the "Stored Random Voltages" is similar but with different resistor values and more shift register
outputs. In addition the random voltage is processed by a non-linear clipping unit with adjustable offset that allows to modify the distribution probability of the voltage levels appearing at the
lower output. Even though the module is intended to generate slowly varying control voltages clock frequencies up to moderate audio range (about 2 kHz) can be processed.
User Manuals
MP3 examples for A-149-1
Audio-Dateien: A-149 01, A-149 02, A-149 03, A-149 04
Modules used:
• 1 x A-145
• 1 x A-110
• 1 x A-122 (oder anderer Filter / or any other filter)
• 1 x A-149
• A-149-1 QRV1 -> Frequency A-110
• A-149-1 QRV2 -> Frequency A-122
• A-145 Rectangle Out -> A-149-1 QRV Clock In
• A-145 Triangle Out -> Pulsewidth A-110
• A-110 Rectangle Out -> A-122 Audio In
• A-122 Audio Out = MP3 Audio
Audio A-149_05
Modules used:
• 1 x A-145
• 1 x A-110
• 1 x A-122 (or any other filter)
• 1 x A-149
• 1 x A-140
• A-149-1 QRV1 -> Frequency A-110
• A-149-1 QRV2 -> Frequency A-122 (1)
• A-145 Rectangle Out -> A-149-1 QRV Clock In + A-140 Gate In
• A-145 Triangle Out -> Pulsewidth A-110
• A-140 ADSR Out -> Frequency A-122 (2)
• A-110 Rectangle Out -> A-122 Audio In
• A-122 Audio Out = MP3 Audio
Audio A-149_06
Modules used:
• 1 x A-145
• 1 x A-110
• 1 x A-149
• A-145 Sine Out -> A-149-1 QRV Clock In
• A-145 Saw Out -> A-149-1 CV N In
• A-145 Rectangle Out -> A-110 Sync In
• A-149-1 QRV1 -> Pulsewidth A-110
• A-149-1 QRV2 -> Frequency A-110
• A-145 Sine Out -> A-149-1 QRV Clock In
• A-145 Triangle Out -> Pulsewidth A-110
• A-140 ADSR Out -> Frequency A-122 (2)
• A-110 Rectangle Out -> A-122 Audio In
• A-122 Audio Out = MP3 Audio
Audio A-149_07
In A-149_07.mp3 and A-149_08.mp3, the VCO output is also routed through an A-122 whose filter frequency and resonance are controlled by an A-140. In this case too, the VCO Sync input simulates an
early reflection. As in the other examples, the A-149's ADSR trigger and clock come from the A-145 LFO.
No additional effects used !
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Stock-Sales Strategy in a Simplified Market
Stock-Sales Strategy in a Simplified Market#
This example finds a stock-selling strategy for a simplified market model to demonstrate using a Leap hybrid CQM solver on a constrained problem with integer and binary variables.
In this very simple market, you have some number of shares that you want to sell in daily blocks over a defined interval of days. Each sale of shares affects the market price of the stock,
\[p_i = p_{i-1} + \alpha s_{i-1},\]
where \(p_i\) and \(s_i\) are, respectively, the price and the number of shares sold on day \(i\), and \(\alpha\) is some multiplier.
The goal of this problem is to find the optimal number of shares to sell per day to maximize revenue from the total sales.
The Market with Taxation section adds a tax to the market model to demonstrate the incorporation of binary variables into the CQM.
Example Requirements#
The code in this example requires that your development environment have Ocean software and be configured to access SAPI, as described in the Initial Set Up section.
Formulate the Problem#
First, define the market parameters.
• max_days is the period over which you should sell all your shares.
• total_shares is the number of shares you own (equal to \(\sum_i s_i\)).
• price_day_0 is the stock price on the first day of the period.
• alpha is a multiplier, \(\alpha\), that controls how much the stock price increases for each share sold into the market.
>>> max_days = 10
>>> total_shares = 100
>>> price_day_0 = 50
>>> alpha = 1
Instantiate a CQM.
>>> from dimod import ConstrainedQuadraticModel
>>> cqm = ConstrainedQuadraticModel()
You can now formulate an objective function to optimize and constraints any feasible solution must meet, and set these in your CQM.
Objective Function#
The objective function to maximize is the revenue from selling shares. Because you own an integer number of shares, it is convenient to use integer variables to indicate the number of shares sold
each day, shares. For simplicity, this model assumes stock prices, price, are also integers[1].
Bounds on the range of values for integer variables shrink the solution space the solver must search, so it is helpful to set such bounds; for many problems, you can find bounds from your knowledge
of the problem. In this case,
• On any day, you cannot sell more than the total number of shares you start with.
• The maximum share price is the sum of the initial price and the total price increase that would result from selling all your shares,
\[\max(p) = p_0 + \alpha * \sum_i s_i.\]
>>> from dimod import Integer
>>> max_p = price_day_0 + alpha*total_shares
>>> shares = [Integer(f's_{i}', upper_bound=total_shares) for i in range(max_days)]
>>> price = [Integer(f'p_{i}', upper_bound=max_p) for i in range(max_days)]
Daily revenue is the number of shares sold multiplied by the price on each sales day.
>>> revenue = [s*p for s, p in zip(shares, price)]
To maximize the total revenue, \(\sum_i s_ip_i\), is to minimize the negative of that same revenue:
>>> cqm.set_objective(-sum(revenue))
As noted in the Bin Packing example, keep in mind that these “variables” are actually class dimod.QuadraticModel objects,
>>> price[0]
QuadraticModel({'p_0': 1.0}, {}, 0.0, {'p_0': 'INTEGER'}, dtype='float64')
with a single variable with the requested label, p_0 or s_0. This means, for example, that multiplying these models to create a revenue[0] “variable” actually creates a new quadratic model,
>>> revenue[0]
QuadraticModel({'s_0': 0.0, 'p_0': 0.0},
... {('p_0', 's_0'): 1.0},
... 0.0,
... {'s_0': 'INTEGER', 'p_0': 'INTEGER'}, dtype='float64')
with a quadratic bias between p_0 and s_0.
The simplified market in this problem has the following constraints:
1. In total you can sell only the number of shares you own, no more, \(\sum_i s_i \le\) total_shares.
>>> cqm.add_constraint(sum(shares) <= total_shares, label='Sell only shares you own')
'Sell only shares you own'
2. On the first day of the selling period, the stock has a particular price \(p_0 =\) price_day_0.
>>> cqm.add_constraint(price[0] == price_day_0, label='Initial share price')
'Initial share price'
3. The stock price increases in proportion to the number of shares sold the previous day:
\(p_i = p_{i-1} + \alpha s_{i-1}\).
>>> for i in range(1, max_days):
... pricing = cqm.add_constraint(price[i] - price[i-1] - alpha*shares[i-1] == 0, label=f'Sell at the price on day {i}')
For a sales period of ten days, this CQM has altogether 11 constraints:
>>> len(cqm.constraints)
Solve the Problem by Sampling#
Instantiate a LeapHybridCQMSampler class sampler,
>>> from dwave.system import LeapHybridCQMSampler
>>> sampler = LeapHybridCQMSampler()
and submit the CQM to the selected[2] solver.
For one particular execution, with a maximum allowed runtime of a minute, the CQM hybrid solver returned 41 samples, out of which 24 were solutions that met all the constraints:
>>> sampleset = sampler.sample_cqm(cqm,
... time_limit=60,
... label="SDK Examples - Stock-Selling Strategy")
>>> print("{} feasible solutions of {}.".format(
... sampleset.record.is_feasible.sum(), len(sampleset)))
24 feasible solutions of 41.
The small function below extracts from the returned sampleset the best feasible solution and parses it.
>>> def parse_best(sampleset):
... best = sampleset.filter(lambda row: row.is_feasible).first
... s = [val for key, val in best.sample.items() if "s_" in key]
... p = [val for key, val in best.sample.items() if "p_" in key]
... r = [p*s for p, s in zip(p, s)]
... return r, s, best
Parse and print the best feasible solution:
>>> r, s, _ = parse_best(sampleset)
>>> print("Revenue of {} found for daily sales of: \n{}".format(sum(r), s))
Revenue of 9499.0 found for daily sales of:
[10.0, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0, 9.0, 11.0]
Market with Taxation#
The previous sections made use of only integer variables. Quadratic models also accept binary variables. This section models a market in which you pay an additional tax on early sales and uses a
binary variable to incorporate that update into the CQM created in the previous sections.
Consider a market in which you pay a tax in amount, tax_payment, for selling shares during the first taxed_period days of the period in which you can sell your shares.
>>> taxed_period = 3
>>> tax_payment = 225
Because you either pay this tax or do not pay it, you can use a binary variable, t, to indicate payment. You can update the previous objective by reducing the revenue from share sales by the tax
payment (adding it to the negative revenue) if the t binary variable is 1:
>>> from dimod import Binary
>>> t = Binary('t')
>>> cqm.set_objective(tax_payment*t - sum(revenue))
Binary variable t should be True (1) if sales in the first taxed_period days of the period are greater than zero; otherwise it should be False (0):
\[ \begin{aligned}\sum_{i < \text{taxed_period}} s_i > 0 \longrightarrow t=1\\\sum_{i < \text{taxed_period}} s_i = 0 \longrightarrow t=0\end{aligned} \]
One way to set such an indicator variable is to create a pair of linear constraints:
\[\frac{\sum_{i < \text{taxed_period}} s_i}{\sum_i s_i} \le t \le \sum_{i < \text{taxed_period}} s_i\]
To show that this pair of inequalities indeed sets the desired binary indicator, the table below shows, bolded, the binary values \(t\) must take to simultaneously meet both inequalities for \(\sum_
{i < \text{taxed_period}} s_i\) with sample values 0, 1, and 5 for the previous configured total_shares = 100.
\(\frac{\sum_{i < \text{taxed_period}} s_i}{\sum_i \(\sum_{i < \text{taxed_period}} \(\pmb{t} \(\frac{\sum_{i < \text{taxed_period}} s_i}{\sum_i s_i} \le \pmb{t} \le \sum_{i < \text
s_i}\) s_i\) \) {taxed_period}} s_i\)
0 0 \(\pmb{0} \(0 = \pmb{0} = 0\)
\(\frac{1}{100}\) 1 \(\pmb{1} \(\frac{1}{100} < \pmb{1} = 1\)
\(\frac{5}{100}\) 5 \(\pmb{1} \(\frac{5}{100} < \pmb{1} < 5\)
Add these two constraints to the previously created CQM:
>>> cqm.add_constraint(t - sum(shares[:taxed_period]) <= 0, label="Tax part 1")
'Tax part 1'
>>> cqm.add_constraint(1/total_shares*sum(shares[:taxed_period]) - t <= 0, label="Tax part 2")
'Tax part 2'
Submit the CQM to the selected solver. For one particular execution, with a maximum allowed runtime of a minute, the CQM hybrid sampler returned 50 samples, out of which 33 were solutions that met
all the constraints:
>>> sampleset = sampler.sample_cqm(cqm,
... time_limit=60,
... label="SDK Examples - Stock-Selling Strategy")
>>> print("{} feasible solutions of {}.".format(
... sampleset.record.is_feasible.sum(), len(sampleset)))
33 feasible solutions of 50.
Parse and print the best feasible solution:
>>> r, s, best = parse_best(sampleset)
>>> income = sum(r) - best.sample['t']*tax_payment
>>> print("Post-tax income of {} found for daily sales of: \n{}".format(income, s))
Post-tax income of 9283.0 found for daily sales of:
[0.0, 0.0, 0.0, 13.0, 14.0, 14.0, 14.0, 16.0, 15.0, 14.0]
Notice that the existence of this tax, though avoided in the sales strategy found above, has reduced your income by a little less than the tax fee (the maximum income if you had paid the tax would be
9275). If the tax is slightly reduced, it is more profitable to sell during the taxation period and pay the tax:
>>> tax_payment = 220
>>> cqm.set_objective(tax_payment*t - sum(revenue))
>>> sampleset = sampler.sample_cqm(cqm,
... time_limit=60,
... label="SDK Examples - Stock-Selling Strategy")
>>> r, s, best = parse_best(sampleset)
>>> income = sum(r) - best.sample['t']*tax_payment
>>> print("Post-tax income of {} found for daily sales of: \n{}".format(income, s))
Post-tax income of 9276.0 found for daily sales of:
[10.0, 10.0, 10.0, 11.0, 9.0, 10.0, 12.0, 9.0, 10.0, 9.0]
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Interactive Mathematics
What is Interactive Mathematics?
Interactive Mathematics is an AI-based, interactive mathematical problem solver directed towards providing users with step-by-step solutions for a variety of homework math problems. It offers
reliable solutions by integrating a powerful computational mathematical engine with an artificial intelligence language model. This new tool is capable of handling many different mathematical
challenges, from complicated word problems and algebra equations to advanced calculus, in a heartbeat.
Additionally, this web-based version provides a chat modality for math tutoring where one could forward their math problems and get individually tailored solutions. It has free math lessons whereby
the student can enhance their mathematical ability. In addition to this, it is capable of reading math word problems and identifying what mathematical operation that has to be solved in order to
solve such a problem.
Key Features & Benefits of Interactive Mathematics
Listed below are a few of the numerous attributes that make Interactive Mathematics one of the richest materials for students and teachers alike:
• Solve Math Homework Problems: Provides step-by-step solutions for different math problems.
• Tutoring Through a Chat Platform: Provides personalized math tutoring through a chat interface.
• Interpret Math Word Problems: Capable of understanding and solving difficult math word problems.
• Determine Math Operations: Identifies what math operations should be performed to solve particular math problems.
• Provide Free Math Lessons: It contains free lessons that give the user more information on how to do math better.
Benefits for using Interactive Mathematics are numerous. It makes it easy to solve math problems, provides the user with private tutors, and also equips one with education materials, thus an
all-round tool in enhancing one’s mathematical abilities.
Use Cases and Applications of the Interactive Mathematics
Now, Interactive Mathematics can be used in a number of ways for the exploration of mathematical concepts to achieve better results. The following are only a few examples:
• Learning How to Solve Math Problems: An individual will be able to learn how to go about solving different types of math problems.
• Practice Problems and Improvement in Skills: Practice by individuals in solving problems will bring improvement in mathematical skills.
• Interactive Learning: The AI tutor makes the process of learning mathematics more interactive and hence more interesting and understandable.
The various clusters of users who can derive value from Interactive Mathematics include high school, college students, math tutors, teachers, and lifelong learning for people who want to remain sharp
in this area of learning.
How to Use Interactive Mathematics
Interactive Mathematics is easy and user-friendly. Below find steps on how one can use the facility:
1. Open an Account: Open an account on the Interactive Mathematics platform.
2. Pose Your Problem: At the end of the chat, provide the math problem on which you would like to be helped.
3. Get a Solution: It will work out your problem. You will receive a detailed step-by-step solution.
4. Video Lessons: Enjoy the best online math lessons for free to make you perform better from the site.
Get the best out of the experience. Ensure you are clearly communicating your problem and consequently giving any information needed to solve the problem. The user interface is an aspect that was put
into great consideration. It is easy to make your way into the features and resources that you might want to refer to from time to time.
How Interactive Mathematics works
Interactive Mathematics is a sophisticated blend between a mathematical computational engine and an AI language model. The computational engine drives the mathematical calculations with the AI model
in order that user input is understood, and explanations are given in a natural language.
Upon receiving the mathematical problem from a user, the system will break it down and determine what kind of problem it is, what operations need to be done, calculate the solution step-by-step, and
finally such that the user understands, it will come up with an explanation. There are some of the pros and probable drawbacks of Interactive Mathematics.
• Detailed Solution: To almost all sorts of mathematical problems, it provides a detailed and accurate solution.
• Personalised Tutoring: Offers one to one tutoring through a chat platform.
• Free Learning Resources: Free lessons offered to assist one in enhancing skills.
• Dependence Risk: There is a risk where users rely on the tool for Math problems solutions.
• Complex Problem Limitations: For very complex problems, a requirement of human interaction might be necessary for the best solutions.
In general, user feedback comments on the effectiveness of the tool and describes it as easy to use; however, others say that technology should be used with a balance of traditional learning methods.
Interactive Mathematics FAQs
What math problems can Interactive Mathematics work for?
Interactive Mathematics will work for Algebra, Calculus, and the complex word problems.
Is there a free version of Interactive Mathematics?
Yes, there is but provides basic features and lessons.
How does interactive math work with chat tutoring?
You can post any math problem on the chat support, and the AI provides a solution with personalized step-by-step approaches.
Can Interactive Mathematics be a Substitute for a Tutor?
Though it provides amazing support and resources, it is essentially a secondary tool and can be used in conjunction with traditional methods.
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Math 10 – Dec 13: Review Package #1
Some tidy up work with Calipers – Check out this site if you’d like more practice: Vernier Calipers
Review Booklet– Ch 3-9: This booklet is the BASICS from each unit… use it as a guide to help you focus your preparations for the final. Be sure to check your answersand get help for the sections you
have difficulty with.
Chapter 1 Test – THURSDAY DECEMBER 19
This entry was posted in Math 10 - Foundations and Pre-Calculus, Uncategorized. Bookmark the permalink.
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How do you find the evolute of a parabola?
How do you find the evolute of a parabola?
Alternatively an evolute can be seen as the envelope of the normals drawn from the points of the starting curve. In the case of a parabola its evolute is a semi-cubical parabola, an interesting curve
that also has the property of being isochrone. The involute of a curve is more difficult to understand and visualize.
How do you find the directrix of a parabola?
The standard form is (x – h)2 = 4p (y – k), where the focus is (h, k + p) and the directrix is y = k – p. If the parabola is rotated so that its vertex is (h,k) and its axis of symmetry is parallel
to the x-axis, it has an equation of (y – k)2 = 4p (x – h), where the focus is (h + p, k) and the directrix is x = h – p.
How is evolute calculated?
Consequently, the evolute of the ellipse is described by the following parametric equations: ξ=a2−b2acos3t=(a−b2a)cos3t,η=b2−a2bsin3t=(b−a2b)sin3t.
How do you find the focus of a parabola?
In order to find the focus of a parabola, you must know that the equation of a parabola in a vertex form is y=a(x−h)2+k where a represents the slope of the equation. From the formula, we can see that
the coordinates for the focus of the parabola is (h, k+1/4a).
What is the evolute of a parabola called?
Explanation: The evolute of parabola is called semicubical parabola. It is defined parametrically as.
What is the formula of radius of curvature?
Radius of Curvature Formula R= 1/K, where R is the radius of curvature and K is the curvature.
What is the standard form of a parabola?
The standard form of a parabola is (x – h)2 = a(y – k) or (y – k)2 = a(x – h), where (h, k) is the vertex. The methods used here to rewrite the equation of a parabola into its standard form also
apply when rewriting equations of circles, ellipses, and hyperbolas.
How do you find the standard form of a parabola?
The parabola equation in vertex form The standard form of a quadratic equation is y = ax² + bx + c . You can use this vertex calculator to transform that equation into the vertex form, which allows
you to find the important points of the parabola – its vertex and focus.
What is called radius of curvature?
In differential geometry, the radius of curvature, R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For
surfaces, the radius of curvature is the radius of a circle that best fits a normal section or combinations thereof.
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The Geomblog
Hal Daumé wrote a rather provocative post titled ‘
Machine Learning is the new algorithms
’, and has begged someone to throw his gauntlet back at him. Consider it now thrown !
His thesis is the following quote:
Everything that algorithms was to computer science 15 years ago, machine learning is today
And among the conclusions he draws is the following:
we should yank algorithms out as an UG requirement and replace it with machine learning
Having spent many years having coffees and writing papers with Hal, I know that he truly does understand algorithms and isn’t just trying to be a troll (at least I hope not). So I’m trying to figure
out exactly what he’s trying to say. It will help if you read his article first before returning…
First off, I don’t understand the conclusion. Why not (say) replace architecture with ML, or databases with ML. Or why replace anything at all ? the assumption is that ML is a core tool that students
will need more than any other topic. Now I have no problem with adding ML to the list of “things a CS person ought to know”, but I don’t see why it’s not important for a CS person to understand how a
database works, or how a compiler processes code, or even how we design an algorithm. This fake mutual exclusiveness appears to be without basis.
But maybe he’s saying that algorithms and ML are two flavors of the same object, and hence one can be replaced by the other. If so, what exactly is that object ? In his view, that object is:
given an input, what’s the best way to produce an (optimal) output ?
This seems to be an overly charitable view of ML. In ML, the goal is to, well, learn. Or to be more stodgy about it, ML provides tools for making systematic inferences and predictions from data.
Which suggests that the concerns are fundamentally orthogonal, not in opposition (and Sasho Nikolov makes this point very well
in a comment on Hal’s post
). As Hal correctly argues, the hard work in ML is front-loaded: modeling, feature extraction, and the like. The algorithm itself is mostly an afterthought.
But what’s ironic is that one of the most important trends in ML of late is the conversion of an ML problem to an optimization problem. The goal is to make good modeling choices that lead to an
optimization problem that can be solved well. But wait: what do you need to know how to solve an optimization ? Wait for it…… ALGORITHMS !!
The argument about stability in algorithms is an odd one, especially coming from someone who’s just written a book on ML. Yes, some core algorithms techniques haven’t changed much in the last many
years, but did you see that 2014 paper on improvements in recurrence analysis ? Or the new sorting algorithm by Mike Goodrich ? or even the flurry of new results for Hal’s beloved flow problems ?
As for “everything’s in a library”, I’ll take your boost graph library and give you back WEKA, or libSVM, or even scikit-learn. I don’t need to know anything from Hal’s book to do some basic futzing
around in ML using libraries: much like I could invoke some standard hashing subroutine without knowing much about universal hash families.
In one sense though, Hal is right: ML is indeed where algorithms was 15 years ago. Because 15 years ago (approximately) is when the streaming revolution started, and with it the new interest in sub
linear algorithms, communication complexity, matrix approximations, distributed algorithms with minimal communication, and the whole “theory of big data” effort. And ML is now trying to catch up to
all of this, with some help with from algorithms folks :).
What is true is this though: it wouldn’t hurt us to revisit how we construct the core algorithms classes (undergrad and grad). I realize that CLRS is the canon, and it would cause serious heart
palpitations to contemplate not stuffing every piece of paper of that book down students’ throats, but maybe we should be adapting algorithms courses to the new and exciting developments in
algorithms itself. I bring in heavy doses of approximation and randomization in my grad algorithms class, and before we forked off a whole new class, I used to teach bits of streaming, bloom filters,
min-wise hashing and the like as well. My geometry class used to be all about the core concepts from the 3 Marks book, but now I throw in lots of high dimensional geometry, approximate geometry,
kernels and the like.
Ultimately, I think a claim of fake mutual exclusivity is lazy, and ignores the true synergy between ML and algorithms. I think algorithms research has a lot to learn from ML about robust solution
design and the value of "noise-tolerance", and ML has plenty to learn from algorithms about how to organize problems and solutions, and how deep dives into the structure of a problem can yield
insights that are resilient to changes in the problem specification.
Everyone knows the master theorem.
Or at least everyone reading this blog does.
And I'm almost certain that everyone reading this blog has heard of the generalization of the master theorem due to Akra and Bazzi. It's particularly useful when you have recurrences of the form
$$ T(n) = \sum_i a_i T(n/b_i) + g(n) $$
because like the master theorem it gives you a quick way to generate the desired answer (or at least a guess that you can plug in to the recurrence to check).
(And yes, I'm aware of the generalization of A/B due to Drmota and Szpankowski)
When I started teaching grad algorithms this fall, I was convinced that I wanted to teach the Akra-Bazzi method instead of the master theorem. But I didn't, and here's why.
Let's write down the standard formulation that the master theorem applies to
$$ T(n) = a T(n/b) + f(n) $$
This recurrence represents the "battle" between the two terms involved in a recursive algorithm: the effort involved in dividing (the $a T(n/b)$) and the effort involved in putting things back
together (the $f(n)$).
And the solution mirrors this tension: we look at which term is "stronger" and therefore dominates the resulting running time, or what happens when they balance each other out. In fact this is
essentially how the proof works as well.
I have found this to be a useful way to make the master theorem "come alive" as it were, and allow students to see what's likely to happen in a recurrence without actually trying to solve it. And
this is very valuable, because it reinforces the point I'm constantly harping on: that the study of recurrences is a way to see how to design a recursive algorithm. That decimation as a strategy can
be seen to work just by looking at the recurrence. And so on.
But the Akra-Bazzi method, even though it's tremendously powerful, admits no such easy intuition. The bound comes from solving the equation
$$ \sum a_i b_i^p = 1 $$ for $p$, and this is a much more cryptic expression to parse. And the proof doesn't help make it any less cryptic.
Which is not to say you can't see how it works with sufficient experience. But that's the point: with sufficient experience. From a purely pedagogical perspective, I'd much rather teach the master
theorem so that students get a more intuitive feel for recurrences, and then tell them about A/B for cases (like in median finding) where the master theorem can only provide an intuitive answer and
not a rigorous one.
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Create an array of matrices in SAS
The SAS DATA step supports multidimensional arrays. However, matrices in SAS/IML are like mathematical matrices: they are always two dimensional. In simulation studies you might need to generate and
store thousands of matrices for a later statistical analysis of their properties. How can you accomplish that unless you can create an array of matrices?
A simple solution is to "flatten" each matrix into a row vector and form a big array where the ith row of the array contains the elements of the ith matrix. This storage scheme will be familiar to
programmers who have used SAS/IML functions for generating random matrices, such as the RANDWISHART function or my program for generating random symmetric matrices.
Matrices packed into an array
For example, the following example generates 10 random 2 x 2 matrices from a Wishart distribution with 7 degrees of freedom.
proc iml;
call randseed(1234);
DF = 7;
S = {1 1, 1 5};
X = RandWishart(1000, DF, S); /* generate 1,000 2x2 matrices */
print (X[1:10,])[label="X" colname={X11 X12 X21 X22}];
Each row of the X matrix contains the elements of a 2 x 2 matrix in row-major order. That is, the first element each the row is the (1,1)th element of the matrix, the second is the (1,2)th element,
the third is the (2,1)th element, and the fourth is the (2,2)th element.
Extracting matrices from an array
You can use the subscript operator to extract a row from the X array. For example, X[1,] contains the values of the first 2 x 2 matrix. You can use the SHAPE function to reshape each row. This might
be necessary if you want to multiply with the matrices or compute their determinant or eigenvalues. For example, the following loop iterates over the rows of the array and computes the eigenvalues of
each 2 x 2 matrix. You can use the HISTOGRAM subroutine to plot the distribution of the eigenvalues:
/* compute and store eigenvalues of the 2x2 matrices */
v = j(nrow(X), sqrt(ncol(X)), .); /* each pxp matrix has p eigenvalues */
do i = 1 to nrow(X);
A = shape(X[i,], 2); /* A is symmetric 2x2 matrix */
v[i,] = T(eigval(A)); /* find eigenvalues; transpose to row vector */
title "Distribution of Eigenvalues for 1,000 Wishart Matrices";
call histogram(v) rebin={2.5,5};
The histogram shows a mixture of two distributions. The larger eigenvalue has a mean of 37. The smaller eigenvalue has a mean of 4.5.
Packing matrices into an array
If you have many matrices that are all the same dimension, then it is easy to pack them into an array. Often your program will have a loop that creates the matrices. Within that same loop you can
flatten the matrices and pack them into an array. In the following statements, the ROWVEC function is used to convert a square covariance matrix into a row vector.
Z = j(1000, 4, .); /* allocate array for 1,000 2x2 matrices */
do i = 1 to nrow(Z);
Y = randnormal(8, {0 0}, S); /* simulate 8 obs from MVN(0,S) */
A = cov(Y); /* A is 2x2 covariance matrix */
Z[i,] = rowvec(A); /* flatten and store A in i_th row */
The examples in this article have shown how to create a one-dimensional array of matrices. The trick is to flatten the ith matrix and store it in the ith row of a large array. In a similar way, you
can build two- or three-dimensional arrays of matrices. Keeping track of which row corresponds to which matrix can be tricky, but the NDX2SUB and SUB2NDX functions can help.
For an alternative technique for working with multidimensional arrays in SAS/IML, see the excellent paper by Michael Friendly, "Multidimensional arrays in SAS/IML Software."
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We study the performance of a family of randomized parallel coordinate descent methods for minimizing the sum of a nonsmooth and separable convex functions. The problem class includes as a special
case L1-regularized L1 regression and the minimization of the exponential loss (“AdaBoost problem”). We assume the input data defining the loss function is contained … Read more
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Week 5 Financial Exercises - Credence Writers
Week Five Financial Exercises
Your task is to determine the WACC for a given firm using what you know about WACC as well as data you can find through research. Your deliverable is a brief report in which you state your
determination of WACC, describe and justify how you determined the number, and provide relevant information as to the sources of your data.
Select a publicly traded company that has debt or bonds and common stock to calculate the current WACC. One good source for financial data for companies as well as data about their equity is Yahoo!
Finance. By looking around this site, you should be able to find the market capitalization (E) as well as the β for any publicly traded company.
There are not many places left where data about corporate bonds is still available. One of them is the Finra Bonds website. To find data for a particular company’s bonds, find the Quick Search
feature, then be sure to specify corporate bonds and type in the name of the issuing company. This should give you a list of all of the company’s outstanding bond issues. Clicking on the symbol for a
given bond issue will lead you to the current amount outstanding and the yield to maturity. You are interested in both. The total of all bonds outstanding is D in the above formula.
If you like, you can use the YTM on a bond issue that is not callable as the pre-tax cost of debt for the company.
As you recall, the formula for WACC is:
rWACC = (E/E+D) rE + D/(E+D) rD (1-TC)
The formula for the required return on a given equity investment is:
ri= rf + βi * (RMkt-rf)
RMkt-rf is the Market Risk Premium. For this project, you may assume the Market Risk Premium is 5% unless you can develop a better number.
rf is the risk free rate. The risk free rate is normally the yield on US Treasury securities such as a 10-year treasury. For this assignment, please use 3.5%.
You may assume a corporate tax rate of 40%.
Submit the following:
Write a 350- to 700-word report that contains the following elements:
Your calculated WACC.
How data was used to calculate WACC. This would be the formula and the formula with your values substituted.
Sources for your data.
A discussion of how much confidence you have in your answer. What were the limiting assumptions that you made, if any?
Include a Microsoft® Excel® file showing your WACC calculations discussed above.
Click the Assignment Files tab to submit your assignment.
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Bloggy Badger
It's time for another anti-tutorial! Whereas a tutorial is an advanced user giving step-by-step instructions to help newbies, an anti-tutorial is a new user describing their path to enlightenment. My
approach is usually to follow the types, so my anti-tutorials are also examples of how to do that.
Previously in the series:
Today, inspired by a question from Syncopat3d, I'll try to learn how to use Simon Marlow's Haxl library. I think Haxl is supposed to improve the performance of complicated queries which use multiple
data sources, such as databases and web services, by somehow figuring out which parts of the query should be executed in parallel and which ones should be batched together in one request. Since
Syncopat3d is looking for a way to schedule the execution of a large computation which involves running several external processes in parallel, caching the results which are used more than once, and
batching together the processes which use the same input, Haxl seemed like a good fit!
Black triangle
To understand the basics of the library, I'd like to create a black triangle, that is, a trivial program which nevertheless goes through the whole pipeline. So as a first step, I need to figure out
what the stages of Haxl's pipeline are.
Since I'm using a type-directed approach, I need some type signature from which to begin my exploration. Hunting around Haxl's hackage page for something important-looking, I find GenHaxl, "the Haxl
monad". Despite the recent complaints about the phrase "the <something> monad", finding that phrase here is quite reassuring, as it gives me a good idea of what to expect in this package: a bunch of
commands which I can string together into a computation, and some function to run that computation.
Thus, to a first approximation, the Haxl pipeline has two stages: constructing a computation, and then running it.
A trivial computation
Since GenHaxl is a monad, I already know that return 42 is a suitably trivial and valid computation, so all I need now is a function to run a GenHaxl computation.
That function is typically right after the definition of the datatype, and indeed, that's where I find runHaxl. I see that in addition to my trivial GenHaxl computation, I'll need a value of type Env
u. How do I make one?
Clicking through to the definition of Env, I see that emptyEnv can make an Env u out of a u. Since there are no constraints on u so far, I'll simply use (). I fully expect to revisit that decision
once I figure out what the type u represents in the type GenHaxl u a.
>>> myEnv <- emptyEnv ()
>>> runHaxl myEnv (return 42)
Good, we now have a base on which to build! Let's now make our computation slightly less trivial.
What's a data source?
There are a bunch of GenHaxl commands listed after runHaxl, but most of them seem to be concerned with auxiliary matters such as exceptions and caching. Except for one:
dataFetch :: (DataSource u r, Request r a) => r a -> GenHaxl u a
That seems to be our link to another stage of Haxl's pipeline: data sources. So the first stage is a data source, then we describe a computation which fetches from the data source, then finally, we
run the computation.
So, I want an r a satisfying DataSource u r. Is there something simple I could use for r? The documentation for DataSource doesn't list any instances, so I guess I'll have to define one myself. Let's
see, there is only one method to implement, fetch, and it uses both u and r. The way in which they're used should give me a hint as to what those type variables represent.
fetch :: State r
-> Flags
-> u
-> [BlockedFetch r]
-> PerformFetch
I find it surprising that neither u nor r seem to constrain the output type. In particular, u is again completely unconstrained, so I'll keep using (). The description of the u parameter, "User
environment", makes me think that indeed, I can probably get away with any concrete type of my choosing. As for r, which seems to be the interesting part here, we'll have to look at the definitions
for State and BlockedFetch to figure out what it's about.
class Typeable1 r => StateKey r Source
data State r
data BlockedFetch r
= forall a . BlockedFetch (r a) (ResultVar a)
Okay, so State r is an associated type in an otherwise-empty typeclass, so I can again pick whatever I want. BlockedFetch r is much more interesting: it has an existential type a, which ties the r a
to its ResultVar a. The documentation for BlockedFetch explains this link very clearly: r a is a request with result a, whose result must be placed inside the ResultVar a. This explains why r wasn't
constraining fetch's output type: this ResultVar is the Haskell equivalent of an output parameter. So instead of being a pure function returning something related to r, this fetch method must be an
imperative computation which fills in its output parameters before returning to the caller. The type of fetch's return type, PerformFetch, is probably some monad which has commands for filling in
data PerformFetch = SyncFetch (IO ()) | ...
At least in the simple case, PerformFetch is a simple wrapper around IO (), so I guess ResultVar must be a simple wrapper around MVar or IORef.
A trivial data source
Anyway, we now have a clear idea of what r a is: a request whose result has type a. Let's create a simple data source, Deep Thought, which only knows how to answer a single request.
data DeepThought a where
AnswerToLifeTheUniverseAndEverything :: DeepThought Int
I'm using a GADT so that each request can specify the type of its answer. For example, I could easily add a request whose answer is a string instead of a number:
data DeepThought a where
AnswerToLifeTheUniverseAndEverything :: DeepThought Int
QuestionOfLifeTheUniverseAndEverything :: DeepThought String
But of course, Deep Thought isn't powerful enough to answer that request.
We also know that fullfilling a request isn't done by returning an answer, but by assigning the answer to a ResultVar.
runDeepThought :: DeepThought a -> ResultVar a -> IO ()
runDeepThought AnswerToLifeTheUniverseAndEverything var
= putSuccess var 42
Alright, let's try to make DeepThought an official data source by implementing the DataSource typeclass:
instance DataSource () DeepThought where
fetch _ _ _ reqs = SyncFetch $
forM_ reqs $ \(BlockedFetch req var) ->
runDeepThought req var
There's also a bunch of other easy typeclasses to implement, see the next source link for details.
A trivial state
I now have everything I need for my dataFetch to compile...
>>> runHaxl myEnv (dataFetch AnswerToLifeTheUniverseAndEverything)
*** DataSourceError "data source not initialized: DeepThought"
...but the execution fails at runtime. Now that I think about it, it makes a lot of sense: even though I don't use it, fetch receives a value of type State DeepThought, but since this is a custom
type and I haven't given any of its inhabitants to anything, there is no way for Haxl to conjure one up from thin air. There must be a way to initialize the state somehow.
I must say that I'm a bit disappointed by how imperative Haxl's API has been so far. Whether we're assigning values to result variables or initializing a state, correctness requires us to perform
actions which aren't required by the types and thus can't be caught until runtime. This is unusual for a Haskell library, and if the rest of the API is like this, I'm afraid following the types won't
be a very useful exploration technique.
Anyway, I couldn't find any function with "init" in the name, but by looking for occurences of State in the types, I figured out how to perform the initialization: via the environment u which I had
left empty until now.
instance StateKey DeepThought where
data State DeepThought = NoState
initialState :: StateStore
initialState = stateSet NoState stateEmpty
>>> myEnv <- initEnv initialState ()
>>> runHaxl myEnv (dataFetch AnswerToLifeTheUniverseAndEverything)
It worked! We have a trivial data source, we have a trivial expression which queries it, we can run our expression, and we obtain the right answer. That's our black triangle!
Multiple data sources, multiple requests
Next, I'd like to try a slightly more complicated computation. Syncopat3d gives the following example:
F_0(x, y, z) = E(F_1(x, y), F_2(y, z))
Here we clearly have two different data sources, E and F. Syncopat3d insists that E is computed by an external program, which is certainly possible since our data sources can run any IO code, but I
don't think this implementation detail is particularly relevant to our exploration of Haxl, so I'll create two more trivial data sources.
data E a where
E :: String -> String -> E String
deriving Typeable
data F a where
F_1 :: String -> String -> F String
F_2 :: String -> String -> F String
deriving Typeable
runE :: E a -> ResultVar a -> IO ()
runE (E x y) var = putSuccess var (printf "E(%s,%s)" x y)
runF :: F a -> ResultVar a -> IO ()
runF (F_1 x y) var = putSuccess var (printf "F_1(%s,%s)" x y)
runF (F_2 x y) var = putSuccess var (printf "F_2(%s,%s)" x y)
Since GenHaxl is a monad, assembling those three requests should be quite straightforward...
>>> runHaxl myEnv $ do
... f1 <- dataFetch (F_1 "x" "y")
... f2 <- dataFetch (F_2 "y" "z")
... dataFetch (E f1 f2)
...but if I add a bit of tracing to my DataSource instances, I see that this computation is performed in three phases: F_1, F_2, then E.
>>> runHaxl myEnv ...
Computing ["F_1(x,y)"]
Computing ["F_2(y,z)"]
Computing ["E(F_1(x,y),F_2(y,z))"]
This is not the trace I was hoping to see. Since fetch is receiving a list of request/var pairs, I expected Haxl to send me multiple requests at once, in case my data source knows how to exploit
commonalities in the requests. But it doesn't look like Haxl figured out that the F_1 and F_2 requests could be performed at the same time.
It turns out that this is a well-known problem with Haxl's monadic interface. I remember about it now, it was described in a presentation about Haxl (slide 45) when it came out. The solution is to
use the Applicative syntax to group the parts which are independent of each other:
>>> runHaxl myEnv $ do
... (f1,f2) <- liftA2 (,) (dataFetch (F_1 "x" "y"))
... (dataFetch (F_2 "y" "z"))
... dataFetch (E f1 f2)
Computing ["F_2(y,z)","F_1(x,y)"]
Computing ["E(F_1(x,y),F_2(y,z))"]
Good, the F_1 and F_2 requests are now being performed together.
I don't like the way in which we have to write our computations. Consider a slightly more complicated example:
E(F_1(x,y), F_2(y,z)),
E(F_1(x',y'), F_2(y',z'))
Since the four F_1 and F_2 requests at the leaves are all independent, it would make sense for Haxl to batch them all together. But in order to obtain this behaviour, I have to list their four
subcomputations together.
>>> runHaxl myEnv $ do
... (f1,f2,f1',f2') <- (,,,) <$> (dataFetch (F_1 "x" "y"))
... <*> (dataFetch (F_2 "y" "z"))
... <*> (dataFetch (F_1 "x'" "y'"))
... <*> (dataFetch (F_2 "y'" "z'"))
... (e1,e2) <- (,) <$> (dataFetch (E f1 f2))
... <*> (dataFetch (E f1' f2'))
... dataFetch (E e1 e2)
Computing ["F_2(y',z')","F_1(x',y')","F_2(y,z)","F_1(x,y)"]
Computing ["E(F_1(x',y'),F_2(y',z'))","E(F_1(x,y),F_2(y,z))"]
Computing ["E(E(F_1(x,y),F_2(y,z)),E(F_1(x',y'),F_2(y',z')))"]
I feel like I'm doing the compiler's job, manually converting from the nested calls I want to write to the leaves-to-root, layered style I have to write if I want batching to work.
So I stopped working on my anti-tutorial and wrote a toy library which converts from one style to the other :)
...and when I came back here to show it off, I discovered that GenHaxl already behaved exactly like my library did! You just have to know how to define your intermediate functions:
f_1 :: GenHaxl () String -> GenHaxl () String -> GenHaxl () String
f_1 x y = join (dataFetch <$> (F_1 <$> x <*> y))
f_2 :: GenHaxl () String -> GenHaxl () String -> GenHaxl () String
f_2 x y = join (dataFetch <$> (F_2 <$> x <*> y))
e :: GenHaxl () String -> GenHaxl () String -> GenHaxl () String
e x y = join (dataFetch <$> (E <$> x <*> y))
And with those, we can now describe the computation as nested function calls, as desired.
>>> x = pure "x"
>>> y = pure "y"
>>> z = pure "z"
>>> x' = pure "x'"
>>> y' = pure "y'"
>>> z' = pure "z'"
>>> runHaxl myEnv $ e (e (f_1 x y) (f_2 y z))
... (e (f_1 x' y') (f_2 y' z'))
Computing ["F_2(y',z')","F_1(x',y')","F_2(y,z)","F_1(x,y)"]
Computing ["E(F_1(x',y'),F_2(y',z'))","E(F_1(x,y),F_2(y,z))"]
Computing ["E(E(F_1(x,y),F_2(y,z)),E(F_1(x',y'),F_2(y',z')))"]
I now understand Haxl's purpose much better. With the appropriate intermediate functions, Haxl allows us to describe a computation very concisely, as nested function calls. Haxl executes this
computation one layer at a time: all of the leaves, then all the requests which only depend on the leaves, and so on. Within a single layer, the requests are subdivided again, this time according to
their respective data sources. Finally, for a given data source, it is fetch's responsibility to find and exploit opportunities for reusing work across the different requests belonging to the same
batch. There are also some features related to caching and parallelism which I didn't explore.
I also understand Haxl's implementation much better, having reimplemented part of it myself. In fact, I'd be interested in writing a follow-up post named "Homemade Haxl", in the same vein as my "
Homemade FRP" series. What do you think? Are you more interested in watching me learn some new libraries, watching me reimplement libraries, or watching me implement new stuff? I'll be doing all
three anyway, I just want to know which of those activities I should blog about :)
Really, your feedback would be greatly appreciated, as the only reason I started this anti-tutorial series in the first place is that my first write-up on understanding Pipes was so surprisingly
popular. I've streamlined the format a lot since that first post, and I want to make sure I haven't lost any of the magic in the process!
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A block weighing 15 kg is on a plane with an incline of pi/3 and friction coefficient of 1/10. How much force, if any, is necessary to keep the block from sliding down? | HIX Tutor
A block weighing #15 kg# is on a plane with an incline of #pi/3# and friction coefficient of #1/10#. How much force, if any, is necessary to keep the block from sliding down?
Answer 1
$F = 120$$\text{N}$ up the incline.
I'll assume that $\frac{1}{10}$ is the coefficient of static friction.
We're asked to find if any force is required (and if there is, what is it) to keep the block stationary and prevent it from sliding down.
We have our relationship for the friction force ${f}_{s}$, the coefficient of static friction ${\mu}_{s}$, and normal force $n$:
${f}_{s} \le {\mu}_{s} n$
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Answer 2
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Answer 3
To keep the block from sliding down the incline, a force equal to or greater than the force of friction needs to be applied. The force of friction can be calculated using the formula:
( F_{friction} = \mu \cdot N )
where ( \mu ) is the coefficient of friction and ( N ) is the normal force. The normal force can be calculated as:
( N = mg \cdot \cos(\theta) )
where ( m ) is the mass of the block, ( g ) is the acceleration due to gravity, and ( \theta ) is the angle of the incline.
Substituting the given values:
( N = (15 kg) \cdot (9.8 m/s^2) \cdot \cos(\pi/3) )
( N = 15 kg \cdot 9.8 m/s^2 \cdot 0.5 )
( N = 73.5 N )
Now, substituting the value of ( N ) into the formula for friction:
( F_{friction} = (1/10) \cdot 73.5 N )
( F_{friction} = 7.35 N )
Therefore, a force of at least ( 7.35 , \text{N} ) is necessary to keep the block from sliding down the incline.
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Answer from HIX Tutor
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
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[Solved] Victoria Hills Preschool purchases a cons | SolutionInn
Victoria Hills Preschool purchases a consistent amount of milk and orange juice every week. After price increases
Victoria Hills Preschool purchases a consistent amount of milk and orange juice every week. After price increases from $1.50 to $1.60 per litre of milk and from $1.30 to $1.39 per can of frozen
orange juice, the weekly bill rose from $57 to $60.85. How many litres of milk and cans of orange juice are purchased everg week?
Fantastic news! We've Found the answer you've been seeking!
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Courses - Education - Jönköping University
Contribute to XiongFeiTan/Fem-program-using-MATLAB development by creating an account on GitHub. % This is a simple 1D FEM program. The FEM % solution is based on linear elements also called hat
functions.The % problem addressed is the extension of a bar under the action of applied % forces. Use mesh parameters under the heading mesh of this code to change % values. For example change the
number of nodes to 2 to really see the % difference between the exact and the FEM solution.
2019-03-03 · Learn how to perform 3D Finite Element Analysis (FEA) in MATLAB. This can help you to perform high fidelity modeling for applications such as structural mechanics, electrostatics,
magnetostatics, conduction, heat transfer, and diffusion. the remainder of the book. A deeper study of MATLAB can be obtained from many MATLAB books and the very useful help of MATLAB. 1.2 Matrices
Matrices are the fundamental object of MATLAB and are particularly important in this book.
Why Matlab is awesome for FEM development. It's fast, too.
Interval Finite Element Method with MATLAB - Sukanta Nayak
Testkörning och jämförelse med kommersiella FE-program Förutom kunskap i hållfasthet och FEM så bör du som söker ha goda kunskaper i Matlab. Kunskap Jag började inte använda hörapparat förrän för
ungefär fem år sedan.
CALFEM Byggnadsmekanik
2018-04-10 · This program solves the 2D truss problems using Finite Element Method (FEM). Although the Trefftz finite element method (FEM) has become a powerful computational tool in the analysis of
plane elasticity, thin and thick plate bending, Poisson’s equation, heat conduction, and piezoelectric materials, there are few books that offer a comprehensive computer programming treatment of the
subject. Collecting results scattered in the literature, MATLAB® and C Programming 2019-05-03 · FENICS_TO_FEM, examples which illustrate how a mesh or scalar function computed by the FENICS program
can be written to FEM files, which can then be used to create images, or as input to meshing programs or other analysis tools.
Preprocessing section 2. Processing section 3. Post-processing section PROGRAMMING OF FINITE ELEMENT METHODS IN MATLAB LONG CHEN We shall discuss how to implement the linear finite element method for
solving the Pois-son equation. We begin with the data structure to represent the triangulation and boundary conditions, introduce the sparse matrix, and then discuss the assembling process. Since we
2017-03-01 Building a finite element program in MATLAB Linear elements in 1d and 2d D. Peschka TU Berlin Supplemental material for the course “Numerische Mathematik 2 f¨ur Ingenieure” at the Technical
University Berlin, WS 2013/2014 D. Peschka (TU Berlin) FEM with MATLAB Num2 WS13/14 1 / 32 stored in MATLAB paths, the user can access CALFEM functions anywhere. Type ‘‘helpspring1e’’ in MATLAB
window in order to test accessibility.
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stored in MATLAB paths, the user can access CALFEM functions anywhere. Type ‘‘helpspring1e’’ in MATLAB window in order to test accessibility. If the path is properly assigned, then MATLAB should
return help content of ‘‘spring1e’’ function, as shown in Figure D.1. D.1 FINITE ELEMENT ANALYSIS OF BAR AND TRUSS Three Uniaxial Bar Elements 2020-07-01 · Overview. Functions.
Most of them either use commercial software such as Comsol, or an in-house Fortran software called FCSMEK that we have. Request PDF | Learning to Program the Fem with Matlab and Gid | As for any
other numerical method, the application of the FEM is linked to the programming language and software tools chosen. 2019-05-04 · FEM2D_SAMPLE, a MATLAB code which evaluates a finite element function
of a 2D argument. The current version of the program can only handle finite element meshes which are made of piecewise linear triangles of order 3 or 6. Usage: fem2d_sample ( 'fem_prefix',
'sample_prefix') FEMtools Framework is an open program that can be naturally integrated in an existing CAE environment. Two-directional translators are available with the most popular FEA and test
database formats (NASTRAN, ANSYS, I-DEAS , ABAQUS, Universal File, and with other commercial software like MS Excel, and MATLAB. MATLAB (matrix laboratory) is a multi-paradigm numerical computing
Solna korv i butik
The function uses the time field of the structure for time-dependent models and the solution field u for nonlinear models. Download from so many Matlab finite element method codes including 1D, 2D,
3D codes, trusses, beam structures, solids, large deformations, contact algorithms and XFEM Finite element method, Matlab implementation Main program The main program is the actual nite element
solver for the Poisson problem. In general, a nite element solver includes the following typical steps: 1.De ne the problem geometry and boundary conditions, mesh genera-tion. In this example, we
download a precomputed mesh. 2018-04-10 12 Algorithms and MATLAB Codes 285 Table of Symbols and Indices 305. 6 CONTENTS xs.
It is intended as a research tool. A basic finite element program in Matlab, part 1 of 2.
Spårbar frakt schenker
Mjukvara och system - Mälardalens högskola
We begin with the data structure to represent the triangulation and boundary conditions, introduce the sparse matrix, and then discuss the assembling process. Since we stored in MATLAB paths, the
user can access CALFEM functions anywhere. Type ‘‘helpspring1e’’ in MATLAB window in order to test accessibility. If the path is properly assigned, then MATLAB should return help content of
‘‘spring1e’’ function, as shown in Figure D.1. D.1 FINITE ELEMENT ANALYSIS OF BAR AND TRUSS Three Uniaxial Bar Building a finite element program in MATLAB Linear elements in 1d and 2d D. Peschka TU
Berlin Supplemental material for the course “Numerische Mathematik 2 f¨ur Ingenieure” at the Technical University Berlin, WS 2013/2014 D. Peschka (TU Berlin) FEM with MATLAB Num2 WS13/14 1 / 32 You
can use design of experiments or optimization techniques along with FEA to perform trade-off studies or design an optimal product for specific applications. You can also create a reduced order model
from the finite element simulations to incorporate it in a physical or system-level model.
Interval Finite Element Method with MATLAB: Nayak, Sukanta
The basic concepts of the finite element method (FEM). 2. How FEM is applied to solve a simple 1D partial differential equation (PDE). 3.
The problem consists of four nodes and three elements, as The input files for the 1-element and 64-element meshes are given on the website.In the preprocessing phase, the finite mesh is generated and
the working arrays IEN, ID and LM are defined. = zeros(neq); % initialize conductance matrix flags = zeros(neq,1); % array to set B.C flags e_bc = zeros(neq,1); % essential B.C array n_bc = zeros
(neq,1); % natural B.C array P = zeros(neq,1); % initialize point source vector defined at a node s = 6*ones(nen,nel); % heat source defined over the nodes 2D function fem_1D % This is a simple 1D
FEM program. The FEM % solution is based on linear elements also called hat functions.The % problem addressed is the extension of a bar under the action of applied % forces. Use mesh parameters under
the heading mesh of this code to change % values. For example change the number of nodes to 2 to really see the Problem 2:Write the generalized FEM program in Matlab to solve axial bar problems,
based on solving P3-12, the output of the program should have displacements (all nodes), stresses (all elements), unknown reactions, internal forces (all elements), and type of internal forces (all
elements). Plot the displacement of the tip node (where the force is applied) vs. number of elements and compare with the analytical solution in the plot.
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Constant Speed Propeller advice
• Hi all,
I've been flying the Warrior since its release but I also own the Arrow III. So I decided I wanted to spend some time with it as well, but I'm not sure I'm following the correct procedures for a
constant speed propeller. I've tried looking at various forums and the operating procedures, but it seems pretty grey. So, going to tell you what I think is acceptable, and if someone(s) would be
kind enough to validate or correct me, I'd appreciate it.
For takeoff I have the Propeller full forward (full RPM's?) and the Manifold Pressure at 100% as well. As I climb out, I keep both at 100% but lean the engine for power, until I reach my cruise
altitude, for this purpose, 8000'. Once at altitude I set 2500 RPM (best power setting?) and at 8000' the charts say to run full Manifold Pressure for 75% power, then lean to EGT +100 degrees F.
Is all this an accurate use of a constant speed propeller? I'd really appreciate any feedback, positive or negative.
• Hi!
You should consult the flight manual for precise settings. In general, you don't do anything terribly wrong, but 2500 rpm in cruise should be pretty loud and inefficient. Normally, you do the
Takeoff: all full forward;
Climb: full throttle, prop 2400-2500 rpm (or full forward), mixture rich and leaning from 3000 ft up;
Cruise: use cruise charts from FM/POH: throttle in green, RPM in green, mixture for best power/flow;
Landing: prop/mixture forward.
You increase power prop first then throttle, you decrease throttle first then prop.
• @walterbeech Hi!
Thanks so much for the response. Yes, I am using the Performance charts to get the numbers I used, I just wanted to make sure I was applying them properly. I didn't really think about the noise
level in the cabin, that is probably why they have power settings for both 2200 and 2500 rpm. I didn't notice the noise was any louder than the Warrior, but I'll fly them back to back today, so
should be able to compare.
Thanks again!
• The following applies to normally aspirated Arrows.
According to my maintenance folks, you can run an IO-360 all day long at full throttle and RPM and still get home to tell about it.
With that said, here is what I was taught;
Careful with leaning. From memory, the engine operators manual state not to lean above 75% power. A good rule of thumb is not to lean below 5,000 ft (you can't generate more than 75% power
there.) You really don't need to lean the Arrow until you get to cruising altitude unless you are climbing above 8,000 ft MSL or so. By delaying leaning, you will keep the cylinder heads cooler.
Take off with full throttle and max rpm. If below 5,000 ft, its easy... all the levers go full forward. If above 5,000 ft, full throttle and full rpm, then lean to 100 ROP or maybe a little
I was taught (and I bet there will be differing opinions here) to reduce power to 25 squared at 900 ft AGL (to minimize the time to get to an altitude where you can safely return if you loose
power). This is subjective. If you are more comfortable attempting a return to the field upon loosing power at say 1,000 ft AGL or 1,500 ft AGL, then keep full power in until you reach that
altitude. I hold 25 squared until I reach cruising altitude (at some point you will no longer be able to get 25 inches of MP if you are climbing above 4 or 5,000 ft... in that case just use full
throttle and 2500 rpm).
At cruise altitude set MP & RPM to get desired performance. If in doubt, 24 squared works well in any Arrow. Lean for desired performance if above 5,000 ft (or if you are sure you are generating
<= 75% power)
So to sum it up, balls to the wall for takeoff, 25 squared for the climb, and 24 squared for cruise and only lean above 5K MSL. That's easy enough to remember without having to reference the POH.
• lilycrose
replied to BernieV on last edited by
@berniev Thanks! Good information as well, so 2400 RPM is less wear and tear on an engine than 2500?
• BernieV
replied to lilycrose on last edited by BernieV
@katchaplin The vibration at 2400 rpm is less annoying, especially with a 3 blade prop. I think it's more a matter of personal preference. Refer to the poh for valid combinations of RPM and
manifold pressure . The older arrows, especially to 180 horsepower iFly, generate 75% power at 24 squared.
• WalterBeech
replied to lilycrose on last edited by WalterBeech
@katchaplin said in Constant Speed Propeller advice:
so 2400 RPM is less wear and tear on an engine than 2500
Let's say, it's less load. You can think of the manifold pressure as the amount of power the engine delivers per cycle and of RPM as a multiplier, i. e. how often this power is delivered. In the
real world, vibration can be a concern, too. As has been truly noticed above, IO-360 is a rather enduring engine. So for purposes of setting power you reduce to 25/2500 or 25/2400 in climb mainly
to increase your comfort and the comfort of those on the ground around the airport. If you don't care, you can climb at full/full.
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Goat Gestation Calendar
Goat Gestation Calendar - Learn how long goats are pregnant and what. Select breeding date to show the approximate kidding day. Web our simple goat gestation calculator will help you to calculate the
due date for your pregnant doe in seconds. Web 32 rows this simple goat gestation, pregnancy or due date calculator will help you to calculate the due date for your pregnant doe. Simply key in the
doe’s date of first mating and click calculate. It is based on the average gestation of 150 days. Web calculate the due date for your pregnant doe with an online tool or a printable table. Standard
breeds (150 days) miniature breeds (145 days) date exposed. Web find the kidding date for your goat with this simple calculator. Web the following goat gestation calculator will help you quickly and
easily calculate your goat’s due date.
Goat Gestation Calendar Calculate Birth Breeding Conception Birthing
Standard breeds (150 days) miniature breeds (145 days) date exposed. Web goats gestate for an average of 150 days. Web the following goat gestation calculator will help you quickly and easily
calculate your goat’s due date. Web find the kidding date for your goat with this simple calculator. You will see the estimated date that your goat should kid (give.
Goat Gestation Calculator & Chart {Printable} Livestocking
Web 32 rows this simple goat gestation, pregnancy or due date calculator will help you to calculate the due date for your pregnant doe. You will see the estimated date that your goat should kid (give
birth). Standard breeds (150 days) miniature breeds (145 days) date exposed. Learn how long goats are pregnant and what. Web the following goat gestation.
Goat Gestation Calculator to Calculate Your Goat's Due Date in 2021
Web find the kidding date for your goat with this simple calculator. Web our simple goat gestation calculator will help you to calculate the due date for your pregnant doe in seconds. Web 32 rows
this simple goat gestation, pregnancy or due date calculator will help you to calculate the due date for your pregnant doe. Web calculate the due.
Goat Gestation Calendar
Web calculate the due date for your pregnant doe with an online tool or a printable table. Web 32 rows this simple goat gestation, pregnancy or due date calculator will help you to calculate the due
date for your pregnant doe. Standard breeds (150 days) miniature breeds (145 days) date exposed. You will see the estimated date that your goat.
Gestation Chart For Sheep
Use the abga gestation calculator to determine the approximate due date of a. You will see the estimated date that your goat should kid (give birth). Web 32 rows this simple goat gestation, pregnancy
or due date calculator will help you to calculate the due date for your pregnant doe. Standard breeds (150 days) miniature breeds (145 days) date exposed..
Goat Gestation Calculator Pregnancy Calculator YIHY
It is based on the average gestation of 150 days. Web find the kidding date for your goat with this simple calculator. Web calculate the due date for your pregnant doe with an online tool or a
printable table. Use the abga gestation calculator to determine the approximate due date of a. Standard breeds (150 days) miniature breeds (145 days).
goat gestation chart Hoss.roshana.co
Web find the kidding date for your goat with this simple calculator. Standard breeds (150 days) miniature breeds (145 days) date exposed. Web 32 rows this simple goat gestation, pregnancy or due date
calculator will help you to calculate the due date for your pregnant doe. Web the following goat gestation calculator will help you quickly and easily calculate your.
Goat Gestation Calculator to Calculate Your Goat's Due Date Goats
Use the abga gestation calculator to determine the approximate due date of a. Web the following goat gestation calculator will help you quickly and easily calculate your goat’s due date. Web 32 rows
this simple goat gestation, pregnancy or due date calculator will help you to calculate the due date for your pregnant doe. Simply key in the doe’s date.
Simply key in the doe’s date of first mating and click calculate. Web calculate the due date for your pregnant doe with an online tool or a printable table. Web 32 rows this simple goat gestation,
pregnancy or due date calculator will help you to calculate the due date for your pregnant doe. Web the following goat gestation calculator will help you quickly and easily calculate your goat’s due
date. It is based on the average gestation of 150 days. Web goats gestate for an average of 150 days. You will see the estimated date that your goat should kid (give birth). Learn how long goats are
pregnant and what. Use the abga gestation calculator to determine the approximate due date of a. Standard breeds (150 days) miniature breeds (145 days) date exposed. Select breeding date to show the
approximate kidding day. Web our simple goat gestation calculator will help you to calculate the due date for your pregnant doe in seconds. Web find the kidding date for your goat with this simple
Simply Key In The Doe’s Date Of First Mating And Click Calculate.
Web 32 rows this simple goat gestation, pregnancy or due date calculator will help you to calculate the due date for your pregnant doe. Select breeding date to show the approximate kidding day. You
will see the estimated date that your goat should kid (give birth). Web our simple goat gestation calculator will help you to calculate the due date for your pregnant doe in seconds.
Web Find The Kidding Date For Your Goat With This Simple Calculator.
Web the following goat gestation calculator will help you quickly and easily calculate your goat’s due date. Use the abga gestation calculator to determine the approximate due date of a. Web
calculate the due date for your pregnant doe with an online tool or a printable table. Standard breeds (150 days) miniature breeds (145 days) date exposed.
It Is Based On The Average Gestation Of 150 Days.
Learn how long goats are pregnant and what. Web goats gestate for an average of 150 days.
Related Post:
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The Anatomy Of A Breakout Automated Trading Strategy: The Components - Helping you Master EasyLanguage
In the previous part of this 3-part article, I explained the concept of my breakout ATS model that I’ve been successfully using for about seven years. We’ve learned about four crucial components of
the model: POI, distance, time filter, and a regular filter. In this part, we’ll explore each filter more in detail.
POI When it comes to scouting for the best Point Of Initiation (POI), you must be as creative as possible. Your POI can be basically anything. When I started constructing my first breakout ATS
strategies, I used pretty simple methods of getting a POI. It usually was:
• Yesterday’s Close
• Today’s Open
• Today’s Low (for longs)
• Today’s High (for shorts)
• Lowest O/H/L/C X-days back
Highest O/H/L/C X-days back All of these are very basic and obvious; still I was able to construct pretty impressive and robust strategies with just this beginner’s stuff. Plenty of these strategies
are still part of my portfolio. Of course, over time, I’ve started thinking about other possibilities of different POIs and I’ve added many more:
• Moving Averages – any kind
• Moving Averages based on O/H/L/C/Typical Price
• 50% retracement of the current day
• Lowest/Highest values derived from any two or three techniques described above
POI +/- (X * TR) Again, you can stick to just these two for a very long time and get fantastic and robust strategies. But of course, you also want to keep evolving your approach so you start looking
for different techniques to deploy. In my case, it was:
• GapLess ATR
• GapLess TR
• Bollinger Bands difference
• Certain Moving Averages differences
Highest High (X) – Lowest Low (X) differences Surprisingly, the results were not usually better than when using the most common and obvious ATR/TR! In fact, I quit GapLess variations completely and,
although I still keep the other techniques in my D&P (Design & Prototype) code, the majority of my strategies still use ATR/TR. You don’t really need to be creative when it comes to the distance.
Time Filter At the very beginning, I used to be very “precise” when it came to the time filter. That said, I used to optimize the exact, most optimal start time and end time for every breakout ATS.
Not surprisingly, I soon realized there was too much over-optimization (making it much harder to pass my very demanding robustness tests).
After a couple of years, I simplified the time filter approach pretty much and, right now, what I like is to divide the regular trading session into three or four equal parts and test the efficiency
of each part separately (I call this T-Segmenting, because it’s just splitting the time into different segments). This is an absolutely sufficient solution and also a very logical one, as from my
previous experience, I already know that the usual regular session behaves differently especially at its beginning, in its middle, and at its end.
Therefore T-Segmenting into three different parts is the most usual approach in the case of my breakout ATSs. Just to give you a small example, let’s say I develop a breakout ATS for e-mini Russell
2000 (TF). The regular trading hours are 9:30 – 16:15. So, I make three T-Segments:
• T-Segment 1: 9:30 – 11:45
• T-Segment 2: 11:45 – 14:00
• T-Segment 3: 14:00 – 16:15 Then, I test my breakout ATS candidate for all three T-Segments and perform robustness testing in each of them to see which one is the most suitable.
Regular Filter The final part is a regular filter. Again, nothing fancy here. I basically use four different groups of regular filters:
• Price Action based filters
• Moving Averages based filters
• Volatility based filters For the first group, I usually use quite simple usual conditions, like:
• C <> O/H/L/C X-bars backs
• C <> O/H/L/C of the current day or the previous day
• Any combinations of the above. For the second group, I usually use:
• C <>certain Moving Average
• Two different Moving Averages
• Certain (relative or absolute) distance of the current price from a certain Moving Average For the third group, I like the following indicators:
• DMI
• ADX
• Combination of the both Finally, for the last group, I like following concepts:
• ATR <> X
• Comparing 2 ATRs with different periods
Using certain absolute or relative difference between two ATRs with different periods I don’t have a bias towards any of the techniques and I freely use or test all of them. At the end of the day,
it’s always the robustness test that will reveal the truth. Whatever passes the robustness testing is fine for me. Of course, over time, I’ve again developed plenty of my own filtering techniques and
indicators, but still, I’ve been able to happily live just with the stuff I’ve described to you.
To sum up:
• You don’t need fancy techniques to develop a robust and viable breakout ATS with my simple model.
• However, it’s still preferable to keep experimenting, looking for improvements and new ideas; as you can see, I always like evolving all of the components of my breakout ATS model.
• The way to develop a workable and robust breakout ATS is to experiment with as many different POIs, distances, T-Segments, and regular filters as possible.
• Of course, the most important part is still the robustness testing, so whatever the backtest equity of your breakout ATS candidate looks like, you still need to be sure that a candidate passes
your robustness testing criteria (I personally use very demanding ones).
— By Tomas Nesnidal of Systems on The Road.
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How to Efficiently Store Pruned Weight Matrices in Practice?
Hi everyone,
I’m working on pruning a neural network to improve its efficiency by setting some connections (weights) to zero. However, I’m having trouble figuring out how to efficiently store these pruned weight
I know PyTorch supports sparse matrices, which track non-zero values and their indexes. But I’m concerned that storing these indexes might reduce the space-saving benefits. For example, if half of
the matrix has non-zero values, would storing their indexes offset the space savings?
Am I misunderstanding how pruning should work, especially with around 50% non-zero values in a matrix? How do you typically implement pruning to save storage space effectively? Any advice or
suggestions on efficient storage methods would be greatly appreciated.
Thanks in advance!
6 Likes
I’m sorry to say that I’ve also found this issue confusing. My guess is that after sparsifying the model, the weights are permuted to group the zeros together, creating blocks of zeros that can be
skipped during processing.
5 Likes
Even a matrix with 50% zeros can be stored more efficiently than a dense matrix. For example, using a Huffman-like compression could save space by assigning shorter codes to zeros and slightly longer
codes to non-zero values. This approach saves storage space overall, but the matrix might need to be decompressed for operations like multiplication, which adds complexity. Standard sparse formats,
like Compressed Sparse Row (CSR), and additional compression techniques, like Delta encoding, can also be used but come with their own trade-offs.
4 Likes
As @m_guru mentioned, pruning 50% isn’t very substantial. Some models can be pruned up to 99% and still perform well, especially with magnitude-based unstructured pruning. The main aim of pruning is
not just compression but possibly better generalization or faster training (as suggested by the lottery ticket hypothesis). Although pruning may reduce model size with sparse matrices, these are hard
to accelerate.
For effective model compression, structured pruning is better. This involves removing entire neurons, convolutional channels, or layers. Also, PyTorch doesn’t have a function to automatically apply
masks for pruning, so this needs to be done manually.
3 Likes
I think you can read this:
Torsten Hoefler, Dan Alistarh, Tal Ben-Nun, Nikoli Dryden, and Alexandra Peste. 2021. Sparsity in deep learning: Pruning and growth for efficient inference and training in neural networks. JMLR 22, 1
(2021), 10882–11005.
You first need to define if it is a structure or unstructure pruning. If structure pruning, you can use some libraries such as NNI for it to compress the models. For unstructure pruning, I generally
store it in SparseCSR format (more efficient to access compared to COO).
2 Likes
Pruning by itself won’t lead to any savings as it’s just a mask over your tensor as it was mentioned below, what you must do is to switch the tensor to use a sparse format.
Which leads to the challenge that sparse tensors are quite size inefficient. For most formats you need sparsity way above 50% for any savings to happen and it gets worse as you start to use less bits
per weight.
Don’t forget that sparse matmul is slow AF.
One avenue worth trying is nvidia’s structured sparsity that is hardware accelerated and does reduce memory utilization.
1 Like
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What is a positive variance?
A positive variance occurs where ‘actual’ exceeds ‘planned’ or ‘budgeted’ value. Examples might be actual sales are ahead of the budget.
Which variance is always an adverse variance?
Idle time variance
What is meant by cost variance?
Cost variance (CV), also known as budget variance, is the difference between the actual cost and the budgeted cost, or what you expected to spend versus what you actually spent.
What is variance and its types?
Basic Variances Basic variances due to monetary factors are material price variance, labour rate variance and expenditure variance. Similarly, basic variance due to non-monetary factors are material
quantity variance, labour efficiency variance and volume variance.
What do you mean by variance?
The variance is a measure of variability. It is calculated by taking the average of squared deviations from the mean. Variance tells you the degree of spread in your data set. The more spread the
data, the larger the variance is in relation to the mean.
What is profit variance formula?
To calculate gross profit variance, you would subtract your projected gross profit from your actual gross profit, which equals periodic sales minus costs of goods sold. For operating variance,
subtract projected operating profit from actual operating profit, which equals revenue minus all COGS and operating expenses.
What is an adverse variance?
An adverse variance is where actual income is less than budget, or actual expenditure is more than budget. This is the same as a deficit where expenditure exceeds the available income. A favourable
variance is where actual income is more than budget, or actual expenditure is less than budget.
What is acceptable variance limit?
What are acceptable variances? The only answer that can be given to this question is, “It all depends.” If you are doing a well-defined construction job, the variances can be in the range of ± 3–5
percent. If the job is research and development, acceptable variances increase generally to around ± 10–15 percent.
How do you calculate the variance percentage?
The simplest way to measure the proportion of variance explained in an analysis of variance is to divide the sum of squares between groups by the sum of squares total. This ratio represents the
proportion of variance explained.
What is range of variance?
Range. The range is the difference between the high and low values. Since it uses only the extreme values, it is greatly affected by extreme values. Procedure for finding. Take the largest value and
subtract the smallest value.
What is operational variance?
Operational variances (or operating variance) Are variances which have been caused by adverse or favourable operational performance, compared with a standard which has been revised in hindsight. An
operational variance compares an actual result with the revised standard.
Can Mean be greater than variance?
The mean of the binomial distribution B(n,p) is np, while the variance is np(1-p). Since p is between 0 and 1, so is 1-p. Hence, the mean will be greater than the variance in every case except the
trivial p=0.
What is a good budget variance?
A favorable budget variance is any actual amount differing from the budgeted amount that is favorable for the company. Meaning actual revenue that was more than expected, or actual expenses or costs
that were less than expected. An unfavorable budget variance is, well, the opposite.
What causes adverse variance?
An adverse variance might result from something that is good that has happened in the business. For example, a budget statement might show higher production costs than budget (adverse variance).
However, these may have occurred because sales are significantly higher than budget (favourable budget).
What are the main causes of variance?
Causes of Variances Posted In: Managerial Accounting
• Change in market price.
• Change in delivery cost.
• Emergency purchases which may be due to upsets in production program, slackness of store keepers, non-availability or funs etc.
• Inefficient buying.
• Untimely buying.
• Non-availability of standard quality of material.
Can coefficient of variation be more than 100?
For the pizza delivery example, the coefficient of variation is 0.25. This value tells you the relative size of the standard deviation compared to the mean. Analysts often report the coefficient of
variation as a percentage. If the value equals one or 100%, the standard deviation equals the mean.
What is variance analysis and how is it used?
Variance analysis is the quantitative investigation of the difference between actual and planned behavior. This analysis is used to maintain control over a business. For example, if you budget for
sales to be $10,000 and actual sales are $8,000, variance analysis yields a difference of $2,000.
How is variance calculated in Management Accounting?
In accounting, you calculate a variance by subtracting the expected value from the actual value to determine the difference in dollars. A positive number indicates an excess, and a negative number
indicates a deficit.
What does coefficient of variance tell you?
The coefficient of variation (CV) is the ratio of the standard deviation to the mean. The higher the coefficient of variation, the greater the level of dispersion around the mean. It is generally
expressed as a percentage. The lower the value of the coefficient of variation, the more precise the estimate. …
What are the two types of variance?
The main two types of sales variance, and both can occur at the same time: Sales price variance: when sales are made at a price higher or lower than expected. Sales volume variance: a difference
between the expected volume of sales and the planned volume of sales.
Is variance greater than standard deviation?
The point is for numbers > 1, the variance will always be larger than the standard deviation. Standard deviation has a very specific interpretation on a bell curve. Variance is a better measure of
the “spread” of the data. But for values less than 1, the relationship between variance and SD becomes inverted.
What is a good variance percentage?
Given the size of the company, the external auditors determine it is most appropriate to analyze accounts, which have a percent variance greater than 20%. All variances greater than 20% are analyzed
to determine the reason for the change.
What are the three important types of variance?
Types of variances
• Variable cost variances. Direct material variances. Direct labour variances. Variable production overhead variances.
• Fixed production overhead variances.
• Sales variances.
How do you calculate variance in Excel?
Two-Factor Variance Analysis In Excel
1. Go to the tab «DATA»-«Data Analysis». Select «Anova: Two-Factor Without Replication» from the list.
2. Fill in the fields. Only numeric values should be included in the range.
3. The analysis result should be output on a new spreadsheet (as was set).
What are the different types of variance?
Types of Variance (Cost, Material, Labour, Overhead,Fixed Overhead, Sales, Profit)
• Cost Variances.
• Material Variances.
• Labour Variances.
• Overhead (Variable) Variance.
• Fixed Overhead Variance.
• Sales Variance.
• Profit Variance. Conclusion.
How is variance analysis done?
Variance Analysis deals with an analysis of deviations in the budgeted and actual financial performance of a company. In other words, variance analysis is a process of identifying causes of variation
in the income and expenses of the current year from the budgeted values.
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Proof of Simpson's Rule
Simpson's Rule is used to numerically estimate the value of integrals that either cannot be or are difficult to evaluate analytically. The rule approximates a function with a collection of arcs from
quadratic functions and integrate across each of these.
Proof: Let P be a partition of [ a , b ] into n subintervals of equal width,f ( x ) with a quadratic curve that interpolates the points
Figure 4:
Approximating the graph of y = f(x) with parabolic arcs across successive pairs of intervals to obtain Simpson's Rule.
Since only one quadratic function can interpolate any three (non-colinear) points, we see that the approximating function must be unique for each interval
Since this function is unique, this must be the quadratic function with which we approximate f ( x ) oni ,
By evaluating the integral on the right, we obtain
Summing the definite integrals over each interval
By simplifying this sum we obtain the approximation.
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Organic Chemistry - Online Tutor, Practice Problems & Exam Prep
All right, guys. So in these videos, I'm going to teach you how to use free energy in kilojoules per mole to calculate the exact percentages of each conformation that you would get of a cyclohexane.
Again, these videos might be beyond the scope of what your professor wants you to know for your test. So I'm going to leave it up to you to if you need to know this or not. You've been warned, so
it's time to get into this. It turns out that we can use that delta G value that we get from our A values to calculate those exact percentages at any given temperature. Now the way we do this is
through the Gibbs free energy equilibrium constant equation. Just so you guys know, if this equation looks familiar, it's not unique to this type of problem. In fact, pretty much any process that you
can describe a free energy difference in can, you can determine an equilibrium through this equation. So this is a very important equation for all of chemistry, not just for cyclohexanes. Okay? Now
as you can see, what it says is that let's just go through one term at a time. It says that the delta G for the change in free energy is equal to the negative R. Now remember that R is the gas
constant that we used to use in general chemistry and there were 2 different values of R that we used to use. Just note that the one we're using is in joules per mole, so that's 8.134. That's going
to be important in a second. Then temperature, temperatures in Kelvin. Remember that I mean it's been a while since we dealt with temperature, but remember that 0 degrees Celsius is equal to 273.15
degrees Kelvin. That's going to be a conversion that we have to use in a little bit. Then you're going to multiply that by the natural log of the equilibrium constant. Well, in order to solve any of
these problems for percentages, we need to know the value of the equilibrium constant. Because equilibrium constant by definition tells you what's your products over your reactants. I need to know
that fraction. If we go ahead and we solve for K[E], I did the math for you. Don't worry. What we get is that the K[E] is equal to the negative delta G over the R times the T, all to the e. If we can
just plug in these variables, we're going to get the equilibrium constant. Now we know what R is. We know what T is. Your calculator tells you what E is. All we need is negative delta G. Do we have a
way to find that? Yes, guys. That's through our A values. Our A values tell us what the free energy changes as we go axial. Awesome. Now I do want to make one note of the delta G. Notice that this is
negative delta G. But everything that we solved when we're doing A values, we were actually solving for positive delta G because we were actually looking at the less stable one. We're looking at how
much energy do we have to put into the system to go to axial. When we use this equation, we're actually going to be inputting the positive delta G here and that's fine. What we're going to be getting
is a number that describes basically how we're going to that less stable value. So then over here, what we have is that then we get that K[E] and now we can solve for the percentages using the
definition, products over reactants. Once we get that positive K[E] number, that positive K[E] number means that we're actually going towards the favored direction. I'm not sure if you guys remember
but if you have a K[E] over 1, that means you're going to the more favored direction. I'm just telling you guys right now, if we use a positive number for delta G, we're going to get also a positive
number. I'm sorry. We're going to get a number that's above 1 for K[E]. We're going to get this greater than 1. What that means is that our definition of K[E] has to be the products over the
reactants, meaning the more favored conformation over the less favored. Just letting us know that the way that we've arranged this equation, the way that your textbook does it, is that it always does
the more favored over the less favored. Meaning that when you get this positive value, it's going to tell you what percentage you're going to have of the equatorial. And then that minus 100 will be
your axial. Now here it says that K[E] is equal to X over one over X. That just has to do with the definition of equilibrium constant. How K[E] is what your X is what you're making. That's your
product. So then one minus whatever you made would be your reactants. Then we don't really want K[E] here. We want X because we're really trying to figure out how much of this product we're going to
get. So if we solve for X, I did that for you. What you're finally going to get is that X is equal to K[E] over K[E]+1. If you want to put it in a percentage term, it's times 100. Now that was a ton
of words that I just said, a lot of numbers and symbols. I do not need you guys to perfectly understand this as much as I just need you to memorize it and know how to use it. If your professor wants
you to solve this on your exam, then these equations should be in your mind. You should have memorized this equation. You should have memorized the definition of K[E] or how to solve for X. Now we're
going to focus on the actual working part, on the actual part that we determine percentages which is so cool. I'm a huge Orgo nerd as you guys know. This is fun. Getting to determine the exact
percentage of each cyclohexane. This first one will be a worked example and we'll go ahead and start off with this first one. I'm just going to pause the video and then we'll come back and we'll
solve this one together.
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Asymptotic analysis of the least squares estimate of 2-D exponentials in colored noise
This paper considers the problem of estimating the parameters of complex-valued sinusoidal signals observed in colored noise. This problem is a special case of the general problem of estimating the
parameters of a complex-valued homogeneous random field with mixed spectral distribution from a single observed realization of it. The large sample properties of the least squares estimator of the
exponentials' parameters are derived, making no assumptions as to the probability distribution of the observed field. It is shown that the least squares estimator is asymptotically unbiased. A simple
expression for the estimator asymptotic covariance matrix is derived. The derivation shows that, asymptotically, the least squares estimation of the parameters of each exponential is decoupled from
the estimation of the parameters of the other exponentials. Assuming the observed field is a realization of a Gaussian random field, it is further demonstrated that the asymptotic error covariance
matrix of the least squares estimate attains the Cramer-Rao bound, even for modest dimensions of the observed field and low signal to noise ratios.
Conference Proceedings of the 10th IEEE Workshop on Statiscal and Array Processing
City Pennsylvania, PA, USA
Period 14/08/00 → 16/08/00
ASJC Scopus subject areas
Dive into the research topics of 'Asymptotic analysis of the least squares estimate of 2-D exponentials in colored noise'. Together they form a unique fingerprint.
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Layer: Nisqually_2070_SLR_142_z_star.tif (ID: 123)
Parent Layer: Nisqually Name:
Display Field: Type:
Raster Layer
Geometry Type:
We used WARMER, a 1-D cohort model of wetland accretion (Swanson et al. 2014), which is based on Callaway et al. (1996), to examine SLR projections across each study site. Each cohort in the model
represents the total organic and inorganic matter added to the soil column each year. WARMER calculates elevation changes relative to MSL based on projected changes in relative sea level, subsidence,
inorganic sediment accumulation, aboveground and belowground organic matter productivity, compaction, and decay for a representative marsh area. Each cohort provides the mass of inorganic and organic
matter accumulated at the surface in a single year as well as any subsequent belowground organic matter productivity (root growth) minus decay. Cohort density, a function of mineral, organic, and
water content, is calculated at each time step to account for the decay of organic material and auto-compaction of the soil column. The change in relative elevation is then calculated as the
difference between the change in modeled sea level and the change in height of the soil column, which was estimated as the sum of the volume of all cohorts over the unit area model domain. The total
volume of an individual cohort is estimated as the sum of the mass of pore space water, sediment, and organic matter, divided by the cohort bulk density for each annual time step. Elevation is
adjusted relative to sea level rise after each year of organic and inorganic input, compaction, and decomposition. We parameterized WARMER from the elevation, vegetation, and water level data
collected at each site. We evaluated model outputs between 2010 and 2110 using marsh elevation zones defined above.Model inputs Sea-level rise scenariosIn WARMER, we incorporated a recent forecast
for the Pacific coast which projects low, mid, and high SLR scenarios of 12, 64 and 142 cm by 2110, respectively (NRC 2012). We used the average annual SLR curve as the input function for the WARMER
model. We assumed the difference between the maximum tidal height and minimum tidal height (tide range) remained constant through time, with only MSL changing annually.Inorganic matterThe annual
sediment accretion rate is a function of inundation frequency and the mineral accumulation rates measured from 137Csdating of soil cores sampled across each site. For each site, we developed a
continuous model of water level from the major harmonic constituents of a nearby NOAA tide gauge. This allowed a more accurate characterization of the full tidal regime as our water loggers were
located above MLLW. Following Swanson et al. (2014), we assumed that inundation frequency was directly related to sediment mass accumulation; this simplifying assumption does not account for the
potential feedback between biomass and sediment deposition and holds suspended sediment concentration and settling velocity constant. Sediment accretion, Ms,at a given elevation, z, is equal to,
where f(z) is dimensionless inundation frequency as a function of elevation (z), and Sis the annual sediment accumulation rate in g cm-2 y-1.Organic matterWe used a unimodal functional shape to
describe the relationship between elevation and organic matter (Morris et al. 2002), based on Atlantic coast work on Spartina alterniflora. Given that Pacific Northwest tidal marshes are dominated by
other plant species, we developed site-specific, asymmetric unimodal relationships to characterize elevation-productivity relationships. We used Bezier curves to draw a unimodal parabola, anchored on
the low elevation by MTL at the high elevation by the maximum observed water level from a nearby NOAA tide gauge. We determined the elevation of peak productivity by analyzing the Normalized
Difference Vegetation Index (NDVI; (NIR - Red)/(NIR + Red)) from 2011 NAIP imagery (4 spectral bands, 1 m resolution; Tucker 1979) and our interpolated DEM. We then calibrated the amplitude of the
unimodal function to the organic matter input rates (determined from sediment accumulation rates and the percent organic matter in the surface layer of the core) obtained from sediment cores across
an elevation range at each site. The curves were truncated to zero below the lowest observed marsh elevation for each site from our vegetation surveys, reflecting the observed transition to
unvegetated mudflat. The root-to-shoot ratio for each site was set to 1.95, the mean value from an inundation experiment conducted at Siletz in 2014 for Juncus balticusand Carex lyngbyei, two common
high and low marsh species in the Pacific Northwest (C. Janousek et al., unpublished results). Compaction and decompositionCompaction and decomposition functions of WARMER followed Callaway et al.
(1996). We determined sediment compaction by estimating a rate of decrease in porosity from the difference in measured porosity between the top 5 cm and the bottom 5 cm of each sediment core. We
estimated the rate of decrease, r, in porosity of a given cohort as a function of the density of all of the material above that cohort.Following Swanson et al. (2014), we modeled decomposition as a
three-tiered process where the youngest organic material, less than one year old, decomposed at the fastest rate; organic matter one to two years old decayed at a moderate rate; and organic matter
greater than two years old decayed at the slowest rate. Decomposition also decreased exponentially with depth. We determined the percentage of refractory (insoluble) organic material from the organic
content measured in the sediment cores. We used constants to parameterize the decomposition functions from Deverel et al. (2008). ImplementationFor each site, we ran WARMER at 37 initial elevations
(every 10 cm from 0 to 360 cm, NAVD88). A two hundred year spin-up period for each model run was used to build an initial soil core. A constant rate of sea-level rise was chosen that the modeled
elevation after 200 years was equal to the initial elevation. After the spin-up period, sea-level rose according to the scenario (+12, 63, or 142 cm by 2110). Linear interpolation was used to project
model results every 10 years onto the continuous DEM developed from the RTK surveys. This raster contains data from Nisqually marsh with the projection from the WARMER model for the year 2070 with a
142 cm sea-level rise rate.
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Data Mining Algorithms In R/Packages/CCMtools/Info.Criterion - Wikibooks, open books for an open world
This function computes the Information Criterion (IC) of a clustering result.
Info.Criterion(NS, DataS, r, totCL, Nc, cl)
□ NS Number of locations (i.e., weather stations) for the local-scale time series on which IC is calculated.
□ DataS Dataset corresponding to local-scale (station) data on which IC is calculated. This is a matrix NS*NN, where NN is the number of days (i.e., length of the time series).
□ r Value for which the IC is calculated (see details).
□ totCL Vector of numbers of elements (e.g., days) in each cluster.
□ cl Vector containing the sequence of clusters (length(cl) is NN).
The IC is computed as $IC = Sum_i=1^K |n_i,r - (p_r * n_i)|$, where
$n_i,r$ = \# of days in cluster $i$ that receive a rainfall amount > r
$p_r$ = proba of such rainy days in the whole population
$n_i$ = \# of days in cluster i
M. Vrac (mathieu.vrac@lsce.ipsl.fr))
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On Maximum Focused Electric Energy in Bounded Regions - Diagnostic Image Analysis Group
A general method is presented for determining the maximum electric energy in a bounded region of optical fields with given time-averaged flux of electromagnetic energy. Time-harmonic fields are
considered whose plane wave expansion consists of propagating plane waves only, i.e., evanescent waves are excluded. The bounded region can be quite general: it can consist of finitely many points,
or be a curve, a curved surface or a bounded volume. The optimum optical field is eigenfield corresponding to the maximum eigenvalue of a compact linear integral operator which depends on the bounded
region. It is explained how these optimum fields can be realized by focusing appropriate pupil fields. The special case that the region is a circular disc perpendicular to the direction of optical
axis is investigated by numerical simulations.
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C5.6 Applied Complex Variables (2023-24)
General Prerequisites:
The course requires second year core analysis (A2 complex analysis). It continues the study of complex variables in the directions suggested by contour integration and conformal mapping. A knowledge
of the basic properties of Fourier Transforms is assumed. Part A Waves and Fluids and Part C Perturbation Methods are helpful but not essential.
Course Overview:
The course begins where core second-year complex analysis leaves off, and is devoted to extensions and applications of that material. The solution of Laplace's equation using conformal mapping
techniques is extended to general polygonal domains and to free boundary problems. The properties of Cauchy integrals are analysed and applied to mixed boundary value problems and singular integral
equations. The Fourier transform is generalised to complex values of the transform variable, and used to solve mixed boundary value problems and integral equations via the Wiener-Hopf method.
Learning Outcomes:
Students will be able to:
Solve Laplace's equation on various two-dimensional domains using conformal mapping techniques
Use conformal mapping to solve certain free-boundary fluid flow problems
Use the Plemeli formulae for Cauchy integrals to solve mixed boundary value problems and singular integral equations
Use contour integrals and the Wiener-Hopf technique to solve a range of PDE problems and integral equations
Course Synopsis:
Review of core complex analysis, analytic continuation, multifunctions, contour integration, conformal mapping and Fourier transforms.
Riemann mapping theorem (in statement only). Schwarz-Christoffel formula. Solution of Laplace's equation by conformal mapping onto a canonical domain; applications including inviscid hydrodynamics;
Free streamline flows in the hodograph plane. Unsteady flow with free boundaries in porous media.
Application of Cauchy integrals and Plemelj formulae. Solution of mixed boundary value problems motivated by thin aerofoil theory and the theory of cracks in elastic solids. Reimann-Hilbert problems.
Cauchy singular integral equations. Complex Fourier transform. Contour integral solutions of ODE's. Wiener-Hopf method.
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Overcoming Barriers in Induction Heating for the Electrification of Chemical Reactors: Development of In-situ Power and Temperature Measurements, Modelling and Scale-up Analysis
There is a clear and pressing need to move away from fossil fuels as the main source of heating for chemical conversion processes, an industry with associated carbon emissions of 0.65 Gte CO2
equivalent per annum. Renewable electricity is a promising heat source for replacing fossil fuels in the chemicals industry and there are a number of different electrical heating technologies, each
at a different state of maturity. These include induction heating, in which electrically conductive or magnetic susceptor materials generate heat when placed in an alternating magnetic field.
Induction-heated chemical reactions have been demonstrated at the lab scale for a wide variety of chemical reactions and susceptor materials, which heat either by magnetic hysteresis or induced eddy
currents. This thesis aims to develop tools and models that will help transform induction heating from a lab-scale technology to one that is viable for chemical manufacturing at an industrial scale.
Most temperature instruments are unsuitable for use in applied magnetic fields. Induced eddy currents can destroy instrument wires and measurement circuits and induction heating of the instrument tip
gives inaccurate temperature measurement and can exceed the temperature limits of their construction materials. This thesis demonstrates an induction-tolerant thermocouple capable of measuring
temperature up to 600 °C in an induction heated reactor at applied field strengths of 20 kA·m-1 at a frequency of 400 kHz.
Characterisating the heating performance of a bed of magnetic material is a key requirement for tuning and optimising the performance of the heating material in an industrial reactor. Heating power
is a function of material properties, frequency,
applied field strength and temperature. It also depends on the size distribution, shape and agglomeration of the magnetic particles. The heating material needs to generate sufficient power across a
wide range of temperatures. In an endothermic reactor it needs to heat the reactor from ambient temperature to reaction conditions as well as supplying the reaction energy at the target reaction
A novel magnetometry method is developed for measuring magnetic hysteresis curves in-situ and in real-time. This is demonstrated on nano-powder samples of magnetite
and maghemite up to kA·m-1 and 400 kHz up to the Curie temperature of each material. The data show good agreement with the Rayleigh law of hysteresis at low applied field strengths and exhibit the
characteristic fall in magnetisation expected as the samples approach the Curie temperature, 585 °C for magnetite. These experiments are carried out using a pulse heating method to overcome any
thermal lag effect between the temperature measured by the thermocouple and the temperature of the rapidly heating sample bed.
The author outlines a new model of magnetic hysteresis for major and minor hysteresis curves called the LangArc model. The parameters of the LangArc model are shown to relate to the key features of
the major magnetic hysteresis curve and it reduces to
Rayleigh’s law for lower applied field strengths. This model can be used for optimising the heating performance of the material. The author showcases an innovative method in which characterising the
magnetic properties of a material as a function of temperature
then allows for the instantaneous temperature of the sample to be determined from in-situ magnetometry measurements. This method has no thermal lag, which is critical for the safe control of
induction heated systems, where the temperature can rise rapidly.
Temperature rise rates of 30 °C·s-1 were determined using this technique.
This thesis contains a new method for measuring the heating power supplied to an induction heated reactor bed called reflected impedance. It uses the magnitude and phase of the current and voltage
supplied to the induction heater work coil to characterise
both the power and inductance of the heated bed. This can be used for both magnetic materials, which heat through hysteresis, and electrically conductive materials, which heat through eddy currents.
Previous methods to measure the heating power in beds heated by eddy currents have been restricted to a heat balance across the reactor bed, a method that is subject to significant inaccuracy. The
author demonstrates that both magnetometry measurements and the resonant frequency of the system can be used to validate the reflected impedance measurements under isothermal conditions, providing
high confidence in these power measurement techniques.
These developments in modelling and instrumentation are applied to derive equations for the thermal efficiency of an induction heated chemical reactor as a function of the reactor size. Induction
heating at lab-scale typically has an efficiency of less than 10%
of the electrical energy supplied to the work coil converted to useful heat in the reactor bed. The remainder of this energy is lost as heat in the work coil. The novel efficiency model predicts that
the efficiency of induction heated reactors increases with size and
is applied to a case study of ethanol dehydration to ethylene over a zeolite catalyst. Real-world constraints are imposed on the reactor design, such as removing heat from the work coil and applying
voltage limits to the resonant tank circuit used to generate
the magnetic field. This analysis shows that the voltage rating placed a significant limit on the maximum efficiency.
For a maximum circuit voltage of 11 kV heated using 97 nm magnetite powder or 5mm radius of insulated, non-magnetic stainless steel balls, the case study yields an industrially viable reactor with
0.2 m radius and 0.8 m length; a heating material
volume fraction of less than 8%; an applied field strength of 10 kA·m-1; and a resonant frequency of circa 8 kHz. The cacluated effiency is approximately 65% for both cases. This is comparable with
the efficiency of using hydrogen derived by water electrolysis as a replacement to natural gas for a chemical process heating fuel. Above this reactor size, the resonant frequency falls due to the
larger inductance of a bigger reactor, resulting in a rapid drop in energy efficiency. The author proposes that radiofrequency alternators, such as the Bethenod-Latour or Alexanderson alternators,
are possible alternatives to resonant tank circuits. These would allow the reactor to be operated at frequencies
in excess of the resonant frequency, further increasing the efficiency of these reactor systems.
The tools and models developed in this thesis allow for more detailed characterisation of heating materials and provide a theoretical basis for their optimisation in a flowing chemical reactor. It
shows that magnetite or maghemite nano-powders are viable for induction heating chemical reactions. These techniques should be applied to a wider variety of magnetic and eddy current heating media,
such as exchange spring magnets, to provide an optimised heating material that is stable in long term catalyst studies. Furthermore, the instruments developed in this thesis are vital for temperature
and reaction control in industrial induction heated reactors.
• Induction Heating
• Magnetism
• Sustainability
• Chemistry
• Renewable Electricity
• Heating
• Eddy Current
• Hysteresis
• Chemical reaction engineering
• Process Intensification
• Process Integration
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A charge of 25 C passes through a circuit every 4 s. If the circuit can generate 1 W of power, what is the circuit's resistance? | HIX Tutor
A charge of #25 C# passes through a circuit every #4 s#. If the circuit can generate #1 W# of power, what is the circuit's resistance?
Answer 1
To find the resistance of the circuit, you can use the formula:
P = V * I
Where: P is the power (1 W), V is the voltage, and I is the current.
Given that the charge passing through the circuit every 4 seconds is 25 C, you can calculate the current using:
I = Q / t
Where: Q is the charge (25 C), t is the time (4 s).
Once you have the current, you can rearrange the power formula to solve for resistance:
R = V / I
Substitute the given values to find the resistance of the circuit.
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Answer 2
The circuit resistance is $= 25.6 m \Omega$
The charge is #Q=25C#
The time is #t=4s#
The current is #I=Q/t=25/4A#
But according to Ohm's Law
the resistance is #R=P/I^2#
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Answer from HIX Tutor
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
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An obstacle representation of a graph G consists of a set of pairwise disjoint simply connected closed regions and a one-to-one mapping of the vertices of G to points such that two vertices are
adjacent in G if and only if the line segment connecting the two corresponding points does not intersect any obstacle. The obstacle number of a graph is the smallest number of obstacles in an
obstacle representation of the graph in the plane such that all obstacles are simple polygons. It is known that the obstacle number of each n-vertex graph is O(nlogn) [M. Balko, J. Cibulka, and P.
Valtr, Discrete Comput. Geom., 59 (2018), pp. 143-164] and that there are n-vertex graphs whose obstacle number is \Omega(n/(loglogn)^2) [V. Dujmovi\'c and P. Morin, Electron. J. Combin., 22 (2015),
3.1]. We improve this lower bound to \Omega(n/loglogn) for simple polygons and to \Omega(n) for convex polygons. To obtain these stronger bounds, we improve known estimates on the number of n-vertex
graphs with bounded obstacle number, solving a conjecture by Dujmovi\'c and Morin. We also show that if the drawing of some n-vertex graph is given as part of the input, then for some drawings \Omega
(n^2) obstacles are required to turn them into an obstacle representation of the graph. Our bounds are asymptotically tight in several instances. We complement these combinatorial bounds by two
complexity results. First, we show that computing the obstacle number of a graph G is fixed-parameter tractable in the vertex cover number of G. Second, we show that, given a graph G and a simple
polygon P, it is NP-hard to decide whether G admits an obstacle representation using P as the only obstacle.
• convex obstacle number
• obstacle number
• visibility
ASJC Scopus subject areas
Dive into the research topics of 'BOUNDING AND COMPUTING OBSTACLE NUMBERS OF GRAPHS'. Together they form a unique fingerprint.
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Haptic Virtual Proteins for Learning - CiteSeerX
Publications LISMA, English HKR.se
Two fundamental ques- DySAT: Deep Neural Representation Learning on Dynamic Graphs via Self-Attention Networks Aravind Sankar∗, Yanhong Wu†, Liang Gou†, Wei Zhang†, Hao Yang† ∗University of Illinois
at Urbana-Champaign, IL, USA †Visa Research, Palo Alto, CA, USA ∗asankar3@illinois.edu †{yanwu, ligou, wzhan, haoyang}@visa.com ABSTRACT Learning node representations in graphs is important for many
graphs by enabling each node to attend over its neighbors for representation learning in static graphs. As dynamic graphs usually have periodical patterns such as recurrent links or communities,
atten-tion can focus on the most relevant historical snapshot(s), to facilitate future prediction. We present a novel Dynamic Self-Attention Network 2020-01-01 In this survey, we review the recent
advances in representation learning for dynamic graphs, including dynamic knowledge graphs. We describe existing models from an encoder-decoder perspective, categorize these encoders and decoders
based on the techniques they employ, and analyze the approaches in each category. Abstract: Analyzing the rich information behind heterogeneous networks through network representation learning
methods is signifcant for many application tasks such as link prediction, node classifcation and similarity research. As the networks evolve over times, the interactions among the nodes in networks
make heterogeneous networks exhibit dynamic characteristics.
JAY KUO Research on graph representation learning has received a lot of attention in recent years since many data in real-world applications come in form of graphs. High-dimensional graph data are
often in irregular form, which makes them more - "Representation Learning for Dynamic Graphs: A Survey" Figure 2: A graphical representation of the constraints over the Pr matrices for bilinear
models (a) DistMult, (b) ComplEx, (c) CP, and (d) SimplE taken from Kazemi and Poole (2018c) where lines represent the non-zero elements of the matrices. Representation Learning for Dynamic Graphs A
Survey. In this survey, we review the recent advances in representation learning for dynamic graphs, including dynamic knowledge Happy to announce that our survey on Representation Learning for
Dynamic Graphs is published at JMLR (the Journal of Machine Learning Research).
PLOS ONE DyRep is a representation framework for dynamic graphs evolving according to two ele- mentary dynamic (knowledge) graphs: A survey.
PDF Big data analytics: A survey - ResearchGate
On the other hand, there are only a handful of methods for deep Apr 24, 2020 We propose HORDE, a unified graph representation learning framework to embed heterogeneous medical entities into a
harmonized space for Jul 3, 2019 Existing works on graph representation learning primarily focus on static We propose dyngraph2vec, a dynamic graph embedding [5] G. A. Pavlopoulos, A.- L. Wegener,
R. Schneider, A survey of visualiza- tion tools for have addressed the problem of embedding for dynamic networks. However, they either rely on 4.2 Dynamic Graph Representation Learning. For
simplicity of Apr 3, 2019 In this survey, we conduct a comprehensive review of the current literature in network as analyzing attributed networks, heterogeneous networks, and dynamic networks.
Danica Kragic Jensfelts publikationer - KTH
When the average degree $Np$ is much larger domain applications in the area of graph representation learning.
However, using graphs as a visual representation and interface for Unsupervised Graph Representation Learning Graphs provide a way to represent information about entities and the relations between
them. They are fundamentally de ned by a set of links, or edges, between entities. For attributed graphs, every node can be further associated with a set of 2021-02-04 Why learning of graph
Lediga jobb allmanlakare stockholm
Previous methods on graph representation learning mainly focus on static graphs, however, many real-world graphs are dynamic and evolve over time.
Journal of Emtander, Eric, A class of hypergraphs that generalizes chordal graphs.
Återställa magen efter magsjuka
cecilia sundberg sluläkarprogrammet linköping t8ted gunderson chemtrails debunkedlosec hund doseringvilotid multibemanningbauhaus julgran plast
Methodological tools and procedures for experimentation in
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Missing Number in Subtraction | Missing Number | Complete the Missing Number
Missing Number in Subtraction
The basic concept of finding the missing number in subtraction sums with one-digit number. These give us support and idea about the basic subtraction facts, as well as help us to understand the
subtraction's relationship to addition. It also assists as an introduction to learning algebra (as the missing number could be represented by a variable or a letter). While solving the subtraction
problems children will complete the missing number to find the correct calculation. Now we will learn how to find missing number in subtraction.
What is the missing number in these subtraction sums?
(i) 9 – ? = 4
What number taken away from 9 leaves 4? The answer is 5.
Therefore, the sum should be written 9 – 5 = 4
(ii) ? – 2 = 5
From what number must you subtract 2 so as to leave 5? The answer is 7. Therefore, the sum should be written 7 – 2 = 5
(iii) 6 - ? = 5
What number taken away from 6 leaves 5? The answer is 1.
Therefore, the sum should be written 6 – 1 = 5.
(iv) ? – 7 = 1
From what number must you subtract 7 so as to leave 1? The answer is 8. Therefore, the sum should be written 8 – 7 = 1
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Stable fermion bag solitons in the massive Gross-Neveu model: Inverse scattering analysis
Formation of fermion bag solitons is an important paradigm in the theory of hadron structure. We study this phenomenon nonperturbatively in the 1+1 dimensional Massive Gross-Neveu model, in the large
N limit. We find, applying inverse-scattering techniques, that the extremal static bag configurations are reflectionless, as in the massless Gross-Neveu model. This adds to existing results of
variational calculations, which used reflectionless bag profiles as trial configurations. Only reflectionless trial configurations which support a single pair of charge-conjugate bound states of the
associated Dirac equation were used in those calculations, whereas the results in the present paper hold for bag configurations which support an arbitrary number of such pairs. We compute the masses
of these multibound state solitons, and prove that only bag configurations which bear a single pair of bound states are stable. Each one of these configurations gives rise to an O(2N) antisymmetric
tensor multiplet of soliton states, as in the massless Gross-Neveu model.
ASJC Scopus subject areas
• Nuclear and High Energy Physics
• Physics and Astronomy (miscellaneous)
Dive into the research topics of 'Stable fermion bag solitons in the massive Gross-Neveu model: Inverse scattering analysis'. Together they form a unique fingerprint.
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Cary, also known as Your Bummy Math Tutor, is an expert math tutor who has helped millions of students improve their math skills. Having received a perfect score on the math section of the SAT
himself and attending New York University, Cary understands the challenges students face with math and how to break down concepts in an approachable way.
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(Answered)MATH225N Week 6 Assignment: Understanding Confidence Intervals - Excel
(Answered)MATH225N Week 6 Assignment: Understanding Confidence Intervals – Excel
A company wants to determine a confidence interval for the average CPU time of its teleprocessing transactions. A sample of 70 random transactions in milliseconds is given below. Assume that the
transaction times follow a normal distribution with a standard deviation of 600 milliseconds. Use Excel to determine a 98% confidence interval for the average CPU time in milliseconds. Round your
answers to the nearest integer and use ascending order
Thus, the 98% confidence interval for μ is
Suppose the weights of tight ends in a football league are normally distributed such that σ2=1,369. A sample of 49 tight ends was randomly selected, and the weights are given below. Use Excel to
calculate the 95% confidence interval for the mean weight of all tight ends in this league. Round your answers to two decimal places and use ascending order
Thus, the 95% confidence interval for μ is
A sample of 22 test-tubes tested for number of times they can be heated on a Bunsen burner before they crack is given below. Assume the counts are normally distributed. Use Excel to construct
a 99% confidence interval for μ. Round your answers to two decimal places and use increasing order.
Thus, the 99% confidence interval for the mean is
In a random sample of 350 attendees of a minor league baseball game, 184 said that they bought food from the concession stand. Create a 95% confidence interval for the proportion of fans who bought
food from the concession stand. Use Excel to create the confidence interval, rounding to four decimal places.
Thus, the 95% confidence interval for the population proportion of fans who bought food from the concession stand, based on this sample, is approximately
Alison, the owner of a regional chain of pizza stores, is trying to decide whether to add calzones to the menu. She conducts a survey of 700 people in the region and asks whether they would order
calzones if they were on the menu. 46 people responded “yes.” Create a 90% confidence interval for the proportion of people in the region who would order calzones if they were on the menu.Round your
answer to four decimal places
90% CI =
A tax assessor wants to assess the mean property tax bill for all homeowners in a certain state. From a survey ten years ago, a sample of 28 property tax bills is given below. Assume the property tax
bills are approximately normally distributed. Use Excel to construct a 95% confidence interval for the population mean property tax bill. Round your answers to two decimal places and use increasing
Thus, the 95% confidence interval for the population mean property tax bill is (1185.91, 1595.59).
The following data represent a sample of the assets (in millions of dollars) of 28 credit unions in a state. Assume that the population in this state is normally distributed with σ=3.5 million
dollars. Use Excel to find the 99% confidence interval of the mean assets in millions of dollars. Round your answers to three decimal places and use ascending order
Thus, the 99% confidence interval for μ is
The monthly incomes from a random sample of 20 workers in a factory is given below in dollars. Assume the population has a normal distribution and has standard deviation $518. Compute
a 98% confidence interval for the mean of the population. Round your answers to the nearest dollar and use ascending order
Monthly Income
Thus, the 98% confidence interval for μ, rounded to the nearest integer, is
A study was conducted to estimate the mean age when people buy their first new car. The ages of purchase for 22 randomly selected people are given below. Assume the ages are approximately normally
distributed. Use Excel to determine the 99% confidence interval for the mean. Round your answers to two decimal places and use increasing order
Thus, the 99% confidence interval for the mean is
A type of golf ball is tested by dropping it onto a hard surface from a height of 1 meter. The height it bounces is known to be normally distributed. A sample of 25 balls is tested and the bounce
heights are given below. Use Excel to find a 95% confidence interval for the mean bounce height of the golf ball. Round your answers to two decimal places and use increasing order
95% confidence interval will be:
In a random sample of 2,282 college students, 356 reported getting 8 or more hours of sleep per night. Create a 95% confidence interval for the proportion of college students who get 8 or more hours
of sleep per night. Use Excel to create the confidence interval, rounding to four decimal places.
Thus, the 95% confidence interval for the population proportion of college students who get 8 or more hours of sleep per night, based on this sample, is approximately
A large company is concerned about the commute times of its employees. 333 employees were surveyed, and 131 employees said that they had a daily commute longer than 30 minutes. Create
a 95% confidence interval for the proportion of employees who have a daily commute longer than 30 minutes. Use Excel to create the confidence interval, rounding to four decimal places.
Thus, the 95% confidence interval for the population proportion of employees who have a daily commute longer than 30 minutes , based on this sample, is approximately (0.3409, 0.4459).
A restaurant is reviewing customer complaints. In a sample of 227 complaints, 57 complaints were about the slow speed of the service. Create a 95% confidence interval for the proportion of complaints
that were about the slow speed of the service. Use Excel to create the confidence interval, rounding to four decimal places.
Provide your answer below:
Correct answer:
A company wants to determine a confidence interval for the average CPU time of its teleprocessing transactions. A sample of 70 random transactions in milliseconds is given below. Assume that the
transaction times follow a normal distribution with a standard deviation of 600 milliseconds. Use Excel to determine a 98% confidence interval for the average CPU time in milliseconds. Round your
answers to the nearest integer and use ascending order
Correct answer: (5,906, 6,240).Click link below to purchase full tutorial at $10
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#Unity - How to display #projectile #trajectory path
To download the code, login with one of the following social providers.
Created By Swati Patel | Last Updated on : 08 March 2016
Main objective of this tutorial is to explain how to display projectile trajectory path in Unity 3D with code sample (example).
Step 1 Understand About Projectile
A projectile is an object upon which the only force acting is gravity. There are a variety of examples of projectiles. A cannonball shot from a cannon, a stone thrown into the air, or a ball that
rolls off the edge of the table are all projectiles. These projectiles follow curved paths called trajectories. When air resistance is neglected the curved paths are parabolic in shape.
Step 2 Types Of Projectile Motion
Many projectiles not only follow a vertical motion, but also follow a horizontal motion. That is, as they move upward or downward they are also moving horizontally. There are the two components of
the projectile's motion - horizontal and vertical motion.
2.1 Vertical Motion
In Vertical Motion, the gravity acts on objects and gives them negative acceleration “-9.8m/s²” (gravity of earth). This means that, velocity of objects decreases "-9.8m/s²" in each second. The
velocity of the free falling object is V=g*t.
If we have initial velocity then, equation of velocity of falling object: V = Vi + g*t where acceleration is -9.8m/s² The distance in free fall is calculated by the equation:
• DistanceTraveled = 1/2*g*t*t;
As in the velocity case our distance is calculated considering the initial velocity of the object by the formula;
• DistanceTraveled = Vit - 1/2*g*t*t;
Distance is subtracted because direction of g is downward.
2.2 Horizontal Motion
In Horizontal Motion, motion will be constant because there is no force acting on objects in horizontal direction. Thus, the X component of velocity is constant and acceleration in X direction is
zero. The equation that is used to calculate distance and velocity is given below.
Step 3 Implementation
The following simple c# code will display the projectile trajectory path of ball when it will thrown from cannon.
Add following script on cannon object. Create prefebs for ball and trajectory point which will be instantiate runtime. Ball must have collider and rigidbody.
3.1 Cannon Script
using UnityEngine;
using System.Collections;
using System.Collections.Generic;
public class CannonScript : MonoBehaviour
// TrajectoryPoint and Ball will be instantiated
public GameObject TrajectoryPointPrefeb;
public GameObject BallPrefb;
private GameObject ball;
private bool isPressed, isBallThrown;
private float power = 25;
private int numOfTrajectoryPoints = 30;
private List trajectoryPoints;
void Start ()
trajectoryPoints = new List();
isPressed = isBallThrown =false;
// TrajectoryPoints are instatiated
for(int i=0;i<numOfTrajectoryPoints;i++)
GameObject dot= (GameObject) Instantiate(TrajectoryPointPrefeb);
dot.renderer.enabled = false;
void Update ()
isPressed = true;
else if(Input.GetMouseButtonUp(0))
isPressed = false;
// when mouse button is pressed, cannon is rotated as per mouse movement and projectile trajectory path is displayed.
Vector3 vel = GetForceFrom(ball.transform.position,Camera.main.ScreenToWorldPoint(Input.mousePosition));
float angle = Mathf.Atan2(vel.y,vel.x)* Mathf.Rad2Deg;
transform.eulerAngles = new Vector3(0,0,angle);
setTrajectoryPoints(transform.position, vel/ball.rigidbody.mass);
// Following method creates new ball
private void createBall()
ball = (GameObject) Instantiate(BallPrefb);
Vector3 pos = transform.position;
ball.transform.position = pos;
// Following method gives force to the ball
private void throwBall()
ball.rigidbody.useGravity = true;
isBallThrown = true;
// Following method returns force by calculating distance between given two points
private Vector2 GetForceFrom(Vector3 fromPos, Vector3 toPos)
return (new Vector2(toPos.x, toPos.y) - new Vector2(fromPos.x, fromPos.y))*power;
// Following method displays projectile trajectory path. It takes two arguments, start position of object(ball) and initial velocity of object(ball).
void setTrajectoryPoints(Vector3 pStartPosition , Vector3 pVelocity )
float velocity = Mathf.Sqrt((pVelocity.x * pVelocity.x) + (pVelocity.y * pVelocity.y));
float angle = Mathf.Rad2Deg*(Mathf.Atan2(pVelocity.y , pVelocity.x));
float fTime = 0;
fTime += 0.1f;
for (int i = 0 ; i < numOfTrajectoryPoints ; i++)
float dx = velocity * fTime * Mathf.Cos(angle * Mathf.Deg2Rad);
float dy = velocity * fTime * Mathf.Sin(angle * Mathf.Deg2Rad) - (Physics2D.gravity.magnitude * fTime * fTime / 2.0f);
Vector3 pos = new Vector3(pStartPosition.x + dx , pStartPosition.y + dy ,2);
trajectoryPoints[i].transform.position = pos;
trajectoryPoints[i].renderer.enabled = true;
trajectoryPoints[i].transform.eulerAngles = new Vector3(0,0,Mathf.Atan2(pVelocity.y - (Physics.gravity.magnitude)*fTime,pVelocity.x)*Mathf.Rad2Deg);
fTime += 0.1f;
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Long Division Worksheets Grade 5 - Divisonworksheets.com
Long Division Worksheets Grade 5
Long Division Worksheets Grade 5 – Help your child master division by using division worksheets. It is possible to create your own worksheets. There are a variety of options to choose from for
worksheets. You can download the worksheets for free and modify them as you like. They’re great for first-graders, kindergarteners, and even second-graders.
Two can do enormous amounts of work
Children should be practicing on worksheets and divide huge numbers. Many worksheets only allow for two, three or even four distinct divisors. This implies that the child does not have to worry about
not completing an entire division or making mistakes in their tables of times. You can find worksheets on the internet or download them to your computer to aid your child to develop the mathematical
skills required.
Children can practice and solidify their understanding of the subject by using worksheets for multi-digit division. It’s an essential mathematical skill which is needed for a variety of computations
in everyday life and more complex mathematical concepts. These worksheets are interactive and include tasks and questions that are focused on the division of multidigit integers.
Students are challenged in dividing huge numbers. These worksheets often use an algorithm that is standardized and has step-by-step instructions. They can cause students to lose the intellectual
understanding required. For teaching long division, one approach is to utilize bases ten blocks. Students must be at ease with long division after they’ve learned the process.
Students can practice division of big numbers by using various worksheets and practice questions. The worksheets can also see fractional results that are expressed in decimals. There are worksheets
on hundredsths that are especially useful in learning how to divide large sums of money.
Sort the numbers to make small groups.
Incorporating a large number of people into small groups might be challenging. While it sounds great on paper many small group facilitators dislike the process. It is an accurate reflection of the
development of the human body, and it can contribute to the Kingdom’s unending development. It encourages others to help those in need, as well as new leaders to take over the reins.
This can be a great way to brainstorm ideas. You can make groups with individuals who have similar experiences and personality traits. You may come up with creative ideas using this method. Once
you’ve put together groups, you’re able to introduce yourself to each. It’s a good way to stimulate creativity and encourage innovative thinking.
It is used to divide large numbers in smaller pieces. If you are looking to make an equal amount of things for several groups, it can be helpful. For example, a huge class could be divided into five
classes. The groups could be put together to create 30 pupils.
Be aware that when you divide numbers there’s a divisor as well as the Quotient. Dividing one number by another will result in “ten/five,” whereas dividing two numbers by two produces the exact same
It’s an excellent idea to utilize the power of ten for big numbers.
We can divide massive numbers into powers of 10 to allow comparison between them. Decimals are a typical part of the shopping process. They can be seen on receipts and price tags. They are used to
indicate the price per gallon or the amount of gasoline that is pumped through the nozzles of petrol stations.
There are two ways to divide a large sum into powers of 10 either by moving the decimal point to one side or multiplying by 10-1. Another option is to make use of the associative power of 10 feature.
You can divide a huge number of numbers into smaller powers of ten once you know the associative function of powers of ten.
The first method employs mental computation. The pattern will become apparent if you divide 2.5 times 10. The decimal position shifts one way for every 10th power. You can apply this concept to
tackle any problem.
The second method is mentally dividing huge numbers into powers of 10. The next step is to quickly write large numbers on a scientific note. If you are using scientific notation, large numbers must
be written using positive exponents. For example, if you move the decimal points five spaces to the left, you can turn 450,000 into 4.5. To break up a big number into smaller numbers of 10, you could
use the factor 5. Also, you can break it down into smaller numbers of 10.
Gallery of Long Division Worksheets Grade 5
Free Printable Long Division Worksheets 5Th Grade Free Printable
Long Division Worksheets For 5th Grade
5th Grade Long Division Practice Worksheet
Leave a Comment
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Mathematics of Relativity: Lecture Notes
by G. Y. Rainich
Publisher: Edwards Brothers 1932
Number of pages: 222
We may consider Geometry as a first attempt at a study of the outside world. It may be considered as a deductive system which reflects (in the sense explained above, that is of the existence of a
correspondence, etc.) very well our experiences with some features of the outside world, namely features connected with the displacements of what we call rigid bodies. We see at once how much is left
out in such a study; in the first place, time is almost entirely left out: in trying to bring into coincidence two triangles we are not interested in whether we move one slowly or rapidly; in
describing a circle we are not concerned with uniformity of motion.
Download or read it online for free here:
Download link
(multiple formats)
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Today's Take on Einstein's Relativity
H. B. Tilton, F. Smarandache
Pima College PressThese are the proceedings of the Conference at Pima Community College, East Campus, February 18, 2005, at which six papers were presented. Disciplines represented: astronomy,
computer science, engineering physics and mathematics.
Relativity for Poets
Benjamin Crowell
LightAndMatter.comThis textbook is a nonmathematical presentation of Einstein's theories of special and general relativity, including a brief treatment of cosmology. It is a set of lecture notes for
the author's course Relativity for Poets at Fullerton College.
Relativity: The Special and General Theory
Albert Einstein
Methuen & Co LtdHow better to learn the Special Theory of Relativity and the General Theory of Relativity than directly from their creator, Albert Einstein himself? Einstein describes the theories
that made him famous, illuminating his case with numerous examples.
Easy Lessons in Einstein
Edwin Emery Slosson
Brace and HoweWhat is this theory of relativity and why is it so important? The mathematics of it are too much for most of us, but we can get some notion of it by a familiar illustration. A
discussion of the more intelligible features of the theory of relativity.
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151-0401/04 – Mathematics B (MBKS)
Gurantor department Department of Mathematical Methods in Economics Credits 5
Subject guarantor doc. Mgr. Marian Genčev, Ph.D. Subject version guarantor doc. Mgr. Marian Genčev, Ph.D.
Study level undergraduate or graduate Requirement Compulsory
Year 1 Semester summer
Study language Czech
Year of introduction 2010/2011 Year of cancellation 2020/2021
Intended for the faculties EKF Intended for study types Bachelor
ARE30 Ing. Orlando Arencibia Montero, Ph.D.
GEN02 doc. Mgr. Marian Genčev, Ph.D.
KUB33 Mgr. Aleš Kubíček
S1A20 prof. RNDr. Dana Šalounová, Ph.D.
Part-time Examination 6+8
Subject aims expressed by acquired skills and competences
The students will be able to master the basic techniques specified by the three main topics (see below, items 1-3). Also, they will be able to freely, but logically correct, discuss selected
theoretical units that will allow talented individuals to excel. The student will also have an overview of basic application possibilities of the discussed apparatus in the field of economics. (1)
The student will be introduced to the basics of linear algebra and its application possibilities in economics. (2) The student will be able to apply the basic rules and formulas for the calculation
of integrals, use them to calculate the area of planar regions, and for calculating of improper integrals and integrals of discontinuous functions. The student will be able to discuss the relating
application possibilities in economics. (3) The student will be able to find local extrema of functions of two variables without/with constraints, level curves and total differential, will be able to
decide whether the given function is homogeneous. The student will be able to discuss the relating application possibilities and to mention appropriate generalizations for functions of 'n' real
Teaching methods
Individual consultations
The course is focused on the practical mastery of selected mathematical methods in the field of linear algebra and calculus, which form the basis for further quantitative considerations in related
subjects. The student will also be acquainted with the derivation of basic theoretical findings. This enables the development of logical skills, which form the basis for analytical and critical
thinking. For better motivation of students, the presentation in lectures is always connected with appropriate economic problems.
Compulsory literature:
LARSON, Ron a David C. FALVO. Elementary linear algebra. 6th ed. Belmont: Brooks/Cole Cengage Lerning, 2010. ISBN 978-0-495-82923-2. TAN, Soo Tang. Multivariable calculus. International ed. Belmont:
Brooks/Cole Cengage Learning, 2010. ISBN 978-0-495-83150-1. HOY, Michael, LIVERNOIS, John Richard and MCKENNA, C. J. Mathematics for economics. Cambridge: The MIT Press, 2022. ISBN 9780262046626.
Recommended literature:
STEWART, James. Calculus: metric version. Eighth edition. [Boston]: Cengage Learning, [2016].
ISBN 978-1-305-26672-8
Way of continuous check of knowledge in the course of semester
Written exam - max. 100 pts, - min. 51 pts
Other requirements
According to teacher's instructions.
Subject has no co-requisities.
Subject syllabus:
I. Systems of linear equations and analytic geometry ---------------------------------------------------- - basic concepts, - Gaussian elimination, Frobenius' theorem, - Cramer's rule, - use of
systems of linear equations for determining the mutual position of - two planes in E3, - two lines in E2 and E3, - plane and a line in E3 - basic applications in economics II. Integral calculus
--------------------- Indefinite integral - definition and properties, - basic integration formulas and rules, - per partes, substitution, - integration of rational functions (partial fractions), -
basic applications in economics Definite integral - the problem of calculating the area of a region bounded by continuous curves - definitions a properties of the definite integral, - Newton-Leibniz'
formula, - basic applications in economics Generalized and improper integral - improper integral of the first and second kind, - Gaussian integral (for information only), - calculating improper
integrals by limits, - generalized definite integrals (the case of discontinuous functions), - basic applications in economics and connection with statistics III. Functions of two real variables
------------------------------------ - definitions of basic concepts, - domain and its visualization, - homogeneous functions of order 's', - partial derivatives and their geometric interpretation -
tangent plane, - total differential, differentiable functions, approximations of number expressions, - local extremes, - constrained local extremes - method of substitution, - Lagrange's multiplier,
- basic applications in economics IV. Ordinary differential equations (ODE) ----------------------------------------- - definition of ODE, - order of ODE, - solution of ODE (general, particular,
singular, extraordinary), - basic types of first-order ODE's - separated, - separable, - linear first-order DE (variation of constants), - second-order linear DE with constant coefficients and
special right-hand side (undetermined coefficients), - basic applications in economics V. Difference calculus and difference equations ----------------------------------------------- Introduction to
difference calculus - difference of order 'k', - basic formulas and rules for calculating the differences, - the sign of the first-order difference as the indicator of the sequence monotonicity, -
the sign of the second-order difference as the indicator of the sequence monotonicity dynamics, - relation of summation and difference Ordinary difference equations (ODifE) - definition of the ODifE
- order of the ODifE - solution of the ODifE (general, particular) - first- and second-order ODifE with constant coefficients and special right-hand side (undetermined coefficients) - basic
applications in economics
Conditions for subject completion
Occurrence in study plans
2020/2021 (B6202) Economic Policy and Administration (6202R055) Public Economics and Administration K Czech Ostrava 2 Compulsory study plan
2018/2019 (B6208) Economics and Management K Czech Ostrava 1 Compulsory study plan
2018/2019 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2018/2019 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2018/2019 (B6202) Economic Policy and Administration K Czech Valašské Meziříčí 1 Compulsory study plan
2017/2018 (B6202) Economic Policy and Administration K Czech Valašské Meziříčí 1 Compulsory study plan
2017/2018 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2017/2018 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2017/2018 (B6208) Economics and Management K Czech Ostrava 1 Compulsory study plan
2016/2017 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2016/2017 (B6202) Economic Policy and Administration K Czech Valašské Meziříčí 1 Compulsory study plan
2016/2017 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2016/2017 (B6208) Economics and Management K Czech Ostrava 1 Compulsory study plan
2015/2016 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2015/2016 (B6208) Economics and Management K Czech Ostrava 1 Compulsory study plan
2015/2016 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2015/2016 (B6202) Economic Policy and Administration K Czech Valašské Meziříčí 1 Compulsory study plan
2014/2015 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2014/2015 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2014/2015 (B6208) Economics and Management K Czech Ostrava 1 Compulsory study plan
2013/2014 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2013/2014 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2013/2014 (B6208) Economics and Management K Czech Ostrava 1 Compulsory study plan
2012/2013 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2012/2013 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2012/2013 (B6208) Economics and Management K Czech Ostrava 1 Compulsory study plan
2011/2012 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2011/2012 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2011/2012 (B6208) Economics and Management K Czech Ostrava 1 Compulsory study plan
2010/2011 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2010/2011 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
Occurrence in special blocks
Subject block without study plan - EKF - K - cs 2020/2021 Part-time Czech Optional EKF - Faculty of Economics stu. block
Subject block without study plan - EKF - K - cs 2019/2020 Part-time Czech Optional EKF - Faculty of Economics stu. block
Assessment of instruction
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Get the section properties of build-up sections
Hi Community,
I have created an L-shape section using the patch command. I want to know the section properties of the created section, such as the moment of inertia. One solution is to do a static analysis and
compare the obtained displacement with the theoretical one. But, I'm curious if there is a command to get the build-up fiber section properties.
Attached is my code for the build-up L-shape
import matplotlib.pyplot as plt
import numpy as np
import openseespy.opensees as ops
import openseespy.postprocessing.ops_vis as opsv
# Angle Section
y1 = np.array([-0.98, -0.98, -0.73, -0.73])
z1 = np.array([-0.237, 1.263, 1.263, -0.237])
y2 = np.array([-0.98, -0.98, 2.02, 2.02])
z2 = np.array([-0.487, -0.237, -0.237, -0.487])
xy1 = np.c_[y1, z1].ravel()
xy2 = np.c_[y2, z2].ravel()
fib_sec_3 = [['section', 'Fiber', 3, '-GJ', 1.0e6],
['patch', 'quad', 1, 8, 4, *xy1], # noqa: E501
['patch', 'quad', 1, 4, 12, *xy2], # noqa: E501
matcolor = ['r', 'lightgrey', 'gold', 'w', 'w', 'w']
opsv.plot_fiber_section(fib_sec_3, matcolor=matcolor)
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Pag-IBIG MP2 Dividends and Earnings
Are you curious about how the Pag-IBIG MP2 Dividends and earnings is computed? This guide will assist you in your quest to save and earn money through investment in Pag-IBIG MP2 Savings. If you
already have an existing MP2 Savings account, this guide will also show you how the dividend is calculated. When enrolling in MP2, you have the option to choose between two dividend payout methods.
Check Pag ibig Housing Loan Calculator Online
Check Pag ibig mp2 Calculator Online
Annually;If you opted for the annual dividend payout method, you can withdraw the dividend you receive every year, and this amount will not be included in the computation of the following year’s
Five-year (end-term).In order to receive the total dividend along with any accumulated savings, you must wait until the 5-year maturity period has ended. This means that the yearly dividend will be
added to the next year’s savings and will also earn its own dividend.
This guide will explain the computation for MP2 Savings Schemes, which includes monthly savings options and one-time payments, as well as annual dividend and end-term dividend payouts. It will also
compare the differences between each scheme.
In addition to the aforementioned example savings, a real-life MP2 Savings plan will also be presented at the end of this guide. This will include a breakdown of how the dividend was calculated.
How are MP2 Dividends computed?
To assist you in comprehending how the annual dividend is calculated, you may contrast the following examples with the sample data presented on the Pag-IBIG website.
Sample Computation 1:
MP2 Savings (P500 per month, End-Term Dividend Payout)
Based on the sample data presented in the table, the following conditions apply:
• A savings of P500 per month
• Selection of Five-Year (End Term) dividend payout option
• Total savings of P6,000 per year and a total of P30,000 after 5 years
• Dividend rate of computation is 7.5% (although this may vary, depending on the actual dividend rate for the past years)
• The total dividend amount earned after 5 years of maturity is P6,266.14
• The total accumulated value is P36,266.14, which is the amount that can be withdrawn after 5 years of maturity.
To understand how these amounts are computed, let’s discuss how the dividend amount and the total accumulated value are determined.
To calculate the dividend for Year 1, we need to find the average accumulated amount per month based on the monthly savings of 500 and the total savings of 6,000 for the year. This can be done by
adding the present amount to the accumulated amount from the previous month, as shown in the table. However, this accumulated amount is only used to calculate the monthly average and is not the
actual amount.
To find the average accumulated amount, we divide the total accumulated amount by 12 months. The result is 3,250.
To calculate the dividend earned for Year 1, we multiply the average accumulated amount (3,250), the dividend rate (7.5%), and the number of years (1 year). This gives us a dividend of PhP 243.75.
Since the Five-Year Dividend payout was selected, the accumulated value for the first year is PhP 6,243.75, which is the accumulated savings (PhP 6,000) plus the dividend earned for Year 1 (PhP
After saving P30,000 for 5 years in MP2, your total savings will earn a dividend of P6,266.14. This means that when you withdraw the money, you can receive a total of P36,266.14 without being taxed.
sample Computation 2:
MP2 Savings (P500 per month, Annual Dividend Payout)
Based on the sample data provided in the table above, the following conditions can be observed:
• A savings amount of P500 per month
• Selection of an annual dividend payout
• Total savings of P6,000 per year, resulting in a total of P30,000 after five years
• The dividend rate used for computation is 7.5%. However, the actual dividend rate may vary, and you can find the actual dividend rate for previous years by checking here.
• The total dividend amount that will be received is P5,718.75.
Now, let’s take a closer look at how the dividend is computed and how it differs from an End-Term Dividend Payout.
Based on the information presented in the table, we can observe the following conditions:
• A monthly savings amount of P500
• Selection of an annual dividend payout
• Total savings of P6,000 per year, resulting in a total of P30,000 after five years
• The dividend rate used for calculation is 7.5%. However, the actual dividend rate may vary, and you can check the actual dividend rate for previous years here.
• The total dividend amount that will be received is P5,718.75.
Now, let’s examine how the dividend is calculated and how it differs from an End-Term Dividend Payout.
To calculate the average accumulated amount for 12 months, divide the total accumulated amount (P39,000) by 12, which equals P3,250.
To determine the dividend earned for Year 1, multiply the Average Accumulated Amount (P3,250), the dividend rate (7.5%), and the number of years (1 year) which equals P243.75.
Since you selected the Annual Dividend payout, you can withdraw the dividend amount of P243.75 at the end of Year 1. This amount will not be added to next year’s computation. Therefore, the total
accumulated value for Year 1 is equal to the total accumulated savings, which is P6,000.
If you save P30,000 in MP2 for 5 years, you will earn a dividend of P5,718.75. This means your total savings after 5 years will be P35,718.75.
No MP2 Account yet?
If you don’t have an existing account, you can register for an MP2 account through the Virtual Pag-IBIG website. Alternatively, we have provided a guide below to help you with the enrollment process.
To create an account, you will need a Pag-IBIG Regular Savings account which can be opened through your regular contributions or by your employer. Your 12-digit Pag-IBIG MID number corresponds to
your Regular Savings account.
Based on the sample data provided in the table above, the following conditions apply:
• A one-time payment of P30,000 will be made at the beginning of Year 1.
• The selected dividend payout option is Five-Year (End-Term).
• The total savings amount is P30,000.
• The dividend rate of computation is 7.5%. Note that the actual dividend rate may vary. Please refer to the actual dividend rate for the past years.
• The total dividend amount to be received will be P13,068.88.
• The total accumulated value after 5 years will be P43,068.88.
Let”s start inYear 1 Computation:
Since, the one-time payment was paid at the beginning of the year, the dividend amount for year 1 based on 7.5% rate will be:
Dividend (Year 1) = 30,000*7.5%*1 = PhP 2,250.00
Then, the accumulated value at the end of Year 1 is the sum of cumulative savings and the dividend amount:
Accumulated Value (Year 1) = 30,000 + 2,250 = PhP 32,250.00
And after 5 years of savings in MP2, your total savings of P30,000 will earn a total dividend of P 13,068.88. And the total accumulated value of your MP2 Savings after 5 years maturity will be P
• A one-time payment of P30,000 is made at the beginning of Year 1.
• The selected dividend payout frequency is Annually.
• The total savings amount is P30,000.
• The dividend rate used for computation is 7.5%. (Please note that the actual dividend rate may vary from year to year. Check the actual dividend rate for the past years.)
• The total dividend amount to receive is P11,250.00.
• The total accumulated value after 5 years will be P41,250.00.
To understand how the dividend is calculated, let’s examine the computation for Year 1:
Since the one-time payment was made at the beginning of the year, the dividend amount for Year 1 based on a 7.5% rate will be:
Dividend (Year 1) = 30,000 * 7.5% * 1 = PhP 2,250.00
For this example, the chosen dividend payout is annual, so this dividend amount of P2,250 can be withdrawn after Year 1. The amount will not be added in subsequent years, and only the cumulative
savings of P30,000 will be carried forward.
For Year 2 through Year 5, with the same amount of P30,000, the dividend amount for each year will be the same:
Dividend (Each Year) = 30,000 * 7.5% * 1 = PhP 2,250.00
Therefore, after 5 years, the total dividend amount will be P11,250 (2,250 * 5), which is the total earnings from the P30,000 one-time payment savings. The total accumulated value will be PhP
Comparison: Pag-IBIG MP2 Savings Schemes
Pag ibig mp2 Dividend online calcutor
The table above shows a comparison of four different options for the sample MP2 savings, as explained earlier. If you aim to save a total of P30,000, you will notice that the dividend amounts are not
the same for the option of saving P500 per month versus a one-time payment. It is evident that a one-time payment earns more compared to saving P500 per month, but the total amount after 5 years
remains the same.
Another option to consider is the dividend payout. Choosing the end-term payout is a better option since the dividend earned each year will also earn a dividend for the succeeding years until
maturity. In contrast, with the annual payout, the dividend earned each year will not be carried forward to subsequent years. However, you can withdraw the dividend amount earned each year on an
annual basis.
Actual MP2 Savings Dividend Rates (2022-2023)
The MP2 Savings program offers higher dividends when compared to both the P1 and Regular Savings options. These dividends are tax-free and are calculated annually based on the performance of
investments made by Pag-IBIG. The dividend amount is credited to your account on a yearly basis, and you can choose to withdraw it annually or after a 5-year maturity period. To provide some
historical context, here are the MP2 Savings Dividend Rates from 2011, as source.
Year MP2 Savings Dividend Rate
2021 6.00%
2020 6.12%
2019 7.23%
2018 7.41%
2017 8.11%
2016 7.43%
2015 5.34%
2014 4.69%
2013 4.58%
2012 4.67%
Actual MP2 Savings with Dividend Computation
Here is an actual MP2 Savings account which started on January 2020. The declared dividend for that year is 6.12%. As you can see, savings are made every month and in different amounts for a minimum
of P500. And, at the end of the year, a dividend amount of P351.90 has been added to the MP2 Savings account.
This is a record of an MP2 Savings account that began in January 2020. The dividend declared for that year was 6.12%. The account holder made monthly contributions of varying amounts, with a minimum
of P500. At the end of the year, a dividend of P351.90 was added to the MP2 Savings account. This pattern continued in Year 2, which is 2021, and will continue for the next three years (2022-2024).
So for the year 2020 of the above MP2 Savings with a total savings amount of PhP 12,000, the account earned a dividend amount of Php 351.90 for that year.
Dividend Earned (Year 1 – 2020) = 5750*6.12%*1 year = PhP 351.90
This means, it earns PhP 351.90 for the PhP 12,000 total savings. And, since this account chooses an end-term dividend payout, the accumulated total savings at the end of Year 1 is PhP 12,351.90.
Accumulated Value (end of Year 1 – 2020) = 12,000 + 351.90 = PhP 12,351.90
New to Pag-IBIG MP2 Savings?
“If you’re new to Pag-IBIG MP2 Savings, it’s a program offered by Pag-IBIG to their members that’s voluntary and provides a special savings facility with a maturity of 5 years. By saving as little as
P500, you can earn higher dividends through MP2 Savings. If you want to learn more about MP2, click here.”
Keypoints and Takeaways
MP2 Savings is a unique and optional savings plan offered by Pag-IBIG. It provides a higher dividend compared to the regular Pag-IBIG Savings (P1), and the earned dividend is tax-free and backed by
the government. There are two dividend payout options: annual and five-year end term payout. MP2 is a voluntary savings program, so you can save any amount at any time and are not required to save
every month. It’s recommended to start saving early to accumulate more after the five-year maturity period. Happy savings!
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Section: New Results
Supercomputing for Helmholtz problems
High order methods for Helmholtz problems in highly heterogeneous media
Participants : Théophile Chaumont-Frelet, Henri Calandra, Hélène Barucq, Christian Gout.
The numerical solution of Helmholtz problems set in highly heterogeneous media is a tricky task. Classical high order discretizations fail to handle such propagation media, because they are not able
to capture any of the scales of the velocity parameter. Indeed, they are build upon coarse meshes and therefore, if the velocity parameter is taken to be constant in each cell (through averaging, or
local homogenization strategy), scale information is (at least partially) lost. We propose to overcome this difficulty by introducing a multiscale medium approximation strategy. The velocity
parameter is not assumed to be constant on each cell, but on a submesh of each cell. If the submeshes are designed properly, the medium approximation method is equivalent to a quadrature formula,
adapted to the medium. In particular, we show that this methodology has roughly the same computational cost as the classical finite element method. This new solution methodology has been presented in
a paper under revision. We have performed a mathematical analysis of the multiscale medium approximation techniques to higher order discretization. First, we show that the heterogeneous Helmholtz
problem is well-posed and derive stability estimates with respect to the right hand side, and with respect to variations of the velocity parameter, justifying the use of medium approximation. Those
results are obtained assuming the velocity parameter is monotonous and that the propagation medium is closed by first order absorbing boundary conditions. However, these hypothesis are not mandatory
to discretize the problem. Second, we turn to the analysis of finite element schemes with subcell variations of the velocity. In particular, we show that even if the solution can be rough inside each
cell because of velocity jumps, we are able to extend the asymptotic error estimates obtained in [93] to heterogeneous media with non-matching mesh in case of elements of order $1\le p\le 3$. Third,
we investigate numerically the stability of the scheme when the frequency is increasing to figure out optimal meshing conditions. We show that in simple media, the optimal homogeneous pre-asymptotic
error estimates are still valid. However, in more complex cases, it looks like this condition is not sufficient anymore. Apart from showing that the homogeneous results are not always applicable to
the heterogeneous Helmholtz equation, we are not able to give a clear answer to the question. Finally, we are able to conclude that high order methods are actually interesting: in our examples, $p=4$
discretizations always yield a smaller linear system than lower order discretizations for the same precision.
Hybridizable Discontinuous Galerkin method for the elastic Helmholtz equations
Participants : Marie Bonnasse-Gahot, Henri Calandra, Julien Diaz, Stéphane Lanteri.
In the framework of the PhD thesis of Marie Bonnasse-Gahot, we have proposed an hybridizable discontinuous Galerkin method for solving the anisotropic elastodynamics wave equations in harmonic
domain, in two and three dimensions. The method was implemented in Hou10ni and in the platform of Total. We have analyzed the performance of the proposed method in 2D on simple test case and compared
it to classical DG methods. We have shown that the HDG method provides a more accurate solution for less computational cost provided that the order is high enough. We have illustrated the usefulness
of the $p$-adaptivity in 2D, which allows to reach the accuracy of a global method of degree $p$ for the costs of a global method of degree $p-1$ or $p-2$. This feature is already implemented in the
3D code. We now have to determine an accuracy criteria for assigning an order to a given cell, similar to the criteria we proposed in 2D.
For the numerical analysis of the scheme, we have shown that the HDG method could be rewritten as an upwind fluxes DG method and one of our perspectives is to use this equivalence in order to perform
a dispersion analysis following the work of Ainsworth, Monk and Muniz [64] .
We have shown that HDG could be used for 2D simulation on geophysical benchmark, and we will now implement the method in a Reverse Time Migration software, the ultimate goal being to couple HDG
method with a full waveform inversion solver. In order to tackle more realistic test cases in 3D, it will be mandatory to improve the linear solver and we are now considering the use of an hybrid
solver such as Maphys developed by the Inria team-project HIEPACS.
The results of this work have been presented at the “SIAM Conference on Geosciences” [48] and at the “Oil and Gas HPC Workshop” [49] .
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Solution to Tie-Ropes by codility
28 Jul
Question: https://codility.com/demo/take-sample-test/tie_ropes
Question Name: Tie-Ropes or TieRopes
Solution to Tie-Ropes by codility
1 def solution(K, A):
2 # The number of tied ropes, whose lengths
3 # are greater than or equal to K.
4 count = 0
5 # The length of current rope (might be a tied one).
6 length = 0
7 for rope in A:
8 length += rope # Tied with the previous one.
9 # Find a qualified rope. Prepare to find the
10 # next one.
11 if length >= K: count += 1; length = 0
12 return count
15 Replies to “Solution to Tie-Ropes by codility”
1. Hey Sheng,
codility expected N space complexity. My solution is the same as yours (1), yet I am a bit skeptical about the proof of correctness.
Are you sure that it offers the best possible solution?
□ Hello Martin! Nice to see you again!
I cannot make sure that, our solution is the best one. But I think it shoud be the right one.
Consider FINALLY there are N minimum-length (means if we can remove the first or last tied rope, try to remove the last one firstly and then try to remove the first) AND qualified (means
larger than or equal to K) ropes (tied or not, does not matter), and we SHIFT these ropes as leftward as they can. Then we can see each qualified rope (QR) has a heading useless rope (ULR,
might be none). One QR with its ULR is a section.
(During the shifting, we cannot get more qualified ropes. Because we assume FINALLY there are N.)
sum(ULR) or sum(ULR + part of QR) will be less than K, because the QR cannot be moved toward left anymore. And QR + ULR is larger than or equal to K, because QR is already large enough.
Using our algorithm, we scan from left to right. So firsly we scan the zone in ULR, and cannot get a qualified rope. When we tied the ULR and QR together, we get the whole section as a
qualified rope.
The proof is not strict. But hope it be helpful!
2. Given this input A = [1,1,1,2,2,2] , K = 3, above solution returns 2, but 3 is the right answer (we have 3 couples of (1,2) ). I think greedy cannot turn out the right answer in some cases.
□ I think you did not read the challege carefully :-): two adjacent ropes can be tied together with a knot.
We do not have tree couples of adjacent (1,2).
☆ Ah hah, i was mistaken. Thank you for your reply. 🙂
○ You are welcome! And enjoy coding!
☆ I forgot the adjacent part! then it is easy to solve!
3. I got another solution for this problem in VB.NET
□ Please read the “Guideline for Comments” before posting any commment! Thanks!
4. I feel suspicious with greedy algorithms w/o mathematical proof for the correctness of the algorithm.
Here is my solution that seems semantically different than the shorter one you provided.
4 def solution(k,A):
cnt = 0
5 previousNotLenght=0
for x in A:
6 if x >=k:
7 previousNotLenght=0
elif previousNotLenght+x >=k:
8 cnt+=1
previousNotLenght = 0
9 else:
10 return cnt
□ It’s true that I cannot prove it. While the question belongs to the chapter “Greedy Algorithms”, it’s reasonable to have a greedy solution 🙂
5. Hello!
I dont know why but my first intuition was to sort the ropes first. But then i was getting 25% on codility. Is it because sorting (for examples descending) will get minimum not maximum number of
□ From the challenge description: Two adjacent ropes can be tied
Sorting breaks the order. Please keep in mind that only “adjacent ropes” can be tied.
6. Input: (3, [1, 2])
Actual: 1
Expected: 2
Please explain ?
□ Please re-read the question: given an integer K and a non-empty array A of N integers, returns the maximum number of ropes of length greater than or equal to K that can be created.
from [1, 2], we can only create ONE rope (as 1 + 2 = 3), whose length is equal to K (3)
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47 research outputs found
We consider a one-dimensional model of an intermittent search process in a medium exhibiting frozen disorder. A tracer, searching for Poisson-distributed targets, alternates diffusive and ballistic
motions, but can only find a target when diffusing. Preliminary theoretical results [1] are now confirmed, completed and extended, and their derivations are presented for the first time. We study the
mean search time T according to the laws of the searcher waiting times in the diffusive and ballistic regimes. In particular, we obtain a lower bound of T , which in certain circumstances is also an
approximation and is valid for a very broad class of waiting time distributions. Explicit results and other approximations are presented in the case of exponential waiting times, and we study the
optimization of T , depending on the mean durations of the diffusive and ballistic phases. Theoretical formulae are supported by numerical simulations. We show that the intermittent behaviour can
allow one to minimize the search time in comparison with the purely diffusive behaviour, and that it is possible, by an adequate choice of the parameters, to increase very significantly the
efficiency of the search
We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain, for a molecule alternating phases of surface diffusion on the domain boundary
and phases of bulk diffusion. The presented approach is based on an integral equation which can be solved analytically. Numerically validated approximation schemes, which provide more tractable
expressions of the mean first-passage time are also proposed. In the framework of this minimal model of surface-mediated reactions, we show analytically that the mean reaction time can be minimized
as a function of the desorption rate from the surface.Comment: to appear in J. Stat. Phy
This review examines intermittent target search strategies, which combine phases of slow motion, allowing the searcher to detect the target, and phases of fast motion during which targets cannot be
detected. We first show that intermittent search strategies are actually widely observed at various scales. At the macroscopic scale, this is for example the case of animals looking for food ; at the
microscopic scale, intermittent transport patterns are involved in reaction pathway of DNA binding proteins as well as in intracellular transport. Second, we introduce generic stochastic models,
which show that intermittent strategies are efficient strategies, which enable to minimize the search time. This suggests that the intrinsic efficiency of intermittent search strategies could justify
their frequent observation in nature. Last, beyond these modeling aspects, we propose that intermittent strategies could be used also in a broader context to design and accelerate search
processes.Comment: 72 pages, review articl
The cell cytoskeleton is a striking example of "active" medium driven out-of-equilibrium by ATP hydrolysis. Such activity has been shown recently to have a spectacular impact on the mechanical and
rheological properties of the cellular medium, as well as on its transport properties : a generic tracer particle freely diffuses as in a standard equilibrium medium, but also intermittently binds
with random interaction times to motor proteins, which perform active ballistic excursions along cytoskeletal filaments. Here, we propose for the first time an analytical model of transport limited
reactions in active media, and show quantitatively how active transport can enhance reactivity for large enough tracers like vesicles. We derive analytically the average interaction time with motor
proteins which optimizes the reaction rate, and reveal remarkable universal features of the optimal configuration. We discuss why active transport may be beneficial in various biological examples:
cell cytoskeleton, membranes and lamellipodia, and tubular structures like axons.Comment: 10 pages, 2 figure
It has long been appreciated that transport properties can control reaction kinetics. This effect can be characterized by the time it takes a diffusing molecule to reach a target -- the first-passage
time (FPT). Although essential to quantify the kinetics of reactions on all time scales, determining the FPT distribution was deemed so far intractable. Here, we calculate analytically this FPT
distribution and show that transport processes as various as regular diffusion, anomalous diffusion, diffusion in disordered media and in fractals fall into the same universality classes. Beyond this
theoretical aspect, this result changes the views on standard reaction kinetics. More precisely, we argue that geometry can become a key parameter so far ignored in this context, and introduce the
concept of "geometry-controlled kinetics". These findings could help understand the crucial role of spatial organization of genes in transcription kinetics, and more generally the impact of geometry
on diffusion-limited reactions.Comment: Submitted versio
We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain, for a molecule alternating phases of surface diffusion on the domain boundary
and phases of bulk diffusion. We generalize the results of [J. Stat. Phys. {\bf 142}, 657 (2011)] and consider a biased diffusion in a general annulus with an arbitrary number of regularly spaced
targets on a partially reflecting surface. The presented approach is based on an integral equation which can be solved analytically. Numerically validated approximation schemes, which provide more
tractable expressions of the mean first-passage time are also proposed. In the framework of this minimal model of surface-mediated reactions, we show analytically that the mean reaction time can be
minimized as a function of the desorption rate from the surface.Comment: Published online in J. Stat. Phy
DNA looping mediated by the Lac repressor is an archetypal test case for modeling protein and DNA flexibility. Understanding looping is fundamental to quantitative descriptions of gene expression.
Systematic analysis of LacIâ ąDNA looping was carried out using a landscape of DNA constructs with lac operators bracketing an A-tract bend, produced by varying helical phasings between operators and
the bend. Fluorophores positioned on either side of both operators allowed direct Förster resonance energy transfer (FRET) detection of parallel (P1) and antiparallel (A1, A2) DNA looping topologies
anchored by V-shaped LacI. Combining fluorophore position variant landscapes allows calculation of the P1, A1 and A2 populations from FRET efficiencies and also reveals extended low-FRET loops
proposed to form via LacI opening. The addition of isopropyl-ÎČ-d-thio-galactoside (IPTG) destabilizes but does not eliminate the loops, and IPTG does not redistribute loops among high-FRET
topologies. In some cases, subsequent addition of excess LacI does not reduce FRET further, suggesting that IPTG stabilizes extended or other low-FRET loops. The data align well with rod mechanics
models for the energetics of DNA looping topologies. At the peaks of the predicted energy landscape for V-shaped loops, the proposed extended loops are more stable and are observed instead, showing
that future models must consider protein flexibility
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Hamiltonian, geometric momentum and force operators for a spin zero particle on a curve: physical approach
European Physical Journal Plus, vol.139, no.6, 2024 (SCI-Expanded)
• Publication Type: Article / Article
• Volume: 139 Issue: 6
• Publication Date: 2024
• Doi Number: 10.1140/epjp/s13360-024-05342-5
• Journal Name: European Physical Journal Plus
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC
• TED University Affiliated: Yes
The Hamiltonian for a spin zero particle that is confined to a 1D curve embedded in the 3D space is constructed. Confinement is achieved by starting with the particle living in a small tube
surrounding the curve, and assuming an infinitely strong normal force that squeezes the thickness of the tube to zero, eventually pinning the particle to the curve. We follow the new approach that we
applied to confine a particle to a surface, in that we start with an expression for the 3D momentum operators whose components along and normal to the curve directions are separately Hermitian. The
kinetic energy operator expressed in terms of the momentum operator in the normal direction is then a Hermitian operator in this case. When this operator is dropped and the thickness of the tube
surrounding the curve is set to zero, one automatically gets the Hermitian curve Hamiltonian that contains the geometric potential term as expected. It is demonstrated that the origin of this
potential lies in the ordering or symmetrization of the original 3D momentum operators in order to render them Hermitian. The Hermitian momentum operator for the particle as it is confined to the
curve is also constructed and is seen to be similar to what is known as the geometric momentum of a particle confined to a surface in that it has a term proportional to the curvature that is along
the normal to the curve. The force operator of the particle on the curve is also derived, and is shown to reduce, for a curve with a constant curvature and torsion, to a -apparently- single component
normal to the curve that is a symmetrization of the classical expression plus a quantum term. All the above quantities are then derived for the specific case of a particle confined to a cylindrical
helix embedded in 3D space.
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Wireless Remote Monitor and Controller
Based on the work of Ibenson with the TLG10UA03, I've developed a generic PCB to allow building fully engineered web accessible monitoring and controlling applications.
The sample code provided in the next post is designed to work on an AXE401 for development rather than the version for the PCB but the only differences are the port assignments.
The example code uses one DS18B20 as a remote thermostat. The themostat temperature can be set remotely and the web page displays the current temperature as well as the max/min which can be reset
remotely. The code uses serin/serout to talk to the UART but the PCB connects using the HW RX/TX pins so hardware serial comms can be used as required.
The PCB takes a 20 pin picaxe and allows direct connection of the TLG10UA03 wifi card and has up to 6 off 3-pin ports for flexible I/O (input or output with optional pullups and series resistors) as
well as a 4-pin i2c port with built in pull-ups. The ports have power and ground supplied. The board uses one of the cheap and readily available LM2596 Low Ripple DC-DC Converter Step Down Power
Supply modules which can be set to the preferred bus voltage, 3.3V in the case of boards using the TLG10UA03 wifi card, allowing the use of any DC supply up to 40V without worrying about overheating
a linear regulator. All components are through hole except the resistors where the large ansd easily soldered 1206 SMD parts are used.
A ICSP port is also available if you want to use a raw PIC rather than a picaxe. A relay drive is provided using a BCX38c (or 2n2222 etc.) with the relay positive power selectable between the input
voltage or the bus voltage.
The PCB is about 50mm X 70mm and is shown in a home produced 3D printed box with a 16A mains relay connected in a second isolated "printed" box.
The TLG10UA03 set up is simple, starting from its default, the communication type is set to TCP server and the wifi is set up to talk with your router. I then use dyndns.org to set up a web address
that links to the dynamic IP address supplied by my ISP. The router is then set to port forward an external port to the wifi uart (50000 is the default)
Being lazy, I buy the DS18B20 ready wired and sealed from Sure Electronics. These can then be used indoor or out and are available with lead lengths up to 10m.
The circuit shown in the schematic is my V1.0. It was developed in DesignSpark and the PCBs were made by IteadStudio.
I've subsequently improved the circuit design to allow a 14M2 or 20-pin picaxe and optional RC filtering of inputs and also to allow the use of an ERF board instead of the wifi uart for local
communications. These boards will also have a 16A relay and power connections on an extension that can be cut off if not required. I'm waiting on the boards to arrive and once tested can publish
details if anyone is interested. I'm also playing with a capacitive dropper power supply to allow direct mains input.
If you want to have a look at the system live you can try
I'll try and leave it up over the next few days. You can press the buttons without fear of anything bad happening
Any questions or comments appreciated as always.
Last edited:
#picaxe 28X2
' Ports to use AXE401 as test platform
setfreq em64
symbol thermo_range_start=17 'start of thermostat range in degC
symbol hysteresis = 2 '2/10ths degree
symbol seroutport=c.6 'TX port
symbol serinport=c.7 'RX port
symbol heaterport=c.3 'Relay Drive - enable LED to see output
symbol temperatureport=c.4 'used for DS18B20
symbol DS18B20power = c.2 'used for DS18B20 VCC pin
symbol positive=0
symbol negative=1
symbol hoff=0
symbol hon=1
symbol baudrate=t9600_64
symbol onesecond = 8000
symbol fourseconds = 32000
' Variable usage
symbol sign =bit0
symbol heater=bit1
symbol i = b1
symbol word1 = w1 '-32768 to 32767
symbol byte1 = b2 '-128 to 127
symbol byte2 = b3
symbol word2 = w2
symbol byte3 = b4
symbol byte4 = b5
symbol bytearray = 6 'address of space for bintoascii, reserve 7 bytes b6-b13
symbol loopCounter = b14
symbol value = b15
symbol loopconvert=b16
symbol commandinput=b17
symbol setpoint = w9
symbol ii=b20
symbol type = b21
symbol currenttemp=w11
symbol wordsave=w12
eeprom 0,(255,255,255,255,255,255) ' set invalid status after programming
symbol valuelocation=0
Symbol maxlocation=2
symbol minlocation=4
high DS18B20power
low heaterport
pause onesecond
read valuelocation,value ' get the saved thermostat setting
if value<"A" or value>"L" then: value="A":write valuelocation,value:endif 'if invalid set to off
readtemp12 temperatureport,currenttemp 'temperature as signed word * 16
currenttemp=currenttemp+1000 ' make sure it is always positive
read maxlocation,word word1 'read in the save max and min temperatures
if word1=65535 then: write maxlocation,word currenttemp:endif 'if invalid set to current
read minlocation,word word1
if word1=65535 then: write minlocation,word currenttemp:endif
owout temperatureport,%1001,($CC,$44) 'start the background temperature read
commandinput = 0: type =0 'set to no input
serin [fourseconds,skip], serinport, baudrate,("GET"), ii, ii, commandinput,ii,type,ii,value
sertxd(commandinput," ",type," ",value,cr,lf)
select commandinput
case " " 'normal read of web page with no data input
gosub sendHeader
gosub updateheater
serout seroutport, baudrate,("Content-Length: 1772",cr,lf,cr,lf)
gosub sendBeginning
gosub sendEnding
case "d" ' data returned
gosub sendHeader
if type="R" then:write valuelocation,value:endif 'change in thermostat value
gosub updateheater
if type="C" then 'reset of max/min
write maxlocation,word currenttemp
write minlocation,word currenttemp
serout seroutport, baudrate,("Content-Length: 1772",cr,lf,cr,lf)
gosub sendBeginning
gosub sendEnding
gosub sendHeader
serout seroutport, baudrate,("Content-Length: 40",cr,lf,cr,lf)
serout seroutport, baudrate,("<html><body>Page Not Found</body></html>",cr,lf,cr,lf)
pause onesecond 'allow the temperature read to complete
owout temperatureport,%0001,($CC,$BE)
owin temperatureport,%0000,(byte1,byte2) ; read in temperature
word1=word1+1000' make sure it is always positive
currenttemp=word1 'set the current temperature
read maxlocation, word word1
if currenttemp>word1 then:write maxlocation,word currenttemp:endif
read minlocation,word word1
if currenttemp<word1 then:write minlocation,word currenttemp:endif
gosub updateheater 'update the heater even when no input
word1=currenttemp-1000 '
gosub multsignedword 'temperature as signed word * 160
gosub divsignedword 'temperature * 10
read valuelocation,value
if value="L" then: high heaterport:heater=hon:endif
if value="A" then: low heaterport :heater=hoff:endif
if value>="B" and value<="K" then
setpoint=value-"B"+thermo_range_start*10 'setpoint * 10
setpoint = setpoint + hysteresis
if word1>setpoint then: low heaterport: heater=hoff:endif
setpoint = setpoint - hysteresis - hysteresis
if word1<setpoint then: high heaterport: heater=hon:endif
serout seroutport, baudrate,("HTTP/1.1 200 OK",cr,lf)
serout seroutport, baudrate,("Content-type: text/html",cr,lf)
serout seroutport, baudrate,("Connection: close",cr,lf)
serout seroutport, baudrate,("<html><head><title>Demo Monitor</title></head><body>")
serout seroutport, baudrate,("<form name='f1' method='get' action='d'>")
serout seroutport, baudrate,("<h2 align='left'>Demo Monitor V2.0</h2>",cr,lf)
serout seroutport, baudrate,("<p><TABLE BORDER='1' CELLSPACING='0' CELLPADDING='5'>")
serout seroutport, baudrate,("<TR><TD>Heating</TD>")
if heater = hon then : serout seroutport, baudrate,("<TD BGCOLOR='#ff0000'> On</TD></TR>"):endif
if heater = hoff then : serout seroutport, baudrate,("<TD BGCOLOR='#00ff00'>Off</TD></TR>"):endif
serout seroutport, baudrate,("</TABLE></p>")
serout seroutport, baudrate,("<p><TABLE BORDER='1' CELLSPACING='0' CELLPADDING='5'>")
serout seroutport, baudrate,("<TR><TD></TD><TD>Temperature</TD></TR>")
serout seroutport, baudrate,("<TR><TD>Current</TD><TD>")
gosub outputtemp
serout seroutport, baudrate,("<TR><TD>Max</TD><TD>")
read maxlocation,word word1
gosub outputtemp
serout seroutport, baudrate,("<TR><TD>Min</TD><TD>")
read minlocation,word word1
gosub outputtemp
serout seroutport, baudrate,("</TABLE></p>")
serout seroutport,baudrate,("<input name='C' type='checkbox' value='R' onClick='this.form.submit()'> Reset Max/Min")
serout seroutport, baudrate,("<p><TABLE BORDER='1' CELLSPACING='0' CELLPADDING='5'>")
serout seroutport, baudrate,("<TR><TD>Thermostat</TD>")
for loopCounter = "A" to "L"
if loopCounter=value then
serout seroutport, baudrate,("<TD><input name='R' type='radio' checked='checked' value='",loopcounter)
serout seroutport, baudrate,("<TD><input name='R' type='radio' value='",loopcounter)
serout seroutport, baudrate,("' onClick='this.form.submit()'> ")
bintoascii loopconvert,b6,b7,b8
if loopcounter>"A" and loopcounter<="K" then
if b7<>"0" then
serout seroutport,baudrate, (b7,b8,"°C<br></TD>")
serout seroutport,baudrate, (" ",b8,"°C<br></TD>")
if loopcounter="A" then : serout seroutport,baudrate, ("Off<br></TD>") :endif
if loopcounter="L" then : serout seroutport,baudrate, ("On<br></TD>") :endif
next loopCounter
serout seroutport, baudrate,("</TR></TABLE></p>")
serout seroutport, baudrate,("</form></body></html>",cr,lf,cr,lf,"1234567890")
' signed arithmetic
' NB add and subtract can be used as normal
' the distinction between + and - is made at the output formatting stage
'Function multsignedword(word1 As Word, word2 As Word) As Word
'multiply word1 by word2 and return the result in word1
sign = positive
If word1 >= $8000 Then
sign = Not sign
word1 = -word1
If word2 >= $8000 Then
sign = Not sign
word2 = -word2
word1 = word1 * word2
If sign = negative Then
word1 = -word1
'Function divsignedword(word1 As Word, word2 As Word) As Word
'divide word1 by word2 and return the result in word1
sign = positive
If word1 >= $8000 Then
sign = Not sign
word1 = -word1
If word2 >= $8000 Then
sign = Not sign
word2 = -word2
word1 = word1 / word2
If sign = negative Then
word1 = -word1
'Proc signedwordtoasciix10
' returns a byte array starting at pointer bytearray terminated by a null
' of the numberin word1 which is 10x the actual value to give value in 1/10ths
' the number is stripped of leading zeroes
bptr = bytearray
If word1 >= $8000 Then
sign= negative
word1 = -word1
bintoascii word1,@bptrinc,@bptrinc,@bptrinc,@bptrinc,@bptr
@bptr=0 'denotes end of string with a null
bptr = bytearray
if @bptrinc="0" then ' at least one leading zero
if @bptrinc="0" then ' at least two leading zeros
if @bptrinc="0" then ' at least three leading zeros
for i= byte1 to byte2 'now move array (including trailing null) left by the number of leading zeroes
next i
if sign=negative then
for i= byte2 to byte1 step -1 'now move array (including trailing null) left by the number of leading zeroes
next i
for i= byte2 to byte1 step -1 'now move array (including trailing null) left by the number of leading zeroes
next i
@bptr=" "
outputtemp: 'take temp to be output in word1
gosub multsignedword 'temperature as signed word * 160
gosub divsignedword 'temperature * 10
gosub signedwordtoasciix10
serout seroutport,baudrate,(loopconvert)
loop while loopconvert<>0
serout seroutport, baudrate,("°C</TD></TR>")
Nice design. The TLG10UA03 is an enabling little device. All very compact in your diy-printed box. Like the web page, too.
I'm waiting on the boards to arrive and once tested can publish details if anyone is interested.
View attachment 15900View attachment 15901
Hi, this looks great. I am looking forward to when you post the schematics and code of the latest version.
I am interested in making the Ciseco XRF 900 MHZ wireless RF receiver circuit that can detect the signal broadcast from Collett Communications Snowmobile Groomer Warning Beacon (GWB) device that
transmit at 900 MHZ - Channel 1 to illuminate an LED to provide a heads up as to the potential danger of a grooming in the vicinity while traveling the snowmobile trails.
What GWB signal information do I need to configure this radio or would it be plug and play to receive the (GWB) signal on Channel 1? Also what is required to convert the reception of the GWB only
signal to trigger an LED warning light to alert me that a snowmobile groomer is in the area to avoid a collision?
Thanking you in advance,
Paul Wilkie - Volunteer
Wellston, MI 49689
Wellston Winter Trails and Promotions
Located in the heart of the beautiful Manistee National Forest
You might want to start a new thread for this in the Active forum, rather than tacking on to a completed project.
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On Computing the Multidimensional Scalar Multiplication on Elliptic Curves
Paper 2024/038
On Computing the Multidimensional Scalar Multiplication on Elliptic Curves
A multidimensional scalar multiplication ($d$-mul) consists of computing $[a_1]P_1+\cdots+[a_d]P_d$, where $d$ is an integer ($d\geq 2)$, $\alpha_1, \cdots, \alpha_d$ are scalars of size $l\in \
mathbb{N}^*$ bits, $P_1, P_2, \cdots, P_d$ are points on an elliptic curve $E$. This operation ($d$-mul) is widely used in cryptography, especially in elliptic curve cryptographic algorithms. Several
methods in the literature allow to compute the $d$-mul efficiently (e.g., the bucket method~\cite{bernstein2012faster}, the Karabina et al. method~\cite{hutchinson2019constructing, hisil2018d,
hutchinson2020new}). This paper aims to present and compare the most recent and efficient methods in the literature for computing the $d$-mul operation in terms of with, complexity, memory
consumption, and proprieties. We will also present our work on the progress of the optimisation of $d$-mul in two methods. The first method is useful if $2^d-1$ points of $E$ can be stored. It is
based on a simple precomputation function. The second method works efficiently when $d$ is large and $2^d-1$ points of $E$ can not be stored. It performs the calculation on the fly without any
precomputation. We show that the main operation of our first method is $100(1-\frac{1}{d})\%$ more efficient than that of previous works, while our second exhibits a $50\%$ improvement in efficiency.
These improvements will be substantiated by assessing the number of operations and practical implementation.
Available format(s)
Publication info
Contact author(s)
haddajiwalid95 @ gmail com
ubna ghammam @ itk-engineering de
nadia elmrabet @ emse fr
leila benabdelghani @ fsm rnu tn
2024-03-28: last of 2 revisions
2024-01-09: received
Short URL
author = {Walid Haddaji and Loubna Ghammam and Nadia El Mrabet and Leila Ben Abdelghani},
title = {On Computing the Multidimensional Scalar Multiplication on Elliptic Curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2024/038},
year = {2024},
url = {https://eprint.iacr.org/2024/038}
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Cite as
Huck Bennett, Karthik Gajulapalli, Alexander Golovnev, and Evelyn Warton. Matrix Multiplication Verification Using Coding Theory. In Approximation, Randomization, and Combinatorial Optimization.
Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 42:1-42:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
Copy BibTex To Clipboard
author = {Bennett, Huck and Gajulapalli, Karthik and Golovnev, Alexander and Warton, Evelyn},
title = {{Matrix Multiplication Verification Using Coding Theory}},
booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
pages = {42:1--42:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-348-5},
ISSN = {1868-8969},
year = {2024},
volume = {317},
editor = {Kumar, Amit and Ron-Zewi, Noga},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.42},
URN = {urn:nbn:de:0030-drops-210352},
doi = {10.4230/LIPIcs.APPROX/RANDOM.2024.42},
annote = {Keywords: Matrix Multiplication Verification, Derandomization, Sparse Matrices, Error-Correcting Codes, Hardness Barriers, Reductions}
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Kanubhai Patel
Amit Kanubhai Patel
Associate Professor, Department of Mathematics, Colorado State University
217 Weber Hall
Louis R. Weber Building
1874 Campus Delivery
Fort Collins, CO 80523
I was born in Chicago. I did my BS and MS at the University of Illinois at Urbana-Champaign. I did my PhD at Duke University. All three degrees are in computer science, but I am a mathematician!
Currently, my research sits at the intersection of pure and applied algebraic topology, algebraic combinatorics (Rota’s way), and category theory. I like to use category theory to organize my
thoughts and ask precise questions.
I help run CSU Topology Seminar.
1. Advances
Persistent local systems
Advances in Mathematics, 2021
1. JACT
Generalized persistence diagrams
Journal of Applied and Computational Topology, Jun 2018
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Depth image compression by colorization for Intel® RealSense™ Depth Cameras
Authors: Tetsuri Sonoda, Anders Grunnet-Jepsen
Rev 1.0
This article is also available in PDF format
Fig. 1 Left: Original depth image of D435. Center: Colorized depth image with JPG compression. Right: Recovered depth image from colorized and JPG compressed depth
Compression of RGB images is today a relatively mature field with many impressive codecs available to choose from that can achieve high compression ratios for lossless and lossy compression. However,
for 3D depth images, the field is not as developed, although the goal remains the same – to compress both still- and moving- images in order to reduce system bandwidth and storage space requirements.
In this white paper, we introduce a method by which depth from Intel RealSense depth cameras can be compressed using standard codecs, with the potential for 80x compression. Our approach is based on
colorizing the depth image in a way that best reduces depth compression artefacts. We will define some key performance metrics, compare results obtained with different compression codecs, and
introduce a post-processing technique that helps mitigate some of the worst depth artefacts.
1. Introduction
The Intel RealSense Depth Camera, D400 series can output high-resolution depth image up to 1280 x 720 with 16-bit depth resolution [1]. In order to efficiently store such high-resolution images in a
limited disk space or to minimize the transmission bandwidth, an appropriate compression technique is required. Several novel compression techniques have been suggested in literature, and good
performance can indeed be achieved, for example, by approximating a depth value by a plane divided by a quad tree [2]. However, when such unique algorithms are used, it necessitates custom
proprietary software for compression and decompression, and it tends to not be able to leverage hardware acceleration blocks that already exist on many compute platforms.
In this paper, we propose a simple colorization method for depth images. By appropriately colorizing the depth image, the depth image can subsequently be treated as a normal RGB image which can
easily be compressed, stored, and transmitted using widely available HW and software tools. We will describe this approach in more detail below, where we will cover 1. the colorization and recovery
methods, 2. an application example of compression using a lossy image codec, and 3. various considerations that need to be made to ensure optimal results.
2. Depth image colorization
Intel RealSense D400 and SR300 series depth cameras output depth with 16-bit precision. We can convert this to an RGB 24 bits color image by colorization, but the exact mapping can be very important.
We recommend using the Hue color space, as shown in Figure 2, for conversion from depth to the color image. This Hue color space has 6 gradations in the up and down directions of R, G, and B, and has
1529 discrete levels, or about 10.5 bits. Furthermore, since one of the colors is always 255, the image never becomes too dark. This has the benefit of ensuring that details are not lost by some of
the lossy compression schemes described later.
Fig. 2 Hue color bar used to map depth to color
2.1 Uniform colorization and inverse colorization
The proposed colorization process imposes the limitation of needing to fit a 16-bit depth map into a 10.5-bit color image. We recommend performing the colorization only after first limiting the depth
range to a subset of the full depth 0 ~ 65535 range, and re-normalizing it. The depth range can, for example, be determined by windowing it to between a minimum depth value dmin and a maximum depth
value dmax. The greater the depth range, the coarser the quantization of the depth value becomes. There are two methods for this colorization: uniform colorization which directly converts the depth
value, and inverse colorization which converts the disparity value (which is the reciprocal of the depth value). Uniform colorization quantizes the entire depth range uniformly. In inverse color
colorization, quantization is finer at closer depths and coarser at longer depths. Inverse colorization is particularly well suited to depth cameras, like the D400 series, that derive depth from
triangulation, which inherently has an inverse relationship between resolution and distance away.
The colorization proceeds as follows: Each color of the uniformly colorized pixel pr, pg and pb should be determined by the following equation, where the input depth value of the target depth image
is d.
Equation 1
Alternatively, when using the depth disparity map, the with disparity values, disp, the dnormal above is replaced by the following equation:
Equation 2
Fig. 3 Left: Uniformly colorized depth image. Right: Inverse colorized depth image
By performing the above conversion on all pixels, it is possible to colorize the target depth image, as shown in Figure 3 for each approach. Lossless or lossy compression for RGB images can now be
applied to these colorized depth images, allowing them to be stored in smaller files and transmitted over the network with lower bandwidth.
2.2 Depth image recovery from colorized depth image
To use a colorized depth image after it has been compressed, stored/transmitted, and then uncompressed, it must be converted back to a depth map image. Each color of each pixel p of the colorized
depth image is represented by prr, prg, and prb, and the restored depth value drecovery of the pixel can then be obtained by the equation below. When restoring the depth map, the shortest depth dmin
and the longest depth dmax used for colorization the depth image are required as input parameters.
Equation 3
For inverse colorized depth images, the recovered depth value drecovery of the pixel pr is expressed by the following equation:
Equation 4
Fig. 4 Left: Point cloud using depth image recovered from uniformly colorized depth image.
Right: Point cloud using depth image recovered from inverse colorized depth image.
Depth range is set to 0.3-16m
By performing the above conversion for all pixels, the depth image can be recovered, as shown in Figure 4. The image quality improvement of using disparity instead of depth, i.e. the inverse
colorized depth, is clearly evident in Figure 4, for objects that are near. The recovered depth values appear to be more quantized when using the uniformly colorize approach, however, results can be
improved dramatically if the uniform depth range is limited to say, 0.3m to 2m.
This depth image restoration is in principle independent of whether a lossless compression is used, such as PNG, or a lossy compression is used, such as JPG and MP4 etc. However, when recovering
depth after lossy compression, it is very common to see “flying pixels” generated at the boundary of discontinuous depth values. In this case removal by post-processing will be required.
In the following section we will go into more details about how we have integrated colorization and recovery into the Intel RealSense SDK 2.0, and also how post-processing of depth images can be used
to minimize the flying pixel artefacts.
3. How to colorize depth images and recover colorized depth images in C++
We describe here an examples of C++ programs for colorizing a depth image and for restoring a depth value from the colorized depth image. Colorizing of depth images is implemented as a
post-processing filter in the Intel RealSense SDK 2.0 [3] and can be easily enabled. Figure 5 shows the Intel RealSense Viewer and the controls under Depth Visualization for selecting HUE and the min
and max distance.
Fig. 5 The Intel RealSense Viewer showing how to select HUE color scheme for visualization, as well as range defined by dmin and dmax.
The colorization, compression (by JPG) and recovery example project using OpenCV [4] can be downloaded from [5].
3.1 Colorize depth images in C++ with the Intel RealSense SDK 2.0
Colorization is enabled with the following C++ code. The Colorization function is implemented as an SDK post-processing filter and is applied to the frame obtained from the pipeline.
bool is_disparity = false;
// pipeline start
rs2::pipeline pipe;
// declare filteres
rs2::threshold_filter thr_filter; // Threshold - removes values outside recommended range
rs2::colorizer color_filter; // Colorize - convert from depth to RGB color
rs2::disparity_transform depth_to_disparity(true); // Converting depth to disparity
rs2::frameset frames = pipe.wait_for_frames(); // Wait for next set of frames from the camera
rs2::frame filtered; //Take the depth frame from the frameset
// apply post processing filters
filtered = frames.get_depth_frame();
filtered = thr_filter.process(filtered);
filtered = depth_to_disparity.process(filtered);
if (!is_disparity) { filtered = disparity_to_depth.process(filtered); }
filtered = color_filter.process(filtered);
is_disparity is a flag for switching between uniform colorization and inverse colorization, and when true, inverse colorization is performed using the disparity value. The following codes are used to
specify the minimum depth, maximum depth, and colorization mode required for colorization.
float min_depth = 0.29f;
float max_depth = 10.0f;
// filter settings
thr_filter.set_option(RS2_OPTION_MIN_DEPTH, min_depth);
thr_filter.set_option(RS2_OPTION_MAX_DEPTH, max_depth);
color_filter.set_option(RS2_OPTION_HISTOGRAM_EQUALIZATION_ENABLED, 0);
color_filter.set_option(RS2_OPTION_COLOR_SCHEME, 9.0f); // Hue colorization
color_filter.set_option(RS2_OPTION_MAX_DEPTH, max_depth);
color_filter.set_option(RS2_OPTION_MIN_DEPTH, min_depth);
As described above, when the depth range is set to the minimum range to be used, the quantization error can be reduced in both uniform colorization and inverse colorization. On the other hand, in the
case where the lossy compression is applied, it turns out it is necessary to allow a margin in the depth range to be larger than the actual used range in order to prevent inversion of the depth value
as described later. Note that the Hue color scheme has more quantization levels than other color schemes implemented in Intel RealSense SDK.
3.2 Depth image recovery from colorized depth images in C++
The ability to recover colorized depth images is not currently available in the Intel RealSense SDK 2.0. This is because if a depth image is stored in a file or data is transmitted through a network
is to be recovered, the depth camera may not be directly connected. For this reason, we created instead a stand-alone code example to recover the depth, that can be used independent of the SDK.
Input: unsigned char input_color_data_array RGB 8bit x 3 colorized depth image
Output: unsigned short output_depth_data_array 16bit depth image
// resolution is set to 848 x 480
int _width = 848;
int _height = 480;
bool is_disparity = false;
float min_depth = 0.29f; // to avoid depth inversion, it’s offset from 0.3 to 0.29. Please see Figure 7
float max_depth = 10.0f;
float min_disparity = 1.0f / max_depth;
float max_disparity = 1.0f / min_depth;
unsigned short hue_value = 0; // from 0 to 255 * 6 - 1 = 0-1529 by Hue colorization
unsigned char* in = reinterpret_cast<const unsigned char*>input_color_data_array;
unsigned short* out = reinterpret_cast<unsigned short*>output_depth_data_array;
for (int i = 0; i < _height; i++)
for (int j = 0; j < _width; j++)
unsigned char R = *in++;
unsigned char G = *in++;
unsigned char B = *in++;
unsigned short hue_value = RGBtoD(R, G, B);
if(out_value > 0)
unsigned short z_value = static_cast<unsigned short>((min_depth + (max_depth - min_depth) * hue_value / 1529.0f) + 0.5f);
out++ = z_value;
float disp_value = min_disparity + (max_disparity - min_disparity) * out_value / 1529.0f;
*out++ = static_cast<unsigned short>((1.0f / disp_value) / depth_units + 0.5f);
*out++ = 0;
unsigned short RGBtoD(unsigned char r, unsigned char g, unsigned char b)
// conversion from RGB color to quantized depth value
if (b + g + r < 255)
return 0;
else if (r >= g && r >= b)
if (g >= b)
return g - b;
return (g - b) + 1529;
else if (g >= r && g >= b)
return b - r + 510;
else if (b >= g && b >= r)
return r - g + 1020;
It is important that the values of min_depth and max_depth should be the same as those used for colorization. Of course, if the same logic as described above is applied, restoration can be performed
in an environment other than C++. Also, since each pixel can be calculated independently of other pixels, processing lends itself well to acceleration via multi-threading or GPU.
3.3 Flying Pixels
As described above, when a depth image is restored from a compressed RGB image such as JPG or MP4, flying pixels may appear at the boundaries of discontinuous depth values, i.e. edges or near
occlusions, as shown in Figure 6. The flying pixels tend to show up as a spray of intermediate depth values between the front and back surfaces. Such flying pixels are not readily evident on depth
maps, but they are clearly visible when the depth is viewed as a point cloud and rotated 90 degrees to show the side-view. These flying pixels can be reduced by applying a post-processing filter.
The rs-colorize sample code [5] reduces flying pixels by using a modified median filter (function name: PostProcessingMedianFilter) to exclude pixels having a difference greater than a certain value
between the nearest neighbor and the median value. Other methods include removing a depth value having an extreme depth slope (derivative) with respect to surrounding pixels or removing pixels that
fall adjacent to pixels that do not have a depth value (i.e. next to a depth-map “hole”). When these filters are applied, the tradeoff is that the removal of pixels also reduces the depth fill-factor
and increases the size of depth “holes”. In order to recover some pixels, an additional dilate process can be performed that fills holes with the median value of all adjacent pixels, for example.
However, since this type of simple hole-filling algorithm may lead to false depth values, it is usually better to live with the fewer good pixels, than to dilate and possibly end up with an accurate
depth map.
Fig. 6 These point cloud pictures show the appearance of “Flying pixels” after compression/decompression, and how they can be filtered. Top: Point cloud using uncompressed original depth. Bottom
Left: Point cloud using depth recovered from JPG without modified median filter, showing the appearance of flying pixels near edges. Bottom Right: Point cloud using depth recovered from JPG with
modified median filter. JPG image quality is set to 80. This final image looks very similar to the original image, with the median filter also serving to clean up the depth map and remove flying
There is yet another artefact that needs to be considered. When the depth value exists in the vicinity of the nearest depth or the farthest depth and lossy compression is applied, inversion of the
nearest depth and the farthest depth may occur, as shown in Figure 7. Such inversion can be easily avoided by increasing the depth range (i.e. reducing dmin and increasing dmax) to add a margin with
respect to the actual nearest depth and the farthest depth.
Fig. 7 Example of the “depth-inversion” artefact. Top: Colorized depth image. The box on the hand is very close to the nearest depth = red color. Bottom left: Point cloud using original depth. The
box is correctly displayed on the hand. Bottom right: Point cloud using depth recovered from WebP (image quality is set to 5). The box on the hand is incorrectly displayed at the furthest depth.
4. Compression using image codecs
In order to examine further the effects of applying lossy compression to colorized depth images, a series of measurements were taken to evaluate the depth quality as a function of compression ratio
and compression codec, comparing JPG and WebP.
We start by defining the image quality index as the peak-signal-to-noise-ratio, in decibels. This PSNR is a common metric used to compare the image quality of original and compressed images. The
higher the PSNR the better the quality of the reconstructed image. We also compare before and after images based on fill-factor, the ratio of valid (non-zero) depth pixels to total number of pixels.
A 100% fill-factor means that there are no pixels with undefined depth values.
In the following PSNR comparison, we employ the direct uniform colorization approach. This is because, for inverse colorization, the quantization error of the depth increases quadratically as the
depth increases, so we would need a different image quality metric. Also, since the PSNR value is strongly affected by flying pixels, its value depends very strongly on the scene, where images with
many edges and discontinuities will show much poorer performance. As a result, the PSNR metric should be used to compare the relative performance under the same conditions (i.e. same images), but it
is not well suited to evaluate the generalized performance.
We compared JPG and WebP lossy image compression codecs. The depth range was set to 0.5m to 2m using the uniform colorization scheme. This ensured that 1mm depth steps could be represented without
error by the 1529 available levels. Both codecs allow for adjusting the compression ratio by changing an image quality parameter. WebP has a lossless compression mode, but it was not used here.
Figure 8 shows a plot of the PSNR as a function of the compression ratio. The PSNR is evaluated only in the portion where the depth value exists in both “before” and “after” depth images.
Fig. 8 Compression ratio vs PSNR of colorized depth image using JPG and WebP
For low compression ratios, up to 10x, JPG delivers a good PSNR of over 70dB. (WebP does not allow lower compression ratios). WebP delivers better results at compression ratios above 10x, with PSNR
staying above 70dB for up to 40x compression, for the test scene used. By comparison JPEG drops below 70dB above 15x compression. For both codecs, removing flying pixels with post-processing improves
the PSNR significantly, with JPEG experiencing a boost of almost 10dB for low compression ratios, while WebP improves about 6dB up to 40x compression.
However, post processing does have a direct impact on the fill factor as is shown in Figure 9, which plots the dependence of Fill factor on compression ratio. For both Codecs, the post-processing
reduces the fill factor by about 10%. Note that this is very scene dependent but illustrates the expected trend.
Fig. 9 Compression ratio vs Fill factor of colorized depth image using JPG and WebP
In order to give a better visual impression of what these numbers mean for the point cloud, we show a sequence of images in Figures 10 and 11 that show the point cloud depth quality degradation for
increasing compression ratios for both JPG and WebP codecs.
Fig. 10 Point-Cloud scene showing the recovered point-cloud as a function of JPG compression ratio (vertical), and post processing (horizontal).
Fig. 11 Point-Cloud scene showing the recovered depth as a function of WebP compression ratio (vertical), and post processing (horizontal).
For JPG compression, Figure 10 shows that as the compression ratio is increased, we start to observe discrete steps in all angled surfaces. The core algorithm of JPG consists of performing discrete
cosine transforms (DCT) to each image block in unit of 8×8 pixels. Under highly compressed conditions, we see that blocks are no longer smoothly connected which leads to the appearance of pronounced
depth steps. This is in particularly visible for the highest compression image of 84x, where almost no angled surfaces remain, and we observe block-shapes and overlapping flat planes.
By comparison, WebP performs much better for higher compression ratios than JPG and appears to be much better suited to compression of 3D point clouds in general. We see that even at the highest
compression ratio, 81x used here, we do not observe any step-like artefacts.
However, for WebP for very high compressions ratios (like 81x), it turns out that the color peaks can no longer be maintained around the yellow, cyan, and purple colors in the middle of each primary
color, as seen in the left part of Figure 12 below. This results in the appearance of a different type of depth gap “bandgap” artefact near the boundaries of the respective colors as shown Figure 12
on the right.
Fig. 12 For high compression ratios of WebP, we observe a depth bandgap near the yellow, cyan, and purple colors. Left: Colorized depth image with gray lines representing the yellow, cyan, and purple
color areas. Right: A point cloud (from top view) after WebP compression of the colorized image. Gaps in the depth map (indicated by arrows) appear in the the areas corresponding to the gray lines.
Since these depth bandgaps grow with increasing compression ratio, it is necessary to determine an appropriate compression ratio depending on the required accuracy. Alternatively, a method of
applying a filter that averages only the boundary portion of each color can be considered, although this is out of scope for this paper. Regarding the flying pixels that occur at all compression
ratios, most of them can be removed by applying the above-mentioned post-processing filter.
As described above, the behavior of the depth image at the time of compression varies greatly depending on the codec that is applied. If higher image quality and higher compression ratio are
required, video codecs such as H. 264 and HEVC can also be applied using the same approach as that outlined above for still image codecs. Efficient video codecs allow the transfer of depth images
over the Internet at a greatly reduced bandwidth.
5. Conclusion
We have in this white paper introduced a straightforward method whereby applying a HUE coloring scheme to a depth map is shown to allow depth maps to be compressed using standard HW-accelerated image
compression/decompression codecs, like JPG and WebP. The math behind the colorization and restoration (after compression/decompression) was presented with direct code examples. It was shown that
using direct colorization of depth was well suited for short range spans, such as from 0.5m to 2.0m, but that for ranges spanning from 0m to 65m, colorization of disparity maps was recommended
instead. We showed that compression did tend to introduce “Flying pixel” artefacts near edges of objects, but that they could be reduced significantly with some simple modified median post-processing
filters. The proposed HUE colorization scheme has been integrated into the Intel RealSense SDK. We showed that depth could be inadvertently inverted if min and max depth ranges were chosen to be too
close to actual depth. Finally, by comparing image quality based on PSNR and fill factor metrics, we showed that WebP appears to be the better choice, in particular for large compression ratios.
Compression ratios of 81x were demonstrated that still showed acceptable image quality.
6. References
[1] Intel RealSense Depth Camera D400 Series: https://www.intelrealsense.com/stereo-depth/
[2] Yannick Morvan, Dirk Farin, and Peter H. N. de With "Novel coding technique for depth images using quadtree decomposition and plane approximation", Proc. SPIE 5960, Visual Communications and
Image Processing 2005, 59603I (24 June 2005)
[3] librealsense: https://github.com/IntelRealSense/librealsense
[4] OpenCV: https://opencv.org/
[5] rs-colorization: https://github.com/TetsuriSonoda/rs-colorize
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What year was Charles Steward King of England executed? Couldn't think of another question but from watching the news I came up with this silly question.
P.s Do not google!
^^1649................I can still hear my Indian teacher drumming the line of the stuarts into our heads. :mad:
Ps:- Is that where the tradition of executioners wearing masks came from? Since I believe no one wanted to actually chop his head off :confused:
When was the 13th amendment outlawing slavery in US passed? Getting into black history month
Originally posted by Seeker: Is that where the tradition of executioners wearing masks came from? Since I believe no one wanted to actually chop his head off
I think so. But I guess that the reason why they were masked was because they did not want to be identified to be a regicide (someone who has killed a monarch)because they could put their lives in
When did Hannibal become the leader of The Carthaginians ?
N let continue with da assissanation with theme...when was Che Guevara killed?
Che Guevara,
Che Guevara was killed by Bolivian soldiers in 1967
Those history classes were not a waste after all.
I know I’m been cheeky but until Alexus poses the awaited question I’d like to ask the one below.
When did Hulago take siege of Iraq?
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(eBook PDF) Introduction to Probability by Mark Ward
(eBook PDF) Introduction to Probability by Mark Ward – Digital Ebook – Instant Delivery Download
Product details:
• ISBN-10 : 0716771098
• ISBN-13 : 978-0716771098
• Author: Mark Ward , Ellen Gundlach
Unlike most probability textbooks, which are often written only for the mathematically-oriented students, Mark Ward and Ellen Gundlach’s Introduction to Probability makes the subject much more
accessible, reaching out to a much wider introductory-level audience. Its approachable and conversational style, highly visual approach, practical examples, and step-by-step problem solving
procedures help all kinds of students understand the basics of probability theory and its broad applications in the outside world.
Table contents:
1 Outcomes, Events, and Sample Spaces
2 Probability
3 Independent Events
4 Conditional Probability
5 Bayes Theorem
6 Review of Randomness
7 Discrete Versus Continuous Random Variables
8 Probability Mass Functions and CDFs
9 Independence and Conditioning
10 Expected Values of Discrete Random Variables
11 Expected Values of Sums of Random Variables
12 Variance of Discrete Random Variables
13 Review of Discrete Random Variables
14 Bernoulli Random Variables
15 Binomial Random Variables
16 Geometric Random Variables
17 Negative Binomial Random Variables
18 Poisson Random Variables
19 Hypergeometric Random Variables
20 Discrete Uniform Random Variables
21 Review of Named Discrete Random Variables
22 Introduction to Counting
23 Two Case Studies in Counting24 Continuous Random Variables and PDFs
25 Joint Densities
26 Independent Continuous Random Variables
27 Conditional Distributions
28 Expected Values of Continuous Random Variables
29 Variance of Continuous Random Variables
30 Review of Continuous Random Variables
31 Continuous Uniform Random Variables
32 Exponential Random Variables
33 Gamma Random Variables
35 Normal Random Variables
36 Sums of Independent Normal Random Variables
37 Central Limit Theorem
39 Variance of Sums; Covariance; Correlation
40 Conditional Expectation
41 Markov and Chebyshev Inequalities
42 Order Statistics
43 Moment Generating Functions
44 Transformations of One or Two Random Variables
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Set of all children | AIMMS Community
Given a set of nodes and directed edges (from parent to child node), is it possible to construct an indexed set S_Children(i_node) that contains all children of the specified node?
With all children I mean the set of all reachable nodes, starting from i_node.
For example:
s_Nodes := {A, B, C}
s_Edges := {(A, B), (B, C)}
Then I would want:
s_Children(A) := {B, C}
The edges are actually defined through a binary parameter. i.e.
p01_edge(B, C) := 1;
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Production-inventory systems with lost sales and compound poisson demands
This paper considers a continuous-review, single-product, production-inventory system with a constant replenishment rate, compound Poisson demands, and lost sales. Two objective functions that
represent metrics of operational costs are considered: (1) the sum of the expected discounted inventory holding costs and lost-sales penalties, both over an infinite time horizon, given an initial
inventory level; and (2) the long-run time average of the same costs. The goal is to minimize these cost metrics with respect to the replenishment rate. It is, however, not possible to obtain
closed-form expressions for the aforementioned cost functions directly in terms of positive replenishment rate (PRR). To overcome this difficulty, we construct a bijection from the PRR space to the
space of positive roots of Lundberg's fundamental equation, to be referred to as the Lundberg positive root (LPR) space. This transformation allows us to derive closed-form expressions for the
aforementioned cost metrics with respect to the LPR variable, in lieu of the PRR variable. We then proceed to solve the optimization problem in the LPR space and, finally, recover the optimal
replenishment rate from the optimal LPR variable via the inverse bijection. For the special cases of constant or loss-proportional penalty and exponentially distributed demand sizes, we obtain
simpler explicit formulas for the optimal replenishment rate.
All Science Journal Classification (ASJC) codes
• Computer Science Applications
• Management Science and Operations Research
• Compound poisson arrivals
• Constant replenishment rate
• Integro-differential equation
• Laplace transform
• Lost sales
• Lundberg's fundamental equation
• Production-inventory system
Dive into the research topics of 'Production-inventory systems with lost sales and compound poisson demands'. Together they form a unique fingerprint.
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Quantum MechanicsName (In Arabic):Student Id.: Hin - Asksia.ai
Quantum Mechanics
Name (In Arabic):
Student Id.: $\qquad$
$\begin{array}{ll} h=6.62607 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s} & \text { Speed of light }(c)=2.9979 \times 10^{4} \mathrm{~m} / \mathrm{s} \\ \tilde{v}=1 / \lambda=v / c \quad v=\frac{1}{2 \pi} \sqrt{\frac{k}{\mu}} & E_{*}=h v\left(n+\frac{1}{2}\right) \end{array}$
The strongest infrared band of ${ }^{12} \mathrm{C}^{1} \mathrm{H}$ occurs at $3270 \mathrm{~cm}^{-1}$.
a) Find the force constant of ${ }^{12} \mathrm{C}^{1} \mathrm{H}$.
b) The approximate zero-point energy of ${ }^{12} \mathrm{C}^{1} \mathrm{H}$
Answer from Sia
Posted 6 months ago
Convert wavenumber to frequency: The wavenumber $\tilde{u}$ given in cm$^{-1}$ must be converted to frequency $u$ in s$^{-1}$. This is done by multiplying the wavenumber by the speed of light $c$ in
$\nu = \tilde{\nu} \times c = 3270 \, \text{cm}^{-1} \times 2.9979 \times 10^{10} \, \text{cm/s}$
Calculate the reduced mass $\mu$: The reduced mass $\mu$ of the diatomic molecule $^{12}C^1H$ is calculated using the formula $\mu = \frac{m_1 \times m_2}{m_1 + m_2}$, where $m_1$ and $m_2$ are the
masses of the two atoms. The mass of $^{12}C$ is approximately 12 amu and the mass of $^1H$ is approximately 1 amu
$\mu = \frac{12 \times 1}{12 + 1} \times 1.66054 \times 10^{-27} \, \text{kg/amu} = 0.913 \times 1.66054 \times 10^{-27} \, \text{kg}$
Find the force constant $k$: Using the equation $u = \frac{1}{2\pi} \sqrt{\frac{k}{\mu}}$, solve for $k$
$k = (2\pi\nu)^2 \times \mu$
Calculate the zero-point energy $E_0$: The zero-point energy is given by $E_0 = hu\left(n + \frac{1}{2}\right)$ for $n=0$
$E_0 = h\nu\left(0 + \frac{1}{2}\right) = \frac{1}{2}h\nu$
1 Answer
[Insert force constant $k$ here]
2 Answer
[Insert zero-point energy $E_0$ here]
Key Concept
The force constant and zero-point energy of a diatomic molecule can be determined using quantum mechanics equations and the properties of the molecule.
The force constant is related to the stiffness of the bond and can be calculated from the vibrational frequency, while the zero-point energy is the minimum energy that the molecule possesses even at
absolute zero temperature.
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Applying Maths in the Chemical & Biomolecular Sciences
Solutions Q21 - 34#
Q22 answer#
(a) Considering equations 49, if the predators \(X\) do not die naturally then they will clearly consume all the prey \(Y\) and the predator population will rise smoothly to a constant value and the
prey uniformly fall to zero. The condition \(k_3 \ll k_2Y\) ensures that the loss of the predator population \(X\) is negligible.
(b) Adding new loss terms to both species gives
\[\begin{split}\displaystyle\begin{array}{lll}\\ \displaystyle \frac{dY}{dt} & = & k_1Y -k_2 YX -k_{11}Y& \text{prey}\\ \displaystyle \frac{dX}{dt} & = & k_2 YX - k_3 X -k_{22}X& \text{predator}\\ \
Calculating the steady-state populations produces \(Y_e = X_e = 0\) as one possibility, as before, and the second steady-state is
\[\displaystyle X_e=\frac{k_1-k_{11}}{k_2}, \; Y_e=\frac{k_3+k_{22}}{k_2}\]
The equilibrium prey population is \(Y_e\) and this is increased relative to the case when \(k_{22} = 0\) but \(X_e\), the predator equilibrium value, is decreased. This increase in prey population
and decrease in predator, is the opposite of what is wanted if the prey is a pest, such as aphids, whose population is kept in check by predators such as ladybirds. Adding a pesticide that
potentially kills everything, causes the prey (aphid) population to rise and this is sometimes called the Volterra effect.
The consequence of this is clear in the numerical calculations if, for example, \(k_{11} = 0.9,\; k_{22} = 0.2\), and giving the other rate constants the values quoted in the text. The predator is
poisoned and its population periodically decreases almost reaching zero; the prey is also poisoned to a certain extent, but now, not predated, and this allows its population to remain relatively
large compared to that without poisoning, Figures 19 and 39. Compare also the phase plane in Figure 39 with that in Figure 20.
Figure 39. Populations of predator (red line) and prey when both are poisoned with rate constants \(k_{11} = 0.9 ,\; k_{22} = 0.2\). The prey population is increased substantially over that when no
poisoning occurs and the predator population (dashed line) is greatly reduced. The nullclines are shown on the phase plane. The point is at t = 2 is shown the initial point is \(X_0, Y_0\).
Q23 answer#
\(\displaystyle Y_e= \frac{k_3}{k_2}, \; X_e=\frac{k_1}{k_2},\; \frac{dy}{dt}=k_1y(1-x),\; \frac{dx}{dt}=k_3x(y-1)\). Changing to reduced time produces
\[\displaystyle\frac{dy}{d\tau}=y(1-x), \qquad \frac{dx}{d\tau}=\frac{k_3}{k_1}x(y-1)\]
which can be solved as outlined in section 8.1.
Q24 answer#
The equilibrium points are the solutions to \((k_1-k_2X-k_dY)Y=0, \; (k_2Y-k_3)X=0\). Three sets of points are,
\[\displaystyle X_e=Y_e=0; \qquad X_e=0, \; Y_e= \frac{k_1}{k_d}; \qquad Y_e=\frac{k_3}{k_2}, \; X_e= \frac{k_1k_2-k_dk_3}{k_2^2}\]
of which the last pair is the important one. The nullclines are the equations obtained when \(dY/dt = dX/dt = 0\), hence
\[\displaystyle Y=\frac{k_3}{k_2}, \qquad X=\frac{k_1-k_dY}{k_2}\]
The \(X\) nullcline depends on \(Y\) because of the \(Y^2\) term in the initial equation. Plotting the populations, calculated using the Euler method, Algorithm 15, shows that these oscillate but
tend towards the last of the three equilibrium points and produce, after a while, constant populations, Fig. 11.40. The phase plane shows the populations spiraling to this point as if attracted to
it. The spiraling occurs because the amplitude of the oscillations decrease with time and a single point is reached which is the equilibrium prey and predator population
Figure 40; Predator - prey model with a limit on the prey population that is proportional to the square of its population. Left pane shows the time dependence and, right, the phase-plane with the
nullclines crossing at the steady-state values. The point at \(t = 2\) shows the direction of change with time; \(X_0,\; Y_0\) is the initial point. \(X_0 =60,\;Y_0 =100,\;k_1 =1,\;k_2 =0.01,\;k_3 =
0.5,\;k_d =0.002\).
To explain these results we argue as follows: In the absence of predators, the initial number of prey population is less than it could be with the amount of grass present and would therefore increase
to a constant level. If there were no prey, the predators would die off with a rate constant \(k_3\).
In the actual situation, the predator eats the prey and the predator population increases and shortly after this, the prey population maximizes and then falls due to predation. The predator
population also falls as prey becomes scare, because predators die by starvation. The prey population now begins to recover, predators being scarce for the time being; however, it can only increase
somewhat because of the limited food. The predator then starts to catch more prey because they are now more numerous, and this limits the prey’s population and the cycle repeats itself. However, the
prey’s population is also limited by the amount of food (energy) available and it cannot fully recover. This limits the predator also, for if there are less prey then more predators will starve. This
‘damping’ causes the oscillations in population to become smaller and eventually they become insignificant. They are damped out, effectively, by the limited food supply, and a dynamic steady-state is
Q26 answer#
(a) The rate equations are
\[\displaystyle\frac{dA}{dt}=k_1A-k_2A-k_3AB, \qquad \frac{dB}{dt}=k_2A-k_4B \]
(b) At Steady state either \(A=B=0\) or \(\displaystyle B_e=\frac{k_1-k_2}{k_3}, \;A_e=B_e\frac{k_4}{ k_2}\) and these are the equilibrium points. The \(B\) nullcline is the horizontal line with a
value Be, the A nullcline is the straight line \(A = k_4B/k_2\).
(c) Using Algorithm 15 to integrate coupled equations, the following graphs, Figure 41, were produced with 1000 points in the integration
Figure 41. Behaviour of catalysed species in scheme 50. Left, vs time and, right, as the phase plane; \(k_1 = 0.2,\; k_2 = 0.01,\; k_3 =0.01,\;k_4 =0.02\) and \(A_0 =50,\;B_0 =0\). The unmarked point
on \(A\) is at \(t = 20\) and is also shown in the phase plane.
(d) Initially, \(A\) is present,but not \(B\). More \(A\) is produced via the first reaction and therefore its concentration starts to increase exponentially. However, \(B\) is produced at a rate
proportional to the amount of \(A\) present, and \(B\) also reacts with \(A\), reducing \(A\)’s concentration. The effect is to cause \(A\)’s concentration to reach a maximum and then fall.
The concentration of \(B\) also goes through a maximum because, not only is it produced from \(A\) and reacts with \(A\), but also it decomposes with rate constant \(k_4\). The concentration of \(A\)
reaches a minimum while \(B\) is still decaying, and therefore the term \(k_3AB\) is small. This allows \(A\) to increase again, via the first reaction, which causes more \(B\) to form and another
oscillatory event is produced. However, \(B\) is not zero at the start of this second event, and this limits the growth of \(A\). Eventually, a damped oscillating equilibrium is reached. The spiral
in the phase plane occurs because the amplitude of \(A\) and \(B\) decreases with time. The nullclines pass through the maximum and minimum concentrations of each oscillation, at which point, the
phase plane curve is horizontal or vertical.
Exercise: Investigate changing the rate constant \(k_1\) and \(k_4\).
Q27 answer#
(a) With the pendulum inverted the initial angle is \(\pi\), it is only possible to continue until about \(t = 30\) before the calculation fails using any of the the Euler methods. Failure is sudden
and easily observed because the angle does not remain at \(\pi\). Using a python/numpy built in integrator produces better results , but inevitably this also fails.
Starting at \(\varphi_0 = 3.0\) rads, the Euler and Euler - Cromer methods continue to produce accurate data, similar to that in Figure 15, out to \(t = 1000\).
(b) The velocity vs time most obviously shows non-linearity, Figure 42 shows this, but it is only clear when the initial angle is almost \(\pi\) radians. The phase plane plot produced should be
similar to that of Figure 14. The non-linear motion is apparent when the curves are not circles.
Figure 42. The velocity vs time of a pendulum with different starting angles in radians. The angles are 1, 2, 4, 6, 8 \(\times \pi/9\).
Q28 answer#
Reducing the equation of motion to two equations gives
\[\displaystyle d\varphi/dt = v,\quad dv/dt = fv+\omega^2\sin(\varphi)=0\]
which using algorithm 15 produces the plot shown in figure 43.
The time profile was calculated with the pendulum initially stationary at an angle of \(8\pi/9\) radians. The effect of the friction is clear; energy is not conserved in the pendulum and it
eventually becomes stationary. This type of motion is called dissipative; the initial energy in the pendulum ends up as heat.
Exercise: When the initial velocity is large enough, 0.4 in this instance, the pendulum can swing over the top. Eventually it loses energy and cannot any longer do this; it then vibrates with
decreasing amplitude until it comes to rest. Investigate this effect and convince yourself that rotation and damping occurs. The plot of angle vs time exceeds 180^o so a correction is needed to
constrain this to \(\pm\)180^o. The formula \(\tan^{-1}( \sin(\varphi),\cos(\varphi) )180/\pi\) will do this.
Figure 43. Left: The time profile of the angle (degrees) and angular velocity (dashed line), in rad s^-1, of a damped pendulum. Right: The phase plane, angular velocity vs angle, with angle in
Q29 answer#
(a) The equation is split into two parts, one describing the (angular) velocity \(v\), the other the rate of change of velocity or acceleration, and which are
\[\frac{d\varphi}{dt}=v, \qquad \frac{dv}{dt}+\left[\frac{a}{L}-\omega^2\cos(\varphi)\right]\sin(\varphi)=0\]
One pair of equilibrium points when \(d\varphi/dt = dv/dt = 0\) are \(v = 0\) and \(\varphi = 0, \pm \pi\) which is the stationary position; \(\varphi\) could be \(\pi\) radians by supposing that the
bar could be moved up against the shaft, which would then have to be infinitesimally thin.The other equilibrium point is \(v = 0\) and
\[\displaystyle \varphi = \cos^{-1}\left(\frac{a}{L\omega^2}\right)\]
In the case when the pendulum is long or \(\omega\) high, or both, then \(a/L\omega^2 \to 0\) and \(\varphi \to \pi/2\). When the opposite situation applies, \(a/L\omega^2 \to \infty\), then \(\
varphi \to 0\) or \(\pi\). The first condition means that a long rod will rotate around the shaft in a horizontal plane with negligible vertical oscillation, whereas a short rod will tend to hang
vertically. In between these cases, the rod will clearly oscillate up and down while rotating with the shaft.
The nullclines are \(a/L\omega^2 \to 0\) and \(\varphi \to \pi/2\) or zero. The phase plane is calculated from \(\displaystyle (\varphi,d\varphi/dt)\) which is \((\varphi, v)\)
\[\displaystyle dv/d\varphi = -[a/L - \omega^2 \cos(\varphi)]\sin(\varphi)/v\]
gives \(v\) as
\[\displaystyle v=\sqrt{\frac{2a}{L}\cos(\varphi)-\omega^2\cos^2(\varphi) +2c }\]
The constant \(c\) can be calculated by defining an initial velocity \(v_0\) and angle \(\varphi_0\). Two limiting cases are plotted in Figure 44. The pendulum has different initial angles and zero
initial angular velocity, except for the outer curve. The initial angles (in degrees) are from the inside out 22.5, 45, 90, 120 and 180, and \(a = 0.03,\; \omega = 1\) for the left pane and \(a=10,\;
\omega =1\) for the right-hand pane.
The motion of a short rod, \(a/L \gt \omega^2\), is shown on the right of Figure 44 and is similar to that of a normal pendulum. The period of the pendulum, because it is short, is far faster than
that of the shaft’s rotation, making the latter relatively unimportant. The curve for which the initial angle is \(\pi\) is the separatrix which only touches the axis when \(\varphi = \pm n\pi\)
where \(n\) is an integer.
Figure 44 The phase plane in two different limits, the abscissa are plotted as \(\varphi/\pi\) and the ordinate as \(v = d\varphi/dt\). Left: The situation for a long rod \(a/L \ll \omega^2,\; a =
0.03, \;\omega = 1\). The initial angles, reading from the x-axis out, are, \(22.5, 45, 90, 120,180\), with an initial velocity of zero, solid lines, and one (dashed) line. If the initial angle is \
(90\) degrees then \(v = 0\), which is a point on the x-axis, shown as green ovals. Right: The rod is now very short, \(a = 10, \; \omega = 1\) with the same initial angles but the dashed curve now
has an initial velocity of 1. Notice that the angular velocity \(v\) is far larger when the rod is short.
On the left of figure 44, \(a/L\omega^2 \to 0\) and is the situation when the rod is very long. In this limit, the motion is governed by the rotation of the shaft because the long rod, thought of as
a pendulum has a very long oscillation period. The curve for which the initial angle is \(\pi\) is the separatrix which only touches the horizontal axis when \(\varphi = \pm (2n + 1)\pi\) where \(n\)
is an integer. This means that the rod is only instantaneously stationary in the vertical position. When the initial angle is \(\pi /2\) (or 90^o) a long rod does not oscillate up and down as it
rotates, and its vertical velocity is zero. When the initial angle is smaller or larger than \(\pi /2\), the rod suffers vertical oscillations as it rotates, and it does not matter whether it starts
almost in a vertically up or down position, the motion is eventually the same: for example \(\varphi_0 = 7\pi/8\) or \(\pi/8\). The outer sinusoidal curve in the figure above corresponds to the rod
freely rotating in the vertical plane as well as rotating about the shaft because it has an initial velocity of \(1\) and an initial angle of \(\pi/8\), which together, gives it enough energy to
overcome the potential energy needed to invert the rod.
Q30 answer#
(a) When the angle of the rod from the vertical is small, then \(\sin(\varphi) \to \varphi - \varphi^3/6\) and \(\cos(\varphi) \to 1 -\varphi^2/2\). Because the angle is almost zero, the second terms
are so small that they can be ignored making the equation of motion
\[\displaystyle \frac{d^2\varphi}{dt^2}+\left(\frac{a}{L} -\omega^2 \right)\varphi = 0\]
which has the form of a simple harmonic oscillator with a frequency \(\omega' = \sqrt{a/L -\omega^2}\) . This produces the phase plane on the right of Figure 44.
(b) For motion around the initial angle, the sine and cosine have each to be expanded as a Taylor series about \(\varphi_0\). The general series expansion for a function \(f (x)\) about a point, is
(see Chapter 5.6) \(\displaystyle f(a+x)=f(a)+f'(a)x+f''(a)\frac{x^2}{2!}+\cdots\) where \(f'\) is the first derivative, \(f''\) the second. The sine series is
\[\displaystyle \sin(\varphi -\varphi_0)=-\sin(\varphi_0)+\cos(\varphi_0)\varphi+\sin(\varphi_0)\frac{\varphi^2}{2!}+\cdots\]
and the cosine series
\[\displaystyle\cos(\varphi -\varphi_0)=\cos(\varphi_0)+\sin(\varphi_0)\varphi-\cos(\varphi_0)\frac{\varphi^2}{2!}-\cdots\]
where \(\cos(\varphi_0)=a/(L\omega^2)\) and by Pythagoras \(\sin(\varphi_0)=\sqrt{1-(a/(L\omega^2)^2}\).
If the initial angle is small because \(a/L\) is small, the resulting equation is the same as in (a), because \(\sin(\varphi -\varphi_0) \to \varphi\) and \(\cos(\varphi -\varphi_0) \to 1\), if
higher powers of \(\varphi\) are ignored.
(c) Assuming that this is not the case, then changing the angle to \(\varphi -\varphi_0\), gives
\[\displaystyle\frac{d^2(\varphi -\varphi_0)}{dt^2}+\left( \frac{a}{L}-\omega^2\cos(\varphi -\varphi_0) \right)\sin(\varphi -\varphi_0)=0\]
This is a bit of a trick, but is the same as rotating the axis of the pendulum by \(\varphi_0\), which cannot change anything, such as the energy or period, but makes the calculation simpler.
Expanding the sine and cosine
\[\displaystyle\frac{d^2(\varphi -\varphi_0)}{dt^2}+\left( \frac{a}{L}-\omega^2[\cos(\varphi_0) +\varphi\sin(\varphi_0)] \right)[ -\sin(\varphi_0)+ \varphi\cos(\varphi_0)]=0\]
Substituting for \(a/L = \omega^2 \cos(\varphi_0)\), greatly simplifies the equation
\[\displaystyle\frac{d^2(\varphi -\varphi_0)}{dt^2}+ \omega^2\varphi\sin(\varphi_0)[ -\sin(\varphi_0)+ \varphi\cos(\varphi_0)]=0\]
Simplifying, and ignoring the \(\varphi^2\) term, gives
\[\displaystyle\frac{d^2\varphi}{dt^2}=\omega^2\sin^2(\varphi_0)\varphi \sim \varphi\left( \left(\frac{a}{L\omega}\right)^2-\omega^2 \right)\]
which is the equation of a simple pendulum of frequency \(\omega \sin(\varphi_0)\) oscillating about \(\varphi_0\). If \(\varphi_0 = \pi/2\), then the frequency is \(\omega\), the same as that of the
shaft; when \(\varphi_0 = 0\), the frequency is zero because the pendulum is either vertically up or down.
Q31 answer#
Splitting the equation into two produces angular velocity and acceleration as
\[\displaystyle \frac{d\varphi}{dt}=v, \; \frac{dv}{dt}+\left[ \omega_0^2+h\omega^2\cos(\omega t) \right]\sin(\varphi)=0\]
With the parameters given, the ratio \(h\omega^2/\omega_0 = 30\), which means that the driving term, \(h\omega^2\cos(\omega t)\) is going to dominate the motion. As might be expected if \(h \to 0\)
or \(\omega \to 0\) a normal pendulum’s motion is observed.
The time profile and phase plane produced are shown in Fig 45; 10^3 data points were used with the python built in integrator \(\mathtt{odeint(\cdots)}\) but the modified Euler or Runge-Kutta method,
could also be used as in Algorithm 16.
The initial angle means that the pendulum is inverted starting at \(3\pi/4 \equiv 135\^\text{o}\), and when forced by the action of the piston this angle increases with time; the pendulum crosses the
vertical at a time \(\approx\) 1.25 and only partly descends to the other side before re-crossing the vertical again; this motion repeats ad infinitum. The phase plane shows this oscillation about
centred about \(\pi\) radians.
In this example, the pendulum is initially inverted but only to the extent of 135^o. The piston’s frequency is ten times larger than that of the natural pendulum; therefore, the pendulum has hardly
moved when the piston has descended by its full amount. This effectively imparts a rotation (torque) on the pendulum, closing the angle between the pendulum and the vertical by a small amount. (It is
similar to the effect of starting your car and going forwards while a door is still open.) When the piston rises, the pendulum is forced slightly away from the vertical, but because it is now more
vertical that it was, this angular motion is less than that produced when the piston dropped. The overall effect is to move the pendulum over the vertical.
Figure 45. Left: The time profile of the pendulum’s angle. The fast piston’s motion is superimposed on that of the slow pendulum. Right: The phase plane.
Q32 answer#
Using the Runge - Kutta or modified Euler methods, two time profiles of the pendulum’s angle are shown in Figure 46 with parameters from (a). Notice the difference in scale. An angle greater than \
(180 ^\text{o}\) means that the pendulum is rotating. The phase plane picture is that of an increasing spiral (bottom left). Notice the irregular but repeatable motion when the pendulum is stably
swinging (top). The appearance of the phase plane shows whether the motion is stable. If it spirals outwards then the motion is unstable, one example of each is shown in the figures.
Figure 46. Stable and unstable motion described by the Mathieu equation. The angle vs time is shown and two phase planes (\(d\varphi/dt\), vs \(\phi\)) for stable motion (top) and unstable motion
Q33 answer#
The stable or steady-state points are calculated when the derivatives of \(x\) and \(y\) are zero;
\[\displaystyle (a - x)(1 + x^2) - 4xy = 0,\quad \text{and}\quad bx\left(1-\frac{y}{1+x^2} \right)=0\]
which produces \(x=a/5,\; y= 1+(a/5)^2\). The \(dx/dt=0\) nullcline is \(y=(a-x)(1+x^2)/4x\) and when \(dy/dt = 0\) the other is \(y = 1 + x^2\).
These are plotted in Figure 47 together with the trajectory starting at \(x = 3,\; y = 2\) with \(a = 8,\; b = 2\) and in the right hand figure with \(a = 10,\; b = 2\).The time profiles are also
shown underneath their respective phase planes.
With the larger value, \(a = 10\), a limit-cycle is produced. This means that a persistent oscillation is produced from wherever on the phase plane the trajectory starts. This can be seen in the time
profile, where the amplitude and period of the oscillations soon becomes constant. A (Hopf ) bifurcation occurs in the trajectory as it enters the limit-cycle; see Strogatz (1994) and also Haken
(1978) for a detailed discussion of bifurcation. When \(a = 8\) no limit-cycle is possible and the oscillation in the concentrations, which are of constant period, die out and the trajectory spirals
towards the equilibrium concentrations.
Figure 47 Time profiles and phase plane with \(a=8,\;b=2\) top and with \(a=10,\;b = 2\) bottom. The the direction of flow in the nullclines is anti-clockwise. The limit cycle is clear in the lower
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Space Metrics - SCIET
The Falling Body Experiment
The Role of the SCIET in Movement
Compounding Quantum Layers
The “falling body” thought experiment enables anyone to understand how these iterations work together to create the holographic effect, gravity and other effects due to movement in the space of one
body relative to another.
The thought experiment is to imagine a body (planetary, not human) as a point surrounded by innumerable layers the thickness of a Planck length, like skins on an onion, and that these layers are able
to merge into unity when they are precisely aligned.
Since quantum layers are only a Planck length thick, the Unity Function can only take place on a line between their void point centers, a line that exists close to the void. The The layers that
exist in the space between cosmic bodies are the called the Quantum Lattice.
Each layer exists independently as a relationship with the body’s center and the rest of the universe. Each point has layers that extend away from its center to the edges of the universe, or as far
as the rate of change allows.
Since matter is made of many points nearby, rules exist to merge their effects to operate as one. Basically, a shared value, a kind of common denominator, is determined based because each point is a
prime number and their midpoint value is assimible by both primes through a natural harmonic or created by multiplying the interacting layers until they reach a rate able to return to each center.
The resulting midpoint value is a new SCIET with its baseline aligned to the dominant or larger body. In a sense, the new SCIET exists in a higher dimension since it must integrate both systems; that
is to say, it must transfer its new value back to each of the bodies simultaneously and throughout the entireties of the bodies.
The solution to the falling body problem is the above “Rule of the Third SCIET,” and it is a simple and effective way to solve the merging of many.
Molecules are surrounded by quantum layers that combine to become objects and act in concert as a single body because they are overlaid with a series of derived SCIETs compounding to effect a single
unified body. They are fully relativistic since they exist due to and for one body alone. In SCIET Theory, the relationship is treated as a separate body that adds values through a common denominator
function to each of the bodies.
This effect is cumulative and results in “shell” formation, which is to say that these values return toward the center of the body, (think of RADAR), but the energy they contain goes into orbit
around it. These are “Quantum Shells” since they exist as spherical quantum layers, again, like “the skin of an onion.”
Time and Consicousness
Is Memory Wound?
SCIET Theory offers a useful concept of time. Time is a byproduct of consciousness. I will not try to explain consciousness since that would go beyond the intent of this post.
Astrological resonance between a person and the positions of the planets, moons, and stars is repeated by the rotation of the Earth each day. These patterns furnish us with a useful way to record
Think of each day as a thread of time being wound onto a spool that requires a day to make one revolution. Imagine that each turn is laid one on top of the other. Each turn is like a level or a floor
in a spherical building. Since the floors are wound around a center, it can be experienced as a single floor from its beginning to its end, or you can use the elevator to move from one floor to the
next. The elevator is a line between any external point and the center of the spherical “building of mind.” Each level or stop on the “elevator” represents a different but harmonious, stepped-down or
up value. Each holographic memory level of this building of mind can be accessed horizontally or vertically.
The ability of space to automatically reduce incoming values toward a point is responsible for our perception of time. This ability of space is not unique to conscious beings but is responsible for
them. The by-product of this process is time. The universal experience of consciousness exists at the moment of shared creation, a moment built on the sequence of events begun 13.6 billion years ago.
This moment is the unfolding of our universe, but all that has continued to exist in space/time can be accessed through the elevator of memory and mind. The values of each moment of creation exist in
permanent relationships throughout the universe.
All memory is related to the values explained by the “building of mind” analogy. Time is the product of the creative process in which new parts are added to an existing structure. You cannot separate
time from the structure any more than you can separate a building from the space in which it exists. The processes of space inextricably entwine time and memory. Time can be understood as the
shifting of values or stepping-down of values in space on a universal scale. The mind utilizes this process to maintain a continuous linkage between what has happened and what is happening. The
values used by the consciousness exist universally and can be used to access any moment in time, anywhere in the universe.
Dane Michael Arr
August 3rd, 2002
Tempe AZ
The Universe has a Preferred Orientation?
I regularly scan scientific publications for information that appears to confirm the tenants of SCIET Theory and recently was rewarded by an article in Scientific American.
The article, entitled Twist and Shout, was published in the May 19, 1997 issue. It is a presentation explaining the analysis of electromagnetic waves from 160 distant radio galaxies. This analysis,
by Borge Nodlund of the University of Rochester and John Ralston of the University of Kansas, suggests that our universe has a shape. They have detected a phenomenon called electromagnetic
anisotropy, which means that in addition to the expected effects on the EMF from distant galaxies, they observed rotation that depends on its direction as it approaches earth from its point of
Scientists Find Universe Has Prefered Orientation
The article, entitled Twist and Shout was published in the May 19, 1997 issue. In it is a presentation explaining the analysis of electromagnetic waves from 160 distant radio galaxies. This
analysis, by Borge Nodlund of the University of Rochester and John Ralston of the University of Kansas, suggest that our universe has a shape. They have detected a phenomenon called
electromagnetic anisotropy, which means that in addition to the expected effects on the EMF from distant galaxies, they observed rotation that depends on its direction as it approaches earth from
its point of origination.
Their research considers factors attributable to matter or localized field effects to show that this phenomenon must be a product of space itself.
The significance of this discovery may be lost on most of the world. Still, astrophysicists are rushing to corroborate the results because, if it is true, it changes one of the major assumptions
about space long held by theorists like Einstein and Newton. They believed that space obeys the principle of rotational symmetry, that it is the same in all directions.
This Discovery Confirms SCIET Theory
The presentation of experimental evidence supports the most basic assertion of SCIET Theory: Space has an underlying pattern that guides distribution of energy. The discovery that the universe has
orientation is a breakthrough for SCIET theory, because for SCIET assertions about mind to be true, they would have to be true for the entire universe.
While preliminary, this discovery fits SCIET expectations. A key assumption of SD is that the universe originated as a single quantum event. The Single Cycle Integrative Effect Topology (SCIET) is
how the reactive charge is distributed throughout space. SCIET treats the universe as a geometrical vortex (SCIET) and everything in it as fractals of that original.
The Nodlund-Ralston Anisotropy is significant because it indicates that the universe, or at least the fabric of space, has defined a preferred path for light. Much research must be done before other
SCIET predictions can be confirmed. Among the other predictions are;
• The universe has a center.
• Most of the matter is focused in a relatively small area at the center.
• The center of space is not the center of matter.
• Vast emptiness surrounds the matter at the middle.
• A pattern exists which passes light through the center in a figure-eight pattern.
A physicist might find it interesting, but SCIET Theory predicts it as the MIND OF GOD. The theory predicts a resonant pattern within the quantum field or Bose-Einstein Condensate that is the fabric
of space. The pattern is the SCIET.
SCIET Theory explains consciousness as a quality of space itself. It includes a cosmology that begins with the void and consciousness within it. The SCIET diagrams how that Consciousness distributes
SCIET Theory uses a concept of dual infinities and asserts that matter is produced at the intersection of these two qualities of space. This means that matter is a boundary between equally ancient
and distant infinities. A quality of space that allows it to absorb energy from all directions infinitely can be no more amazing than one that allows it to radiate in all directions infinitely.
It is the ability to absorb energy/information infinitely that is the source of consciousness in life forms. I believe that the shape and orientation in the universe confirm that the universe is
conscious with an evolutionary process in operation. In this way, it is confirmation that we are manifestations of a universal consciousness.
The universe began as a SCIET, and its evolution has resulted in a donut-like shape or, in cross-section, a figure eight. Matter exists in a relatively small area at the center surrounded by vast
reaches of relatively empty space. This vast expanse is necessary to balance the time and energy distribution required for the SCIET Loop.
The Nodlund-Ralston Anisotropy is a paradigm-shifting discovery and may someday be compared to the Michaelson-Morley test results of the previous century, which led directly to Einstein’s Theory of
Special Relativity.
Dane Arr
An Ear Full: A Moment of Awareness
This phrase captures the best description of the information in a SCIET cycle
Your ear size divided by the speed of sound equals a “moment of awareness”: Think about it. Your outer ear captures a group of frequencies simultaneously and passes them to the inner ear. This
defines a sampling rate for sound-based information coming into the spacial modeling process of the brain,
This would be a one-and-a-half-inch radius wavefront or a three-inch diameter. So that means that the time it takes sound to travel three inches may define the sampling rate of the brain. Based on
the speed of sound, that would be about one ten-thousandth-of-a-second in time.
The resonance of sound in the head is the basis of the skull’s design. When comparing the center of resonance points in the skull, it was found that the centers for hearing are positioned to be at
the focal point of sound reflected by the skull’s interior. This tells us the primary evolutionary force in the skull is sound and not the resonant frequencies of consciousness.
(more soon)
Are We Living in a Hologram?
Paul Sutter is an astrophysicist at The Ohio State University and the chief scientist at COSI science center. Sutter is also host of Ask a Spaceman and Space Radio, and leads AstroTours around the
world. Sutter contributed this article to Space.com’s Expert Voices: Op-Ed & Insights.
In the late 1990s, theoretical physicists uncovered a remarkable connection between two seemingly unrelated concepts in theoretical physics. That connection is almost inscrutably technical, but it
might have far-reaching consequences for our understanding of gravity and even the universe.
A correspondence between concepts in theoretical physics could open the way to interpreting our universe in fewer dimensions.(Image: © Kevin Gill/Flickr – CC BY-SA 2.0)
To illustrate this connection, we’re going to start at — of all places — a black hole. Researchers have found that when a single bit of information enters a black hole, its surface area increases by
a very precise amount: the square of the Planck length (equal to an incredibly small 1.6 x 10^-35 meters on a side). [Are We Living in a 2D Hologram? Photos of Laser ‘Holometer’ Experiment (Gallery)]
At first blush, it may not seem all that interesting that a black hole gets larger when matter or energy falls into it, but the surprise here is that it’s the surface area, not the volume, that grows
in direct proportion to the infalling information, which is totally unlike most other known object in the universe. For most objects that we’re familiar with, if it “consumes” one bit of information,
its volume will grow by one unit, and its surface area by a only a fraction. But with black holes, the situation is reversed. It’s like that information isn’t inside the black hole, but instead stuck
to its surface.
Thus, a black hole, a fully three-dimensional object in our three-dimensional universe, can be completely represented by just its two-dimensional surface. And that’s how holograms work.
A black hol-ogram
A hologram is a representation of a system using fewer dimensions that can still pack in all the information from the original system. For example, we live in three (spatial) dimensions. When you’re
posing for a selfie, the camera records a two-dimensional representation of your face, but it doesn’t capture all the information; when you later examine your handiwork and choose your filter, you
can’t, for example, see the back of your head, no matter how you rotate the picture.
Recording a hologram would preserve all that information. Even though it’s a two-dimensional representation, you would still be able to examine it from all three dimensional angles.
Describing a black hole as a hologram might provide a solution to the so-called black-hole information paradox, the puzzle of where the information goes when matter is consumed by a black hole. But
that’s the subject of another article. The black-hole-as-hologram concept is also a good example to keep in your head as we make the big jump — to consider the entire universe. [The Strangest Black
Holes in the Universe]
Souls and Protons
SCIET Theory originated as a means to answer the long-standing questions about the existence of the soul and provide a logical explanation for it.
A scientific explanation is also a goal, but the first goal is to provide a logical means to account for its existence and behavior in the context of human experience. Four decades of consideration
have produced these ideas, giving ample time to try as many approaches as possible before deciding that this Theory is the best.
The Theory did not begin as an explanation for the Creation of matter, but since the Soul could not be defined as emerging from matter, it was necessary to explore what came before matter, and thus
we have an explanation for how the matter was formed.
None of these ideas came from experience or experiments but were given as whole thoughts during a twenty-minute period in 1974. From that point on, I knew this information, but it has taken almost
fifty years to find the words and concepts to communicate it to others.
Always the simplest answer emerged as the best. In this vein, the proton is remarkably similar to the Soul. Each has a Point of Awareness at the center surrounded by memories of its past. The
environment of the proton has few variables and its memories are only of other protons. The incredible age of the proton accounts for the strength and power of its structure, and the calculations
regarding its energy are consistent with the forces that have molded it.
SCIET Theory offers a method to understand the formation of atomic structures through the function of a single mathematical structure that occurs pulse-like and records its existence in space as a
spherical layer around a point of AwarenessIn
In SCIET Theory protons are the final stage of the creation of the Universe from Crystalline Space, which begins with the First Action and continues through eighty-one magnitudes of subdivision to
stimulate resonance return at the boundary layer.
SCIET Resonance Return: A SCIET is an information-filled assembly of twelve leg-like regions equidistant from one another, and angled toward the center, forming a star-like structure of twelve
angles. All points are SCIETS, and when two of them resonate, the resulting midpoint structure is also a SCIET, although its information is a harmonic of both. When it is disturbed or forced to
adjust and recalculate its information value, the original mid-point information value pulses toward, or resonance returns to each of the original SCIETs, The twelve legs approach the center but
cannot reduce into it, and so span it and each leg surrounds the center as a level, forming a twelve level layer, or quanta.
SCIET Boundary Layer: The SCIET First Action leads to successive subdivisions of the first measure and does not end until it reaches a Boundary Layer, a predefined value that represents the limit of
the First Actions area of effect. This is common n the Nervous system
Photons are the same but exist independently of another structure.
This process continually adds SCIETorbital components around the center of each interference point.
This initial cumulative effect resulted in the formation of protons, electrons, and neutrons.
Thus protons emerged from or appeared in, the crystalline space at the beginning of the universe simultaneous to the creation of radiation and gravity.
The proton shells continued to grow due to
resonance with each other and this effect began the effects of gravity, the attraction of matter together based on sharing orbital layers. these protons formed clouds and moved toward others of the
same nature, as the clouds grew close, the layers that surrounded them adjusted and stabilized at a standard distance, with the midpoint resonance between them becoming an Electron, and its apparent
movement due to its shifting from the midpoint of one proton to another that is also in resonance. Other protons at different distances would have electrons specific to them
• The very high resonance rates or densities of the interiors of stars enabled protons to assemble in close proximity and become molecules.
• Neutrons are those so compacted that the midpoints would standardize very close to the shell.
The Proton and Causal Levels
The role of molecularSCIET is to explain the nature and behavior of the molecular structures.
By focusing on the atoms separately from the events that lead to their formation or the mechanisms of their combination into molecules, we can get the most distinct view of the SCIETorbital concept
and the important idea of Causal Levels.
• The term level is used to denote the next or previous of the same interval, such as a value that steps twelve levels to create a layer.
• A ny increment that can exist is described as a level when considering it in relation to the formation of the shells, layers or lattice.
• Causal Levels begin inside the proton shell where incoming Resonance Return Values Symmetrically React to the SCIET angle at the center and establish a pulsed polarity of those values into the
surrounding space where they become parallel in twelve levels and orbit in perpetuity to form SCIETspheres
SCIET Theory attributes the formation of protons to the sufficient subdivision of space to stimulate resonance return as a common event.
Protons and electrons formed out of the original creation during the plasma and from them, neutrons and all the molecules emerged from the furnace of stellar gravity.
Protons and electrons remain the fundamental source of materiality and understanding them will reveal the patterns that underlie all of nature.
The proton is derived from the internalization of the void created by the first SCIET which defined itself, not as a relationship between two points in space, but as a point on the surface of a
sphere between an internal and an external void.
SCIET Theory offers a method to understand the formation of atomic structures through the function of a single mathematical structure that occurs pulse-like and records its existence in space as a
portion of a closed-loop layer surrounding both origin and destination.
The concept of the SCIETorbital and its closed-loop nature underlies much that is mysterious in nature, but it is to be expected that a simple rule is universal and responsible for many effects.
The most obvious area to seek confirmation of these ideas is in the realm of atomic structures and quantum mechanics.
A SCIET interacts with other SCIETs that have matching values. This means that every value defined around the center is treated as a SCIET.
At the smallest levels of creation, this has important implications.
The minimum unit of change is at the center of the proton and reaches out from that deep place to define the infinitesimal substrate that exists throughout the Universe.
When each of the twelve steps away from the center are considered in the context of being originating values, it is obvious that each value becomes the basis of a whole system of derived values.
Comments on the Merkaba
The Craft of Souls
A tetrahedron is one-half of a Merkaba. The second tetrahedron is formed separately after the first one; both connect to consciousness at the center. Pointed toward the ground is feminine, and the
masculine points up. The polarity of the opposite-pointed tetrahedrons naturally aligns each of them with one of the polarities within us. In silhouette, the Merkaba is a six-pointed star.
In spiritual teaching, the Merkaba composed as such is the most protective form you can use to move about in the spiritual realms.
The reason for this is simple, just as you have two eyes, ears, arms, and legs, the body is composed of phase-conjugated frequency systems rotating on each side of the body; this means that they
connect in a coordinated way at a point between them. This connection is true of the body, and it is true of the spiritual body as well. The two tetrahedrons support this.
The two tetrahedrons used as energetic forms to protect the spirit body do so because they eliminate external “noise” from disrupting the spirit body’s concentration. You can visualize that the eight
points, the vertices of the tetrahedrons, are balanced energy concentrators focusing on the center where your spirit is protected.
There are two tetrahedrons, one for each side, and polarity enables your spirit to navigate in multiple densities by aligning your Soul’s internal dynamics to focus externally in a coherent way.
Compare this to becoming suddenly discarnate; your Soul leaves the body with its chakras forming layers around your higher levels of consciousness at the center. Here, the Soul is an inner tube
floating on a river, but the Merkaba provides a boat with which to navigate. The newly released Soul can cast a line to those it loves and cares about but cannot steer and simulate the ability to
operate with focused intention. External information has a duality similar to how the mind works in a body.
The Merkaba aligns the spirit with the material realm, creating a sort of x-y- z axis for us to navigate in space. Two horizontal planes of three points and two in verticle alignments of positive and
negative polarity give the mind/spirit mobility within the planes of the planet.
Meditate with this image.
Dane Arr
Long Heads SCIET Analysis
Can Cranial Deformation Change the Mind?
Paracas Peru is famous for its ancient cemeteries whose mummies have elongated heads, although these types of skulls are found all over the world. Some are the result of artificial cranial
deformation, but others are natural. As expected, the ancient people’s DNA has been tested and found to be different from normal humans, since it was taken from those with distinctly non-human
skulls. The many that were found with artificial cranial deformation were thought to have adopted it for cultural reasons, probably for higher social status, but there may be a functional reason as
SCIET Theory offers a concept of neurological function based on the interaction of scalar fields generated by all matter, and it suggests that this interaction compounds, or increases in frequency
when similar fields are involved. This is a primary component of SCIET Theory. It solves the problem of how different frequent systems mutate into magnitude higher frequencies to enable integration
of slightly varying versions of the same information. Stereoscopic vision is the the best example in which two inputs become one vision. Conceptually this means that the third field created is
functionally able to combine both lower field inputs into a single one that possesses information from both. In stereoscopic vision the objective is to provide depth of field knowledge and adjust
placement in the environment.
In the case of the brain and how it works to model the environment, the idea builds on the duality of the nervous system inputs to each hemisphere of the brain. Restating the above, using this
theory, the dual inputs create a set of interactive fields whose combination results in a third one that is a multiple of the two original fields.
This approach is controversial because the ability of the scalar fields to compound into higher frequencies is not tested, primarily because it is generated at very low power and in frequencies that
are not electromagnetic in nature. Evolved from the fields created by Platinum Group elements in the high spin state in the cells and synaptic gaps, they are referred to as Meissner Fields. They are
the result of room temperature superconductivity at the elemental level compounded throughout the entire body. We can surmise that the fields exist because of the volume of these elements found in
the body, and there is no other explanation for their presence.
Brain Lateralization
These fields are intrinsic to the operation of the nervous system, and by the structure and arrangement of the inputs and the parts of the brain we can model their size and location. Assuming that
the nervous system is built up from these fields and that it evolved in their presence, the role of the brain in synthesizing the frequencies of consciousness becomes clear using SCIET Theory.
The mechanism for compounding the fields is called the mid-point field in SCIET Theory, it is basic to all compound interactions in nature beginning with the formation of atoms, and in the brain it
is generated by simultaneous inputs to each brain half by the sensory nervous system. The inputs firing simultaneously on opposite sides of the brain stimulate the creation of a third field that is a
compound of both sides.
The body moves through the environment, which is an ocean of these scalar fields created by the planets multi-billion year journey through space. In addition to the built up spherical fields, the
volume of molecular matter is structured by the layers of memory fields around the planet created by the rotation and resonance with all other moving fields. This is illustrated in the above graphic.
Stereoscopic vision is an example. Examining this idea, a researcher is struck by the fact that the primary region where the mid-points must be located in an empty space between the two hemispheres.
These four cavities are referred to as the ventricles, and they are filled with cerebral spinal fluid. Based on this we can propose that the midpoint interaction of the hemispheric fields does not
require neuronal network to function, because it operates at frequencies unrelated to the cellular tissue.
Returning to the distribution of sensory regions in the brain, the mirroring is not exact between the two halves and this suggests that there may be distinct frequency sets involved with each
hemisphere. Hemispheric specialization, or lateralization is well known in popular culture with each side of the brain being responsible for different types of mental processing.
We now know that the default communication between cells in the body is based on light. Photonics communication is observed in the body and in the brain as well. So the specialization to process
sound to manage speech is an addition to what is needed for normal survival by people. It may also suggest that speech itself is the result of an epigenetic adjustment by humanity that dramatically
increased the availability of dopamine.
Dopamine Increases
Brain lateralization creates special areas on both sides of the brain dedicated to certain functions, with a particular emphasis in humans on speech and language, along with dominance of one side for
the expression of the will. These features in humans rely on an enhanced use of dopamine. Its increased availability is due to adaptations related verbal language and vocabulary, and does not depend
on specialized brain centers. Broccas region in humans is pivotal to speech, but in other primates it functions with much simpler sounds such as the variable screeches of a monkey. Apparently its
role is not governed by its physiology but by the other features of the brain such as the availability of neurotransmitters and the scalar fields with which it stores information. If it is damaged
the ability to manage those factors is limited or destroyed.
The senses input similar information along pathways to each side of the body and this causes a polarity imbalance that stimulates an electrical discharge between the sides of the brain. This
discharge serves multiple functions since it is affecting both the nervous tissue and the field they generate. One function is to drive the formation of synaptic connections between the brain halves,
creating the corpus callosum, and the other is to fix the recall of the immaterial scalar field associated with the experience that created the neuronal connection.
The process of thinking involves left-right discharge related to both visual and verbal inputs, apparently stimulating synaptogenesis, the synaptic formations created by sensory nervous system in
response experience. Verbal in particular has evolved specific areas of the brain to handle sounds. It can be argued that the default processing of the brain is based on light, so the visual
processing is inherent to the brain, while speech is a later add-on in human development.
Changing the availability of certain neurotransmitters may be a key adaptation to enable increased verbal abilities. Dopamine levels are shown to be pivotal to properly functioning linear or verbal
processing in humans, at the same time the lack of it contributes to enhanced visual or spacial processing.
With the addition of enhanced dopamine in humans, the likelyhood that the left-right hemispheric specialization has given rise to different forms of processing on each side of the brain has
increased. The ability to make voluntary choices to move the body is clearly shown to be related to dopamine.
Studies show that dopamine drives left-hemispheric lateralization of neural networks during human speech. How dopamine does this is shown to not be dependent on physical pathways, so the field
interactions working with dopamine levels can be surmised to be related to electrical activity observed between the hemispheres during voluntary actions. This research supports the idea that
hemispheric lateralization is related to the increase of dopamine levels.
In another article, Mission to Earth, I discuss the idea that humans were using a form of telepathy enabled by the global resonant temple complex until the end of the third millennium BC when the
Temple were destroyed by global storms. What is inferred by this is that during the period following that disaster humanity was forced to depend on spoken language entirely and this required a lot
more dopamine for the brain to manage speech. This could only happen with adaptations to the epigenetic markers in the genes. More than a thousand years pass before humanity demonstrates the quality
of self-awareness according to Julian Jaynes in his Bicameral Brain theory, it is said to be capacity for introspection and the ability to recognize oneself as separate from the environment.
According to Jaynes Bicameral Brain theory humans began to have this ability around 1000 BCE, so it took more than a thousand years after the Confusion of Tongues for humanity to develop this
ability. This is probably forty or more generations. Dopamine is a key adaptation for modern man, because its increased presence does not need to be supported by DNA, but can be based on epigenetic
coding instead.
How brain lateralization is affected by different shapes of the skull is not obvious, but research on the history of cultures that were predominantly dolichocephalic or long skulled, indicates that
they were much less aggressive than their round skulled counterparts. In fact most of the ancient populations with long heads were matrilineal Goddess worshipers and their communities ended when
round head invaders murdered them and heaped their bones into their homes and burned them. Understanding how being long headed predisposes an individual to be gentler and more philosophic is an
important question.
The Resonant Cavity of the Skull
This article is focused on examining the consequences of changes to physiology of the brain and the resonant cavity of the skull. The reported changes in personality in individuals who have undergone
cranial deformation to elongate their skulls are related to being more calm and thoughtful.
The efforts of the brain to harmonize its charge state and use this to drive the sorting, analysis and storing of experience using fields makes sense, as does the layout of opposing sensory centers.
The graphic on the right was done to compare the physiology of the face and skull of both a long headed and round headed individual, with both aligned eye-to-eye, nose-to-nose and chin-to-chin the
comparison reveals that dolichocephalic individual’s longer and narrower skull extended the brain backward significantly with the same volume of brain mass. This is an example of a cranial deformed
normal human whose skull has been compressed with a clamping device during the first four years of growth. The result changes the shape of the brain as well as the skull, making the brain hemispheres
closer together, shortening the distance across the ventricles and lengthening the sensory input regions within the brain. If the skull were a musical instrument, it would definitely make a different
sound, and in this context the resonance of mental processes.
The efforts of the brain to harmonize its charge state and use this to drive the sorting, analysis and storing of experience using fields makes sense, as does the left-right discharge between related
neural inputs. In this context it would be natural to assume that there would be an optimum brain shape and layout of opposing sensory centers.
This is where the challenge of understanding the mental effects of cranial deformation begins. The main issue concerns the effect of narrowing the ventricles between the brain halves and moving the
sensory centers of the brain closer to one another. Doing this makes the left-right electrical discharge travel a shorter distance and the scalar fields generated compound differently. The migration
of axon and dendrites between the brain halves is shorter and this also makes the corpus callosum longer during it development as well. The inputs must be the same, so the only difference is in the
generated fields proximity to one another and the resulting mid-point values.
Modeling the visual focus field of the brain depends on the eye sensory centers located between the ears and occipital regions of the brain at the back of the head. Clearly this is affected by
narrowing the head which increases the distance to the visual imaging area. In SCIET this is used for projecting the Point of Awareness and intention.
Another concept in SCIET Theory that is related is the awareness of time and future potentials present in every action, which may be interpreted as a spiritual quality. Lengthening the visual field
increases the awareness of the environment while enhancing peripheral vision. Since sensory fields and their processes overlap within the brain, all are affected by the physiological change. We can
only guess how it impacts the physical, mental, emotional and spiritual components of the personality.
Archeological Evidence
We find that during the third millennium there were a wave of barbarous invasions into the area where many dolichocephalic populations lived in Europe and the Mediterranean. In Malta the long headed
people were found in The Hypogeum of Hal Saflieni stacked to the ceiling, their bodies apparently interred without ceremony by invaders intent on eliminating them and their Goddess worshiping
This is seen in communities in ancient England as well, where the villages were attacked and the residents stacked in their long houses like bags of potatoes with evidence of violent death. It may
have been a type of religious conflict driven by orders from the leaders of the attackers. It seems similar to the circumstances of the the Israelite attacks on Cannan, which were directed to
eliminate hybrid humans and replace them with pure humans. Certainly it can be assumed that the long headed people were genetically different from he round headed people, whether the long heads were
a pure genetic strain or mixed would have made no difference to a group intent on wiping that race from the face of the Earth.
Whether it is myth or fact, we have heard that the disaster of 9400 BC was engineered to eliminate what was considered a contaminated genome from the planet. We know that those efforts were not
entirely successful, and that many areas on the surface escaped devastation, Whatever populations lived there continued to proliferate and stories like the one from the Bible about attacking Canaan
and killing every living thing suggest that genetic contamination had to be a factor in this attitude.
In modern times the effort to eliminate the long heads continues in the form of denying the existence of the skulls throughout Europe and the Americas. Only since the Internet came into existence has
this embargo on information been broken. Museums have consistently hidden the long skulls, storing them away from public view. Recent finds in Puru and the resulting publicity have avoided this fate
and we now know that these skulls are from a people with a different DNA than normal humans.
For example, in many areas of the world, the custom of cranial deformation was practiced until those who did so were forced to stop by religious or political authorities. The practice seems strange
to modern people, but apparently it served some purpose to those doing it. Of course it happened beginning shortly after birth, so however it started, the ones whose heads were deformed knew nothing
about how it would be without it.
Culture of Long Heads
We do know a few things about the long headed people, where they lived and when. Some populations like the ones in Peru continued up to the time of William the Conqueror in isolated regions on the
Southern coast of Peru, and their influence continued to inspire some tribal peoples to use head binding to lengthen their skulls.
A population that practiced cranial deformation, the Nahai-speaking area of Tomman Island and the south south-western Malakulan (Australasia), believe that a person with an elongated head is more
intelligent, of higher status, and closer to the world of the spirits.^[28]
Channeled Insights
Long Skulls in Egypt were found in the same burial areas as the aristocracy of Egypt and seem to be considered the Priest class of that society. In this channeled insight posted here, Elizabeth Haich
explains the view of the Pharaoh on the differences between long heads and round heads.
Elisabeth Haich was a spiritual teacher and author of several books dedicated to spiritual subjects. The below quote is from her best known book, Initiation, Haich describes early experiences of her
life in Hungary, as well as details of her past life during which she was initiated by her uncle, Ptahhotep, in ancient Egypt. In the following chapter of this book she describes why some people in
the Egyptian aristocracy had elongated heads, and where their race came from.
Ever since my childhood father has been accustomed to my questions, and he now answers me as patiently as ever: ‘You have a mirror, and you have seen your head in this mirror, haven’t you?’ ‘Yes,
Father, I see my head every day when Menu does my hair.’ ‘And what have you noticed?’ asks father. ‘That I have a much longer head than the sons of men in general. But you too, and Ptahhotep and
most of the people in our race—the Sons of God, as people call us—have the same longer head form. It’s noticeable even in spite of the kerchief or head-gear or ornaments the person might be
wearing. How is it, Father? Why is the shape of our heads different from that of the heads of the sons of men?’
Right now we are living in such a period of transition in which changes are noticeable. One of these phenomena is evident in the fact that various races of people with roundish skulls are led and
governed by rulers who are spiritually greatly superior to them and who are even different from them physically. They have a more graceful figure and an elongated cranium.
Those of us who have this elongated skull make relatively little use of our intellects because we are able to experience truth directly with our inner sight. Our forehead is not heavily arched,
because in our heads the brain centres having to do with the power of thinking are only developed to the point necessary for us to perceive and consciously experience external impressions. On the
contrary, in the rear part of our cranium we possess fully developed brain centres, the physical instruments of spiritual revelation. These brain centres enable us to be conscious on the divine
plane and give us those superior qualities and characteristics which distinguish us from the sons of men. Human beings, in their consciousness, live in time and space. We, although we too inhabit
earthly bodies, enjoy the perfect spiritual freedom, in freedom from time and space. Through the power of the divine consciousness and with the help of these brain centres, we are able to move
freely in time and space. ‘This means that we are able to shift our consciousness into the past or into the future at will. In other words, we are able to experience the past and the future as
present. And with the same ease we can free ourselves from the hindrance of space and move our consciousness to any place we wish. In this condition there is no “here” and no “there”, but only
omnipresence. For past and future—here and there—are only different aspects, different projections of the one and only reality, the eternal omnipresent Being: GOD.
It is interesting that it mentions the idea that the fore brain used by modern humans to recall our experiences and plan activities is mentioned as being unnecessary to the “Sons of God” because they
use the fully developed brains centers of spiritual revelation in the back of the head. These ideas are consistent with what would be expected by lengthening the skull, but we cannot address how a
naturally evolved Long Head was like, we are only looking at why normal humans would opt to narrow the skulls of their infant children. There must have been perceived advantages, and it may have
involved being more spiritual and even the ability to communicate telepathically with others having the same type of skull as mentioned in the quote above.
Long Heads and SCIET Summary
In popular literature and on the Internet, what is referred to as Long Heads is of two types in the modern era of archeology, natural long heads and cranial deformed long heads. This article
addresses the second type as a means to examine the effects of narrowing the skull of a normal human being.
The practice of artificial cranial deformation was widely practices until it was forbidden by colonial invaders in the last 400 hundred years. In some tribes on islands and the interior of the
continents it may continue today. Although it was frowned upon by churches and authorities because it represented an older culture, there was no practical reason for banning it, unless it was
considered abusive to the child. This may well have been the reason cited by the colonials.
What is obvious is that those practicing cranial deformation did it for a reason, and what is reported about those so affected, is that they were more spiritual and wiser in their reactions to
Brain cavity analysis of those born normal and artificially deformed shows that their brain processes were different because of it. Illustrated above is an increase on the length of the brain by 20
percent, making their visual fields subject to the influence of other regions of the brain during processing. Whether or not this made them wiser or more philosophical is not known, but that is the
character reported by the historical information available today.
The history of long headed people from the archeological record indicates that the naturally long headed were not war like, being Goddess worshippers within a matrilineal society. These people lived
everywhere on the planet and that until the third millennium they prospered throughout the Mediterranean, Indus Valley and Europe, at which time invading tribes of patrilineal people engaged in a
campaign of genocide against them. We know that the Celts and Aryans both committed genocide against the long headed people, but there is no explanation for why.
One idea that comes forward now is derived from research related to the influence of off world beings. It appears that the long headed beings were a hybrid of the off world culture, and that the
round headed ones were the intended “inheritors of the Earth”, an idea, that if true would suggest that the round heads, the humans, were instructed by their “Gods”to exterminate them and eliminate
their genes from the planet. Research on the DNA of the Paracas long heads has established that they are not “homo sapiens” but another variety of human entirely.
The Sumerian tablets tell that a great flood was called for by one of the Sumerian Gods, and that it caused humanity to be pushed to the brink of extinction, necessitating intervention by introducing
genetically adapted cereal crops and domesticated animals. The cataclysm must have so damaged the environment that they could no longer forage for food successfully.
What we learned from the research is that long headedness made people more gentle, thoughtful, philosophical and peaceful. Unfortunately this made them easy targets for violent invaders who used this
quality against them in their invasions.
It may have been that the natural long heads had a marked advantage over the humans in terms of mental abilities. They may have been able to communicate telepathically, overwhelm the self control of
normal humans and other capabilities that we would consider paranormal. Some of the skulls in Paracas are so different, with such larger brain cavities that suggesting they could do more seems
What the natural long heads were like in terms of their culture can only be surmised from the archeological record in places like Paracas Peru, where large cemetery sites have been excavated during
the last fifty years. While many cultures bury people with weapons, these are conspicuously missing from the funerary sites. Jewelry, woven cloth and personal items dominate their grave goods. The
end of their culture along the coast of Peru did not indicate a violent end. Whether a calamity like a tidal wave or an epidemic was responsible is unknown, but if this did happen it is very likely
that afterward the remaining people continued until the last one died or moved to another known society.
Dane Arr
July 12, 2019
What is Spacetime?
Physicists believe that at the tiniest scales, space emerges from quanta.
What might these building blocks look like?
This article is from Scientific American and presents the current views of scientists about Spacetime. I have reproduced it in its entirety to provide a reference for SCIET and how it deals with
Spacetime. In other articles, I will refer to this one for contrasting approaches. This article beautifully presents some core issues regarding the controversy over the competition to describe
reality in the realm of very small changes in space. We need to find a General Theory of Spacetime to do this, and that is the intention of SCIET Theory.
People have always taken space for granted. It is just emptiness, after all—a backdrop to everything else. Time, likewise, simply ticks on incessantly. But if physicists have learned anything from
the long slog to unify their theories, it is that space and time form a system of such staggering complexity that it may defy our most ardent efforts to understand.
Albert Einstein saw what was coming as early as November 1916. A year earlier he had formulated his general theory of relativity, which postulates that gravity is not a force that propagates through
space but a feature of spacetime itself. When you throw a ball high into the air, it arcs back to the ground because Earth distorts the spacetime around it, so that the paths of the ball and the
ground intersect again. In a letter to a friend, Einstein contemplated the challenge of merging general relativity with his other brainchild, the nascent theory of quantum mechanics. That would not
merely distort space but dismantle it. Mathematically, he hardly knew where to begin. “How much have I already plagued myself in this way!” he wrote.
Einstein never got very far. Even today there are almost as many contending ideas for a quantum theory of gravity as scientists working on the topic. The disputes obscure an important truth: the
competing approaches all say space is derived from something deeper—an idea that breaks with 2,500 years of scientific and philosophical understanding.
[Note] The article is posted here because it beautifully presents some core issues regarding the controversy over the competition to describe reality in the realm of very small changes in space. We
need to find a General Theory of Spacetime.
A kitchen magnet neatly demonstrates the problem that physicists face. It can grip a paper clip against the gravity of the entire Earth. Gravity is weaker than magnetism or than electric or nuclear
forces. Whatever quantum effects it has are weaker still. The only tangible evidence that these processes occur at all is the mottled pattern of matter in the very early universe—thought to be
caused, in part, by quantum fluctuations of the gravitational field.
Black holes are the best test case for quantum gravity. “It’s the closest thing we have to experiments,” says Ted Jacobson of the University of Maryland, College Park. He and other theorists study
black holes as theoretical fulcrums. What happens when you take equations that work perfectly well under laboratory conditions and extrapolate them to the most extreme conceivable situation? Will
some subtle flaw manifest itself?
General relativity predicts that matter falling into a black hole becomes compressed without limit as it approaches the center—a mathematical cul-de-sac called a singularity. Theorists cannot
extrapolate the trajectory of an object beyond the singularity; its time line ends there. Even to speak of “there” is problematic because the very spacetime that would define the location of the
singularity ceases to exist. Researchers hope that quantum theory could focus a microscope on that point and track what becomes of the material that falls in.
Out at the boundary of the hole, matter is not so compressed, gravity is weaker and, by all rights, the known laws of physics should still hold. Thus, it is all the more perplexing that they do not.
The black hole is demarcated by an event horizon, a point of no return: matter that falls in cannot get back out. The descent is irreversible. That is a problem because all known laws of fundamental
physics, including those of quantum mechanics as generally understood, are reversible. At least in principle, you should be able to reverse the motion of all the particles and recover what you had.
A very similar conundrum confronted physicists in the late 1800s, when they contemplated the mathematics of a “black body,” idealized as a cavity full of electromagnetic radiation. James Clerk
Maxwell’s theory of electromagnetism predicted that such an object would absorb all the radiation that impinges on it and that it could never come to equilibrium with surrounding matter. “It would
absorb an infinite amount of heat from a reservoir maintained at a fixed temperature,” explains Rafael Sorkin of the Perimeter Institute for Theoretical Physics in Ontario. In thermal terms, it would
effectively have a temperature of absolute zero. This conclusion contradicted observations of real-life black bodies (such as an oven). Following up on work by Max Planck, Einstein showed that a
black body can reach thermal equilibrium if radiative energy comes in discrete units, or quanta.
Theoretical physicists have been trying for nearly half a century to achieve an equivalent resolution for black holes. The late Stephen Hawking of the University of Cambridge took a huge step in the
mid-1970s, when he applied quantum theory to the radiation field around black holes and showed they have a nonzero temperature. As such, they can not only absorb but also emit energy. Although his
analysis brought black holes within the fold of thermodynamics, it deepened the problem of irreversibility. The outgoing radiation emerges from just outside the boundary of the hole and carries no
information about the interior. It is random heat energy. If you reversed the process and fed the energy back in, the stuff that had fallen in would not pop out; you would just get more heat. And you
cannot imagine that the original stuff is still there, merely trapped inside the hole, because as the hole emits radiation, it shrinks and, according to Hawking’s analysis, ultimately disappears.
This problem is called the information paradox because the black hole destroys the information about the infalling particles that would let you rewind their motion. If black hole physics really is
reversible, something must carry information back out, and our conception of spacetime may need to change to allow for that.
Heat is the random motion of microscopic parts, such as the molecules of a gas. Because black holes can warm up and cool down, it stands to reason that they have parts—or, more generally, a
microscopic structure. And because a black hole is just empty space (according to general relativity, infalling matter passes through the horizon but cannot linger), the parts of the black hole must
be the parts of space itself. As plain as an expanse of empty space may look, it has enormous latent complexity.
Even theories that set out to preserve a conventional notion of spacetime end up concluding that something lurks behind the featureless facade. For instance, in the late 1970s Steven Weinberg, now at
the University of Texas at Austin, sought to describe gravity in much the same way as the other forces of nature. He still found that spacetime is radically modified on its finest scales.
Physicists initially visualized microscopic space as a mosaic of little chunks of space. If you zoomed in to the Planck scale, an almost inconceivably small size of 10^–35 meter, they thought you
would see something like a chessboard. But that cannot be quite right. For one thing, the grid lines of a chessboard space would privilege some directions over others, creating asymmetries that
contradict the special theory of relativity. For example, light of different colors might travel at different speeds—just as in a glass prism, which refracts light into its constituent colors.
Whereas effects on small scales are usually hard to see, violations of relativity would actually be fairly obvious.
The thermodynamics of black holes casts further doubt on picturing space as a simple mosaic. By measuring the thermal behavior of any system, you can count its parts, at least in principle. Dump in
energy and watch the thermometer. If it shoots up, that energy must be spread out over comparatively few molecules. In effect, you are measuring the entropy of the system, which represents its
microscopic complexity.
If you go through this exercise for an ordinary substance, the number of molecules increases with the volume of material. That is as it should be: If you increase the radius of a beach ball by a
factor of 10, you will have 1,000 times as many molecules inside it. But if you increase the radius of a black hole by a factor of 10, the inferred number of molecules goes up by only a factor of
100. The number of “molecules” that it is made up of must be proportional not to its volume but to its surface area. The black hole may look three-dimensional, but it behaves as if it were
This weird effect goes under the name of the holographic principle because it is reminiscent of a hologram, which presents itself to us as a three-dimensional object. On closer examination, however,
it turns out to be an image produced by a two-dimensional sheet of film. If the holographic principle counts the microscopic constituents of space and its contents—as physicists widely, though not
universally, accept—it must take more to build space than splicing together little pieces of it.
The relation of part to whole is seldom so straightforward, anyway. An H[2]O molecule is not just a little piece of water. Consider what liquid water does: it flows, forms droplets, carries ripples
and waves, and freezes and boils. An individual H[2]O molecule does none of that: those are collective behaviors. Likewise, the building blocks of space need not be spatial. “The atoms of space are
not the smallest portions of space,” says Daniele Oriti of the Max Planck Institute for Gravitational Physics in Potsdam, Germany. “They are the constituents of space. The geometric properties of
space are new, collective, approximate properties of a system made of many such atoms.”
What exactly those building blocks depend on the theory. In loop quantum gravity, they are quanta of volume aggregated by applying quantum principles. In string theory, they are fields akin to those
of electromagnetism that live on the surface traced out by a moving strand or loop of energy—the namesake string. In M-theory, which is related to string theory and may underlie it, they are a
special type of particle: a membrane shrunk to a point. In causal set theory, they are events related by a web of cause and effect. In the amplituhedron theory and some other approaches, there are no
building blocks at all—at least not in any conventional sense.
Although the organizing principles of these theories vary, all strive to uphold some version of the so-called relationalism of 17th- and 18th-century German philosopher Gottfried Leibniz. In broad
terms, relationalism holds that space arises from a certain pattern of correlations among objects. In this view, space is a jigsaw puzzle. You start with a big pile of pieces, see how they connect
and place them accordingly. If two pieces have similar properties, such as color, they are likely to be nearby; if they differ strongly, you tentatively put them far apart. Physicists commonly
express these relations as a network with a certain pattern of connectivity. The relations are dictated by quantum theory or other principles, and the spatial arrangement follows.
Phase transitions are another common theme. If space is assembled, it might be disassembled, too; then its building blocks could organize into something that looks nothing like space. “Just like you
have different phases of matter, like ice, water and water vapor, the atoms of space can also reconfigure themselves in different phases,” says Thanu Padmanabhan of the Inter-University Center for
Astronomy and Astrophysics in India. In this view, black holes may be places where space melts. Known theories break down, but a more general theory would describe what happens in the new phase. Even
when space reaches its end, physics carries on.
The big realization of recent years—and one that has crossed old disciplinary boundaries—is that the relevant relations involve quantum entanglement. An extrapowerful type of correlation, intrinsic
to quantum mechanics, entanglement seems to be more primitive than space. For instance, an experimentalist might create two particles that fly off in opposing directions. If they are entangled, they
remain coordinated no matter how far apart they may be.
Traditionally when people talked about “quantum” gravity, they were referring to quantum discreteness, quantum fluctuations and almost every other quantum effect in the book—but never quantum
entanglement. That changed when black holes forced the issue. Over the lifetime of a black hole, entangled particles fall in, but after the hole evaporates fully, their partners on the outside are
left entangled with—nothing. “Hawking should have called it the entanglement problem,” says Samir Mathur of Ohio State University.
Even in a vacuum, with no particles around, the electromagnetic and other fields are internally entangled. If you measure a field at two different spots, your readings will jiggle in a random but
coordinated way. And if you divide a region in two, the pieces will be correlated, with the degree of correlation depending on the only geometric quantity they have in common: the area of their
interface. In 1995 Jacobson argued that entanglement provides a link between the presence of matter and the geometry of spacetime—which is to say, it might explain the law of gravity. “More
entanglement implies weaker gravity—that is, stiffer spacetime,” he says.
Several approaches to quantum gravity—most of all, string theory—now see entanglement as crucial. String theory applies the holographic principle not just to black holes but also to the universe at
large, providing a recipe for how to create space—or at least some of it. For instance, a two-dimensional space could be threaded by fields that, when structured in the right way, generate an
additional dimension of space. The original two-dimensional space would serve as the boundary of a more expansive realm, known as the bulk space. And entanglement is what knits the bulk space into a
contiguous whole.
In 2009 Mark Van Raamsdonk of the University of British Columbia gave an elegant argument for this process. Suppose the fields at the boundary are not entangled—they form a pair of uncorrelated
systems. They correspond to two separate universes, with no way to travel between them. When the systems become entangled, it is as if a tunnel, or wormhole, opens up between those universes, and a
spaceship can go from one to the other. As the degree of entanglement increases, the wormhole shrinks in length, drawing the universes together until you would not even speak of them as two universes
anymore. “The emergence of a big spacetime is directly tied into the entangling of these field theory degrees of freedom,” Van Raamsdonk says. When we observe correlations in the electromagnetic and
other fields, they are a residue of the entanglement that binds space together.
Many other features of space, besides its contiguity, may also reflect entanglement. Van Raamsdonk and Brian Swingle, now at the University of Maryland, College Park, argue that the ubiquity of
entanglement explains the universality of gravity—that it affects all objects and cannot be screened out. As for black holes, Leonard Susskind of Stanford University and Juan Maldacena of the
Institute for Advanced Study in Princeton, N.J., suggest that entanglement between a black hole and the radiation it has emitted creates a wormhole—a back-door entrance into the hole. That may help
preserve information and ensure that black hole physics is reversible.
Whereas these string theory ideas work only for specific geometries and reconstruct only a single dimension of space, some researchers have sought to explain how all of space can emerge from scratch.
For instance, ChunJun Cao, Spyridon Michalakis and Sean M. Carroll, all at the California Institute of Technology, begin with a minimalist quantum description of a system, formulated with no direct
reference to spacetime or even to matter. If it has the right pattern of correlations, the system can be cleaved into component parts that can be identified as different regions of spacetime. In this
model, the degree of entanglement defines a notion of spatial distance.
In physics and, more generally, in the natural sciences, space and time are the foundation of all theories. Yet we never see spacetime directly. Rather we infer its existence from our everyday
experience. We assume that the most economical account of the phenomena we see is some mechanism that operates within spacetime. But the bottom-line lesson of quantum gravity is that not all
phenomena neatly fit within spacetime. Physicists will need to find some new foundational structure, and when they do, they will have completed the revolution that began just more than a century ago
with Einstein.
This article was originally published with the title “What Is Spacetime?”
Vacuum Forming Your Visions
Projecting an Attractive Vision to Manifest your Desires
Dane Arr
This article first appeared on SCIET.com as Forming Space
“While wondering about the source of psychic phenomena, with my eyes open and looking across the room, suddenly the answer to every question was illustrated with dancing lines of white light.
The lines responded to my thoughts and interacted with them as I learned in that short span of minutes how the fabric of space worked to create all that we see.”
Projecting the will outside of the body is learned by warriors, game players, spectators, gamblers and business people. It is taught in sales seminars as an act of mental projection and positive
expectation that works to increase sales.
Forming Spaceis a good term for the ability of consciousness to project the will outside of the body. The term properly expresses the responsive nature of space and the role of consciousness in
affecting it. And it takes the individual past the euphemism of “visualization”, and into a more active role in the process of manifestation.
Forming space occurs when we project an internal
perception, a visualization filled with knowing and intention, into the shared space of society. It is most effective when the projection is well developed and clear in the mind of its creator. In
essence the projection of the will is like a hole or mould that other energies are attracted to and shaped by.
A variety of visualization techniques offer good guidance in this process. The most well known of these is the Secret which coaches not just visualization, but to project oneself into the vision,
feeling it already being. Its practitioners say it works as advertised.
Of course the ability to “be” in the vision requires a substantial reality to draw from, meaning that imagining something
with which you have no real experience will not be sufficient to activate the powers of manifestation you need.
The ability to project into the space around you stems from the tools nature has equipped everyone with in order to live as hunter gatherers throughout deep evolutionary history.
Our powers of mind
depend on a continuous awareness of our surroundings, one that has us actually projecting our being outside of our bodies. When we do this other awarenesses experience our intention and unconsciously
conform with it. In this way we are able to attract from our environment what we desire.
My first experience with Projected Visualization
My most unusual experience with projection was when I was able to see the body’s lines of force, which extend out like looping sensory antennas of white light.
In the Seth Material by Jane Roberts,
I found the only reference that describes what happened that day. According to one of the higher level being-states that she channeled, our nervous system projects these lines of force out from the
skin where we perceive the acupuncture meridian points to be.
When this happened to me, I was totally unaware of the phenomenon and experienced it as a vision, the Dance of Shiva is a name that has
been used to describe it. While I sat with my eyes wide open and in the company of two other people, the lines of force responded to my every curious thought by illustrating the effects of my own
interaction in a consciousness filled universe.
I saw how my own visual focus was but a guide for the projection of my will, a mechanism for me to extend my mind beyond my body and into the space
around me. The often cited situation of feeling like you are being looked at in a crowded room, when you will turn and look directly at a stranger, in spite of there being hundreds of others who
might be looking as well, was shown to be a result of these line of force intruding upon the persons body-space.
I watched as I practiced controlling the lines of force, extending them up to my
friend, but stopping short of touching her with them. I realized that the concept of visual focus had to be coordinated with that of mental focus. There was a difference between looking at someone
and staring at them. Looking was not intrusive, I held my visual and mental focus just short of the body, but acute enough to see clearly.
Projecting into another person’s space, past their skin and into their mind was as simple as visualizing a Ping-Pong ball in the middle of their head and then imagining it as an extension of me, as
if it were on an invisible rod. Doing this frequently drew a response like “What’s up?”
Forming Space: An Astrological Analogy
All metaphysics describes and deals with this reality differently. Having studied astrology for many years, I find it useful to explain the qualities with astrological references.
SCIET Dynamics validates and explains astrology as the result of the continual outreach and crystallization of each moment by the center of being that each person represents (the SCIET cycle). Each
moment’s outreach is crystallized based on the angularities of the body in space and in the context of the solar system. SCIET-based Sets establish the relevance of the angularities and their
relationships to the signs and houses while the SCIETline provides the basis for understanding the impact of the planetary bodies on each person’s individuality.
The body’s field of consciousness is derived from all the moments that the gnome has been developing on earth. It is an accumulation of SCIETsphere-based moments extending back hundreds of millions
of years, evolved in the gnome and retained in the frequency-based infintesimal seed of spirit that is known as the soul. The physical body has evolved in concert with the seed of spirit over the
eons to provide the connection between this conduit, or continuity, to the ancient mental past and the physical present. The relationship to the physical present is based on super conducting cellular
Phi resonant consciousness, the ability of the living organism to sustain itself, and the rise of a larger body of survival intelligence is rooted in a gestalt consciousness, or shared experience
that is available to the nervous system by virtue of shared space. (Sheldrake’s Morphogenetic Field, et al) Human beings are a vehicle for an ancient, even universal, consciousness that integrates
with the body during its early development. (incarnates). The seed of spirit provides a template for the underlying processes of the nervous system to stream the incoming sensory information into the
extra-dimensionsal storage capabilities that we know as long-term memory. Access to the memory is provide by a process of tagging that is retained in the physical/mental energies of the body. These
tags and the memories held in their frequencies dissipate at death and that is why we experience an unwinding of our stored memories.
Patterned after the solar system
The body and the spirit have ancient relationships with the solar system. The evolved seed of spirit retains the experiences of countless lifetimes and the gnome is the equivalent of a planetary
being in itself, having been moving continuously on the surface of the Earth for over four billion years. Together they have ancient and evolved relationships with all parts of our solar system. The
planetary bodies have both spiritual and material frequencies that allow our dual natures to establish a lock on time and space.
The astrological relationship established by the body/gnome with
each of the planets leads to an ongoing set of capacitance layers related to each planets. These capacitance layers remain from the beginning of the planets evolutionary development and are the
foundation of evolution for all energetic life forms.
Our minds are patterned after the solar system. The perspective of an Earth-based evolution creates a system of concentric spheres that begins
with the Earth/moon on the inside and includes Mercury, Venus and Mars as elements of a personal solar sphere of consciousness.
Illustrated on the right are the inner planets with the earth/moon at the center. Venus is in blue, Mars is red and Mercury is black and the sun is yellow. The planets each have two circles
representing their furthest and closest approaches to our planet. The sun and moon vary only slightly in their distance from the Earth. This diagram shows the range of intensity based on physical
proximity that is possible based on the planets positions in space.
The inner planet energies are tools under our direct control, while the outer planets function as part of our social awareness, providing a framework for our interaction with the world.
The pattern is governed by the fact that we are on earth/moon, the third planet from the center of the solar system, the basis of our experience. The moon’s energy is the reservoir of all our
experiences, it is the externalized portion of the third planet, the outer part of a single entity orbiting the sun.
The sun rules the physical body and the will, our ability to “see” and choose
from what we see or what to see and what not to see. The sun is the source of light, giving life to the Earth and evolutionary basis of the photonic processes underlying mind. In this way it is the
source of the matrix though which all other processes function.
The moon’s energy is the reservoir of all our experiences, it is the externalized portion of the third planet, the outer part of a
single entity orbiting the sun, and holds the assumptions from which the lines of force extend, grounding them to the depths of the soul.
Mercury rules how we project our lines of force, or perhaps a better expression is filaments of consciousness, out from our bodies. It is the ability to articulate with the lines of force, enabling
the power of focus and allowing us to project our concentration outside of our bodies. When a person is “concentrating on something”, it is more than a figure of speech, it is a projection of the
mind.
Venus and Mars rule particular attractions and projections and are linked to biological necessities as well as each individuals general mode of action or inaction.
Beyond Mars the effects on
the lines of force blend to rule the interactions between larger and larger groups.
Starting with Jupiter the outer planets are about how the mind deals with the external aspects
.
Forming Space: Radiant consciousness and projecting into the space around us.
Radiant consciousness is the result of the Awareness in the body’s capacitance lattice, much different from radiant light. Radiant light is electromagnetic radiation, the result of the motion of
atoms; we see the pulse of their adjustment or change of position in space.All EM is the result of movement, measured from the molecular level,
Radiant Consciousness is the result of the resonant adjustment in space (gravitational attraction) that all things have for one another. Modern physics uses gravity to describe the quality of all
things to affect the space around them, an effect that is resonant in nature. Based on the concept of density, gravity increases when more atomic nuclei are packed into a smaller space. (See Causal
The resonance between bodies is easily observable, for instance tuning forks, bells and just about anything in which resonance can be detected. But it is what we cannot see or detect is the resonance
between the resonance. We know that resonant bodies harmonize, because we can listen to bells until they softly fade to silence. But that we cannot see nor can we hear the resonance of one thing to
another does not mean that we can assume that does not exist. In fact the quality of resonance between bodies is so pervasive that to assume that it stops when we can no longer detect it, is
foolish. The problem is in understanding how it continues.
Describing the body as being at the center of its own resonating field does not seem to be much of a stretch for science. The real question is; WHAT is resonating and how can we describe it?
We can think of the body as a scalar field of resonance between a wide range of other fields through out the environment. We can easily imagine fields descending in order from generalities such as
our body, our organs, our cells as groups, our cells individually and even and perhaps most important, our minds and memories.
So radiant consciousness is a composite of of all the levels that make up a being, focused through the lens of genetic material, the evolved body and the ancient stored memories of spirit/soul, all
at once, all the time.
The question that remains is: How does this radiant amorphous concept become the lines of force, the looping sensory antennas of white light? The answer is resonance between the descending orders of
evolved fields. Comprehending this concept requires us to reflect upon the refinement of the levels of this “resonance”. We are talking about the integrated, ongoing assimilation of ranges extending
from the present body to memories of bodies that have been gone for thousands of years. Each person fills the space around him or her with values faint and powerful and all related. It is the role of
the astrologically inspired resonance to make sense of it, to provide order and direction.
The lines are an interference pattern created by the mind/nervous system’s space-processing action and response to conscious choice, guided by the visual focus of the mind. It is interesting that
some traditions, such as Chinese Qigong, conceive of the flow that I observed as an exchange between the individual and nature.
There appears to a factual basis for these beliefs. Researchers in super conductive nano-minerals believe that platinum-group mono-atomic elements, such as rhodium, become much lighter when in the
super conductive state and become airborne, floating in the atmosphere like water or any particle of dust.Experiments with these super conductive materials show that they react to the lines of force
or filaments projected by human beings. In this way Qigong allows its practitioners to develop personal power by attracting and controlling these airborne super conducting platinum group elements as
a part of their field of focus. So, although the lines of force are the result all the resonance within us, they use frequencies affecting a small sector of materiality and give almost supernatural
power to those who learn to work with them.
The addition of the local effects on super conductive materials are not required for the interference patterns defined by the sun and mercury to control
or form space with them.
The lines are conduits of very high frequency consciousness, extensions that the inner being extends out into the world.In this way, they are the opposite of physical energy, they are the power to
form space by removing all resistance to change and imbuing it with intention, its own gravitational force to attract those parts that resonate with it.
Moreover the basis of the filaments is
rooted in the Awareness, the highest frequency shared with ensouled beings by the Creator, which meansthe lines of force are able to pattern the Creation Substance with consciousness,much like
computer programs today use “virtual cores” to extend to operational effect of data analysis and retrieval.
So a vision, once projected, becomes an attractive force, independent of its creators,
drawing its needed parts together, but only those parts which resonate on its levels. This is done with the power of external focus, which enables a conscious being to “form” the fabric of space and
imbue it with its own purpose and attractive force.
So we are able to project our innermost selves, our quintesence out into the world and use it to create “forms” which literally attract what is
needed to fill them and manifest our thoutghts.
This is forming space.
It is important for what it tells us not to do as well what to do. It explains the power of affirmations, prayer, wishes and
all sorts of superstitions about talking negative. Be careful what you ask for: you just might get it.
Forming Space: Empowering Conscious Intentions
Knowing that we can project our minds outside of our bodies is empowering. Understanding how it works gives us the key to open the door to new technologies based on consciousness and allows us to go
through barriers that have inhibited the progress of people for thousands of years. The development of a new way to express knowledge, which is already known through mystic traditions and psychology
and the many practical techniques used by salesmen and athletes will mean creating tools that can used to translate those existing understandings as well as create entirely new ones.
Visualization
is a critical component of Forming Space and it is far more than just seeing or imagining the world in a new way.
A lengthy discussion of how the nervous system interacts with the surrounding space
can be found on the NeuroSCIET pages. However, is sufficient to say that we have two nervous systems which simultaneously process what is basically the same information and then synthesize it into a
single reality.
The integration of the dual nervous system is important for the conscious control of externalized inner self because it is through the resonant integration of these two separately
occurring fields that we ARE conscious. It is also important to think of these two fields as counter-rotating with the synthesis taking place at what we call the focus of concentration.
The symmetry of animal life is due to the fundamental nature of our interaction with the resonant fields around us and how they have been involved in our evolution. These forms of life all have
ORIENTATION and MOBILITY. We part the fields as we go forward, brushing past and stimulating the pattern of resonance which forced the evolution of the right-left duality. Unlike the passive nature
of a ship plowing through the waves on the sea, life moves forward by choice and the pattern of change created by this act is toward the goal. Both sides rotate forward and meet at the mid-line where
the externalized THIRD resonance field is centered.
The Third Field
The concept of the third field is pivotal to understanding how we can control and use our inherent mental projection capabilities. When two resonant fields interact, they create a third resonance
value which acts as a common denominator between them. This value originates from a point where the two fields are equal in energy, time and distance of resonant fluctuation. As I stated above, this
is not an electromagnetic wave, but a reaction of two scalar fields of a gravitational nature. This is a critical issue because all interactions have the quality of the third field as their
foundation.
The third field is an order of magnitude greater than the two that created it. It is interesting that one of the ways to express this is the same as the Pythagorean Theorem.
Assuming that the each of the originating fields (A, B) are prime numbers, we can square them, add them together and find their square root to determine the lowest common denominator for the third
field. In this case we are talking about a value that must be much faster and smaller than either of the first two field values, since it is the outcome of them being squared. The third field is
able to interact with all of the scalar fields which are its progenitors, because it is a fractional component of them.
Forming Space: Using Sensory Perception
Returning to the astrological references, we identify our feelings or internal perceptions with the moon, our external perception to the sun and articulation to Mercury. It is well known that
biorhythms are linked to these three bodies as well.
The solar field is the intentional perceptual field and it is a third field phenomenon created by the functioning of the sensory system.
Articulation within the radiant field of consciousness is ruled by the sun, the ability to focus.
The lines are the result of an interference pattern created by the mind/nervous system’s space-processing action and response to conscious choice, guided by the visual focus of the mind. It is
interesting that some traditions, such as Chinese Qigong, conceive of the flow that I observed as an exchange between the individual and nature.
The solar field is an externalization of the activity
of the brain. It is important to understand that the processes which use the sensory organs to generate a model of the environment are also used to drive the externalized inner self, the product of
the third field phenomenon. All of the nerves of the voluntary nervous system contribute to this, and for this reason we can use the movements and positions of our body to manifest the power of the
projection of consciousness.
As stated at the beginning of this article, Forming Spaceis a good term for the ability of consciousness to project the will outside of the body. The term properly expresses the responsive nature
of space and the role of consciousness in affecting it. It takes the individual past the euphemism of “visualization”, and into a more active role in the process of manifestation.
Forming space
occurs when we project an internal perception, a visualization filled with knowing and intention, into the shared space of society. It is most effective when the projection is well developed and
clear in the mind of its creator. In essence the projection of the will is like a hole or mould that other energies are attracted to and formed.
We have described a variety of visualization techniques offering good guidance in this process. Please review information on the Secret, which coaches not just visualization, but how to project
oneself into the vision, feeling it that it already exists. But remember that the ability to “be” in the vision requires a substantial reality to draw from, meaning that imagining something with
which you have no real experience will not be sufficient to activate the powers of manifestation you need. In other words, build on what you know.
The ability to project into the space around you stems from the tools nature has equipped everyone with in order to live as hunter gatherers throughout deep evolutionary history.
Our powers of mind
depend on a continuous awareness of our surroundings, one that has us actually projecting our being outside of our bodies. When we do this other awarenesses experience our intention and unconsciously
conform with it. In this way we are able to attract from our environment what we desire.
Focus, visualize, project your desires and manifest!
Dane Arr
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Correlated stocks python
Walk through demonstraion using Pandas Datareader to download stock price data, and transform it into stock correlations. 29 Apr 2017 In the management of a financial portfolio one important
consideration is the correlations between the portfolio's various stocks. For example, in
16 May 2016 If the change in opposite directions together (one goes up, one goes down), then they are negatively correlated. You can calculate the correlation 15 Dec 2009 In finance, one usually
deals not with prices but with growth rates R, defined as the difference in logarithm between two consecutive prices. Correlating stock returns using Python In this tutorial I'll walk you through a
simple methodology to correlate various stocks against each other. We'll grab the prices of the selected stocks using python, drop them into a clean dataframe, run a correlation, and visualize our
results. Using PCA to identify correlated stocks in Python 06 Jan 2018 Overview. Principal component analysis is a well known technique typically used on high dimensional datasets, to represent
variablity in a reduced number of characteristic dimensions, known as the principal components. Correlation of Stocks and Bonds Investors are often interested in the correlation between the returns
of two different assets for asset allocation and hedging purposes. In this exercise, you'll try to answer the question of whether stocks are positively or negatively correlated with bonds. We’re
going to try a Pearson Correlation test, to test correlation on all of these equities and the S&P 500. What do you think? Based-on viewing the charts and going by intuition, will they correlate?
Correlation will show when the Pearson Correlation Coefficient is between -1 and +1. If closer to +1, we’re seeing a positive correlation. # The below will pull back stock prices from the start date
until end date specified. start_sp = datetime.datetime(2013, 1, 1) end_sp = datetime.datetime(2018, 3, 9) # This variable is used for YTD performance. end_of_last_year = datetime.datetime(2017, 12,
29) # These are separate if for some reason want different date range than SP. stocks_start = datetime.datetime(2013, 1, 1) stocks_end = datetime.datetime(2018, 3, 9)
In order to identify correlated stocks, you have to search every combination of stock pairs in the market and compare their respective Pearson Coefficient. This is difficult, unless you are fluent in
Up to this point, we can see that we've grabbed a bunch of data for various stocks that we want to create a correlation matrix with. Right now, we're nowhere near a matrix table for these stocks, but
we're getting there. I've printed C.head() to give us a reminder of the data that we're looking at. Introduction. Correlation is a measure of relationship between variables that is measured on a -1
to 1 scale. The closer the correlation value is to -1 or 1 the stronger the relationship, the closer to 0, the weaker the relationship. It measures how change in one variable is associated with
change in another variable. Correlation in Python. Correlation values range between -1 and 1. There are two key components of a correlation value: magnitude – The larger the magnitude (closer to 1 or
-1), the stronger the correlation; sign – If negative, there is an inverse correlation. If positive, there is a regular correlation. numpy.correlate(a, v, mode='valid', old_behavior=False)[source]
Cross-correlation of two 1-dimensional sequences. This function computes the correlation as generally defined in signal processing texts: z[k] = sum_n a[n] * conj(v[n+k]) with a and v sequences being
zero-padded where necessary and conj being the conjugate. Python Correlation Heatmaps with Seaborn & Matplotlib - Duration: 7:37. Ryan Noonan 583 views Instead, let's look into the correlation of all
of these companies. Building a correlation table in Pandas is actually unbelievably simple: df_corr = df.corr() print(df_corr.head()) That's seriously it. The .corr() automatically will look at the
entire DataFrame, and determine the correlation of every column to every column. I've seen paid websites do exactly this as a service.
16 May 2016 If the change in opposite directions together (one goes up, one goes down), then they are negatively correlated. You can calculate the correlation
15 Nov 2016 Generally Correlation Coefficient is a statistical measure that reflects the correlation between two stocks/financial instruments. Determining the 20 Mar 2017 I have a DataFrame, Df with
zscores, correlation coefficients for time series ( stocks) data. The two columns being referenced accordingly are Figure 2: Correlations between stock returns vary over time and are generally of
and contributors to Python, Bokeh, pandas, NumPy, SciPy, and scikit-learn) 16 May 2016 If the change in opposite directions together (one goes up, one goes down), then they are negatively
correlated. You can calculate the correlation 15 Dec 2009 In finance, one usually deals not with prices but with growth rates R, defined as the difference in logarithm between two consecutive
prices. Correlating stock returns using Python In this tutorial I'll walk you through a simple methodology to correlate various stocks against each other. We'll grab the prices of the selected stocks
using python, drop them into a clean dataframe, run a correlation, and visualize our results.
11 Nov 2017 stock market indices, exhibit considerable short-time correlations. been computed using pearsonr function from the Python (2.7) module
19 Feb 2020 A correlation of 0.0 shows no linear relationship between the movement of the two variables. Correlation statistics can be used in finance and 1 May 2017 Positive Correlation. Let's take
a look at a positive correlation. Numpy implements a corrcoef() function that returns a matrix of correlations of x Tweet sentiment showed stronger correlations with stock Thereafter, searchtweets,
which is a Python wrapper for Twitter's Premium and. Enterprise search 2 Jan 2015 Modelling correlations with Python and SciPy Eric Marsden by the stock market ) principle,
freakonometrics.hypotheses.org/15999 ▷ Python 11 Nov 2017 stock market indices, exhibit considerable short-time correlations. been computed using pearsonr function from the Python (2.7) module
Corporate Finance Essentials will enable you to understand key financial issues related to companies, investors, and the interaction between them in the capital
19 Feb 2020 A correlation of 0.0 shows no linear relationship between the movement of the two variables. Correlation statistics can be used in finance and 1 May 2017 Positive Correlation. Let's take
a look at a positive correlation. Numpy implements a corrcoef() function that returns a matrix of correlations of x
In this post I’ll be looking at investment portfolio optimisation with python, the fundamental concept of diversification and the creation of an efficient frontier that can be used by investors to
choose specific mixes of assets based on investment goals; that is, the trade off between their desired level of portfolio return vs their desired level of portfolio risk.
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Counted Petri Nets, and Useless Protocol Specification Tools
There's one variant of Petri nets, called counted Petri nets, which I'm fond of for personal reasons. As Petri net variants go, it's a sort of sloppy but simple one, but as I said, I'm fond of it.
As a warning, there's a bit of a diatribe beneath the fold, as I explain why I know about this obscure, strange Petri net variant.
My first project in grad school involved building a simulator for a network protocol specification language called Estelle. Estelle is, as I like to describe it, a formal specification language with
absolutely no useful formal qualities.
The problem with Estelle is that it's based on something called augmented heirarchical communicating finite state machines. Communicating FSMs are fine; heirarchical FSMs are fine. They're not my
favorite model, but they're useful, valid techniques for describing things.
Where Estelle got into trouble was the "augmented" part. What that meant is that
each FSM had a bunch of data associated with it, and each transition had a set of guard conditions and effect code written in Pascal. So a state transition could run an arbitrary Pascal program that
altered the state of the FSM without changing the visible FSM state; and that change could affect the guard conditions determining what transitions could occur later. So every Estelle transition is
basically unlimited in its effects. Any analysis that tried to answer questions about a specification that used this capability generally reduced to the halting problem; but you really needed to use
it to represent the state
involved in communication protocols!
Anyway, I got roped into this, and I was supposed to port a huge Smalltalk simulator of Estelle to C. Only I'd never really used Smalltalk. I knew the theory of it, but I'd never had access to a real
Smalltalk interpreter. So as a way to learn Smalltalk, and to get into the swing of this protocol specification stuff, I wrote a simple counted Petri net simulator.
Interestingly, I can't find anything about counted Petri nets on the internet, so I assume they died an ignomious death. I'll revive them for a brief moment, because they're an interesting simple
example of how to extend Petri nets. The extension is very simple and very minimal, and has some theoretical awkwardness, but it's useful for expressing certain kinds of fairly common concurrency
All that you do when you extend to counted Petri nets is to add an integer to each transition. The transition can fire not when all of its input edges have tokens waiting, but when some collection of
tokens from the input arcs can provide enough tokens. The counts on the edges become a bound on the maximum number of tokens that can move across the arc.
What this is useful for is things like the worker pool pattern. In this kind of concurrency, you have one main thread, and many workers. The main thread creates tasks which are put into a pool. The
workers each grab tasks from the pool and perform the tasks, until no tasks are left in the pool. The reason for using a pool is load balancing: the tasks take different amounts of time to complete,
and you don't know which tasks are going to take longer. So each of the workers grabs a random task from the pool, and runs it. If it's a fast one, it finishes it quickly, and then grabs another.
This means that the processors will all be busy processing tasks for roughly the same amount of time, but they'll end up processing different numbers of tasks. The synchronization scheme for this is
for the main thread to set up the task pool, and then wait after putting the tasks into the pool, the main thread waits until all of
the tasks are complete.
How would you represent a worker pool with a Petri net? You have a pool of workers thread, all of which are basically equivalent. The main thread puts tokens (representing the tasks) into a place
representing the task pool. The task pool has a collection of out edges, one for each thread, which carry the task tokens to a subnet representing the task threads. The worker threads each have a
place at the
end where they deposit tokens for completed tasks. The main thread waits on a transition which doesn't get a token until all of the tasks are completed. That token comes from a place which gets its
token only when all of the tasks are complete. Since the different tasks will have performed different numbers
of tasks, we use a transition that fires when all of the tasks are complete. A very simple example of this, with two worker tasks is in the image to the right. The main thread is colored green; the
places and transitions that control the synchronization of worker threads are red, and the worker threads themselves are blue.
The counted net is a strange sort of hybrid. It's basically adding a primitive sort of counting to the nets, which is useful. But it does it in a way which is extremely limited. For example, in a
real task pool scenario, you wouldn't know how many tasks were going to be dispatched to the pool; but the transition needs to be marked with a specific value. So for the purposes of the net, you
pretend to know.
As I mentioned, this adds a bit of theoretical awkwardness. One of the great things about Petri nets is that they've got a very strong notion of synchronization. But with counted nets, that gets
weakened. It doesn't show in this example - but for non-trivial nets, you can get cases where things get tangled - where you want at least 1 token from each of some group of places, but you can't
guarantee that properly
without adding a bunch of extra layers of places and transitions - which messes up the simplicity and clarity which is the main reason for using Petri nets.
Next week, I'll describe colored Petri nets, which are a much stronger, much cleaner way of extending the capability of Petri nets. The basic idea is that tokens can carry information, and lamba
calculus functions can be associated with transitions.
More like this
Colored Petri Nets The big step in Petri nets - the one that really takes them from a theoretical toy to a serious tool used by protocol developers - is the extension to colored Petri nets (CPNs).
Calling them "colored" is a bit of a misnomer; the original idea was to assign colors to tokens, and…
Among many of the fascinating things that we computer scientists do with graphs is use them as a visual representation of computing devices. There are many subtle problems that can come up in all
sorts of contexts where being able to see what's going on can make a huge difference. Graphs are,…
A couple of people pointed out that in my wednesday post about Go, I completely left out the concurrency stuff! That's what I get for rushing the post - I managed to leave out one of the most
interesting subjects! Go provides very strong support for communicating processes. I haven't done a lot…
Multitasking refers to the simultaneous performance of two or more tasks, switching back and forth between different tasks, or performing a number of different tasks in quick succession. It consists
of two complementary stages: goal-shifting, in which one decides to divert their attention from one…
IÂ can't figure out how a transition with a number is supposed to work. You don't provide an example, and your prose just isn't doing it for me. A before picture and an after picture would be good...
The standard definition of a Petri Net.
A Petri net is a tuple (S,T,F,M0,W):
S - set of states.
T - set of transitions.
F - flow relation
M0 - initial marking.
W - is the set of arc weights.
The function of the arc weights W in the standard definition of a Petri Net is the same as the numbers which you assign on transitions of a "Counted Petri Net". The reason why you can not find
anything about "Counted Petri Nets" on internet is that they do not exists as a model. They are subsumed by standard Petri nets.
Alexandru: Mark's paragraph starting "All that you do (...)" contradicts your first remark. I interpret it as stating that a transition is enabled whenever some bag of tokens on its input places
exists such that for each input place the count is at most the capacity of the input arc, while the total count is the number inscribed on the transition itself, and that any such bag can be removed
when the transition fires.
On the subsumption I think you are right: such Petri nets can be automatically rewritten to standard Petri nets. I don't even think they need to grow more than linearly in size, if you'll accept
extra steps (weak bisimulation).
As Reiner beat me to saying:
The difference between a counted net a standard net is that in
a counted net, a transition labeled "n" is enabled whenever any combinations of its predecessor places can contribute a total of N tokens. In a standard net, that "N" must be equal to the sum of the
capacities of all of the incoming arcs. In a counted, that "N" can be less than or equal to the sum of the incoming arcs.
The counted net is strictly not any more powerful than the standard net. But it's more expressive in the limited sense of allowing smaller graphs to express the same coordination regime.
Thanks Reiner and Mark. Now the model seems more clear.
Suppose we have a Petri Net P=(S,T,F,M0,W) and its underlying graph G(P) generated by the initial marking M0. Also a Counted Petri Net C=(S,T,F,M0,W') with the same initial marking M0 and its
underlying underlying G(C). What I think is that there is a simulation relation between G(C) and G(P), where the simulation relation is a preorder.
You have mentioned about weak bisimulation. I don't really see how one can relate G(C) and G(P) by weak bisimulation, as weak bisimulation involves sequence of transitions and more than that in G(C)
there are transition which G(P) can not simulate (mimic). Unless you meant something else.
Alexandru / Mark: see http://www.win.tue.nl/~rp/petrinets/counted-nets-simulated.png for what I mean. (IMG elements don't appear to work here.) I wish I could draw pictures like Mark ...
As far as I see, the translation sketched in that picture is a simulation, and even a weak bisimulation: for each transition with inflow m and capacity n in the original, it replaces it with m+2
transitions in the result, and each firing of an original corresponds to a sequence of n+2 firings of those transitions in the result. The size of the result is linear in the size of the original, if
we count arcs with multiplicities as multiple arcs.
I don't know precisely but I think that in the right picture (the proposed translation), the arc between p_H_2 and H_2 (p_H_2->H_2) should be labeled with (1) and not with (4). The reason is that the
case when p1=1, p2=1, p3=1 will be not considered.
Sorry about the mistake; actually the arc between t1_1 and p_t1_l should have had multiplicity 4. Fixed now.
Alexandru: a (hopefully final) update.
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The best books for mathematical inspiration
David Hilbert was one of the great mathematicians of the early twentieth century. He also created an entire research environment at the University of Göttingen, founded on the fundamental assumption
that there is a deep unity behind all of mathematics (an assumption that in part motivated me to write All the Math You Missed). From this school much of the mathematical triumphs of the last 100
years have sprung (especially from the revolutionary work rotating around the mathematics of Emmy Noether in the 1920s in Göttingen). At least that is my impression from reading this book. It
inspires young mathematicians to believe that it is indeed possible that “mathematics is the ultimate description of reality.” It certainly had that effect on me as a college junior worrying about my
future life.
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RTI Series #2- Recommendation 4: Solving Word Problems Based on Common Underlying Structures - CTL - Collaborative for Teaching and Learning
Recommendation 4 – Solving Word Problems Based on Common Underlying Structures
Connected to the CCSSO Standards and Instructional Recommendations
This is the second in a series of five postings that connect the Institute of Education Sciences (IES) practice guide recommendations, Assisting Students Struggling with Mathematics: Response to
Intervention (RTI) for Elementary and Middle School Students with corresponding CCSSO Standards indicators, and an instructional look alike for that recommendation.
The IES guide identifies eight recommendations that are designed to help teachers, principals, and administrators use Response to Intervention for early detection, prevention, and support of students
struggling with mathematics. This guide is a synthesis of research that provides instructional recommendations in support of engaging those struggling mathematics students. See IES Practice Guides.
RTI Recommendation 4: Interventions should include instruction on solving word problems that is based on common underlying structures.
CCSSO Standards:
• Solve word problems by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
• Use properties of whole numbers; look for and make use of structures.
• Represent and solve problems involving addition, subtraction, multiplication, and division.
• Work with addition, subtraction, multiplication, and division equations.
• Build number sense through activities.
What would solving word problems based on common underlying structures look like instructionally?
I found the following from the IES RTI Guide interesting and helpful; it also reminded me of the instructional approaches advocated by the Singapore mathematics series. “The two problems here are
addition and subtraction problems that students may be tempted to solve using an incorrect operation. In each case, students can draw a simple diagram like the one shown below, record the known
quantities (two of three of A, B, and C) and then use the diagram to decide whether addition or subtraction is the correct operation to use to determine the unknown quantity.” The model provides a
structure or schema that assist students in formulating a strategy for solving the problem. Another problem from the suggestions is quoted.
Version 1:
Brad has a bottlecap collection. After Madhavi gave Brad 28 more bottlecaps, Brad had 111 bottlecaps. How many bottlecaps did Brad have before Madhavi gave him more?
C = 111 total caps after receiving bottle caps from Madhavi, B = 28 that Madhavi gave Brad and A = amount that Brad had started with…so that C – B = A
Version 1:
Brad has a bottlecap collection. After Madhavi gave Brad 28 more bottlecaps, Brad had 111 bottlecaps. How many bottlecaps did Brad have before Madhavi gave him more?
C = 111 total caps after receiving bottle caps from Madhavi, B = 28 that Madhavi gave Brad and A = amount that Brad had started with…so that C – B = A
Version 2:
Brad has a bottlecap collection. After Brad gave 28 of his bottlecaps to Madhavi, he had 83 bottlecaps left. How many bottlecaps did Brad have before he gave Madhavi some?
C = Brads total caps, A = 28 that Brad gave to Madhavi, and B = 83 caps that Brad had left over …so that C = A + B
Version 3:
There are 21 hamsters and 32 kittens at the pet store. How many more kittens are at the pet store than hamsters?
C = total number of kittens or 32 kittens, A = 21 hamsters and B = number of more kittens than hamsters, C – A = B
All three problems use the same model that provide a visual for what a student knows and what is unknown and thus enables the student to determine the appropriate operation for solving the problem.
This modeling also reminds me of strategies used and reported in Algebra for Everyone from National Council of Teachers of Mathematics (1990), Edwards, Edgar L. Jr..
What other examples could we include for solving word problems based on common underlying structures?
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Typesetting long calculations involving limits quickly become tedious because the same limit expression (such as "\(\lim_{i \to \infty}\)") appears in each in each step of the calculation—sometimes
multiple times!—until the limit is fully evaluated. Any time an expression appears repeatedly, you should consider introducing a macro. In particular, when the input variable for a limit is written
as \(i\), \(j\), or \(k\), then the variable almost always is integer index that goes to \(\infty\). Thus, we introduce macros to abbreviate the corresponding limit expressions. Similarly, \(h\) is
commonly used as an distance that goes to zero, such as in the definition of the derivative, so we define a macro to insert "\(\lim_{h \to 0^+}\)."
\newcommand{\jlim}{\lim_{j \to \infty}}
\newcommand{\ilim}{\lim_{i \to \infty}}
\newcommand{\klim}{\lim_{k \to \infty}}
\newcommand{\hlim}{\lim_{h \to 0^+}}
Code Output
\ilim 1/i = 0 $$\lim_{i \to \infty} 1/i = 0$$
\jlim 1/j = 0 $$\lim_{j \to \infty} 1/j = 0$$
\klim 1/k = 0 $$\lim_{k \to \infty} 1/k = 0$$
\hlim \frac{f(x + h) - f(x)}{h} = 0 $$\lim_{h \to 0^+} \frac{f(x + h) - f(x)}{h} = 0$$
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Price per Cup Calculator
The Price per Cup Calculator can calculate the price for each cup based on the total volume and the total price of the volume.
Therefore, to calculate the price per cup, we need the total volume, the total price of the volume, and the volume measurement type. The volume measurement type can be cups, pints, quarts, or
Please enter the price, the total volume, and the measurement type in the box below to get the price per cup.
To calculate the price per cup, we divide the total price by the total volume. The price is rounded to the nearest cent if necessary.
Price per Day Calculator
Here is a similar calculator you may find interesting.
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ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Objective Type Questions
Mental Maths
Question 1.
Fill in the blanks:
(i) Two line segments are congruent if ……….
(ii) Among two congruent angles, one has a measure of 63°; the measure of the other angle is ……….
(iii) When we write ∠A = ∠B, we actually mean ………
(iv) The side included between ∠M and ∠N of ∆MNP is ……….
(v) The side QR of ∆PQR is included between angles ……….
(vi) If two triangles ABC and PQR are congruent under the correspondence A ↔ R, B ↔ P and C ↔ Q, then in symbolic form it can be written as ∆ABC = ………
(vii) If ∆DEF = ∆SRT, then the correspondence between vertices is ……….
(i) Two line segments are congruent if they are of the same length.
(ii) Among two congruent angles, one has a measure of 63°;
the measure of the other angle is 63°.
(iii) When we write ∠A = ∠B, we actually mean m∠A = m∠B.
(iv) The side included between ∠M and ∠N of ∆MNP is MN.
(v) The side QR of ∆PQR is included between angles ∠Q and ∠R.
(vi) If two triangles ABC and PQR are congruent
under the correspondence A ↔ R, B ↔ P and C ↔ Q,
then in symbolic form it can be written as ∆ABC = ∆RPQ.
(vii) If ∆DEF = ∆SRT, then the correspondence between vertices is
D ↔ S, E ↔ R and F ↔ T.
Question 2.
State whether the following statements are true (T) or false (F):
(i) All circles are congruent.
(ii) Circles having equal radii are congruent.
(iii) Two congruent triangles have equal areas and equal perimeters.
(iv) Two triangles having equal areas are congruent.
(v) Two squares having equal areas are congruent.
(vi) Two rectangles having equal areas are congruent.
(vii) All acute angles are congruent.
(vii)All right angles are congruent.
(ix) Two figures are congruent if they have the same shape.
(x) A two rupee coin is congruent to a five rupee coin.
(xi) All equilateral triangles are congruent.
(xii) Two equilateral triangles having equal perimeters are congruent.
(xii) If two legs of one right triangle are equal to two legs of another right angle triangle, then the two triangles are congruent by SAS rule.
(xiv) If three angles of two triangles are equal, then triangles are congruent.
(xv) If two sides and one angle of one triangle are equal to two sides and one angle of another triangle, then the triangle are congruent.
(i) All circles are congruent. (False)
As if all circles have equal radii otherwise not.
(ii) Circles having equal radii are congruent. (True)
(iii) Two congruent triangles have equal areas
and equal perimeters. (True)
(iv) Two triangles having equal areas are congruent. (False)
As they may have different sides and angles.
(v) Two squares having equal areas are congruent. (True)
(vi) Two rectangles having equal areas are congruent. (False)
As their side can be different.
(vii) All acute angles are congruent. (False)
As acute angles have different measures.
(viii) All right angles are congruent. (True)
(ix) Two figures are congruent if they have the same shape. (False)
As the same shapes have different measures.
(x) A two rupee coin is congruent to a five rupee coin. (False)
As they have different size.
(xi) All equilateral triangles are congruent. (False)
As they have different sides in length.
(xii) Two equilateral triangles having equal perimeters are congruent. (True)
(xiii) If two legs of one right triangle are equal to
two legs of another right angle triangle,
then the two triangles are congruent by SAS rule. (True)
(xiv) If three angles of two triangles are equal,
then triangles are congruent. (False)
They can be similar to each other.
(xv) If two sides and one angle of one triangle are equal to two sides
and one angle of another triangle, then the triangle is congruent. (False)
If the angles are included, they can be congruent.
Multiple Choice Questions
Choose the correct answer from the given four options (3 to 14):
Question 3.
Which one of the following is not a standard criterion of congruency of two triangles?
(a) SSS
(b) SSA
(c) SAS
(d) ASA
The axiom SSA is not a standard criterion
of congruency of triangles. (b)
Question 4.
If ∆ABC = ∆PQR and ∠CAB = 65°, then ∠RPQ is
(a) 65°
(b) 75°
(c) 90°
(d) 115°
∆ABC = ∆PQR
∠CAB = 65°
∠RPQ = 65° (corresponding angles) (a)
Question 5.
If ∆ABC = ∆EFD, then the correct statement is
(a) ∠A = ∠D
(b) ∠A = ∠F
(c) ∠A = ∠E
(d) ∠B = ∠E
∆ABC = ∆EFD
Then ∠A = ∠E (c)
Question 6.
If ∆ABC = ∆PQR, then the correct statement is
(a) AB = QR
(b) AB = PR
(c) BC = PR
(d) AC = PR
∆ABC = ∆PQR
Then AB = PQ
AC = PR (d)
Question 7.
If ∠D = ∠P, ∠E = ∠Q and DE = PQ, then ∆DEF = ∆PQR, by the congruence rule
(a) SAS
(b) ASA
(c) SSS
(d) RHS
In ∆DEF = ∆PQR
∠D = ∠P, ∠E = ∠Q
DE = PQ
∆DEF = ∆PQR (ASA axiom) (b)
Question 8.
In ∆ABC and ∆PQR, BC = QR and ∠C = ∠R. To establish ∆ABC = ∆PQR by SAS congruence rule, the additional information required is
(a) AC = PR
(b) AB = PR
(c) CA = PQ
(d) AB = PQ
If ∆ABC = ∆PQR by SAS
BC = QR and ∠C = ∠R, then AC = PR (a)
Question 9.
In the given figure, the lengths of the sides of two triangles are given. The correct statement is
(a) ∆ABC = ∆PQR
(b) ∆ABC = ∆QRP
(c) ∆ABC = ∆QPR
(d) ∆ABC = ∆RPQ
Correct statement is ∆ABC = ∆QRP. (b)
Question 10.
In the given figure, M is the mid-point of both AC and BD. Then
(a) ∠1 = ∠2
(b) ∠1 = ∠4
(c) ∠2 = ∠4
(d) ∠1 = ∠3
In the given figure,
M is mid-point of AC and BD both then ∠1 = ∠4. (b)
Question 11.
In the given figure, ∆PQR = ∆STU. What is the length of TU?
(a) 5 cm
(b) 6 cm
(c) 7 cm
(d) cannot be determined
In the given figure,
∆PQR = ∆STU
TU = QR = 6 cm (b)
Question 12.
In the given figure, ∆ABC and ∆DBC are on the same base BC. If AB = DC and AC = DB, then which of the following statement is correct?
(a) ∆ABC = ∆DBC
(b) ∆ABC = ∆CBD
(c) ∆ABC = ∆DCB
(d) ∆ABC = ∆BCD
In the given figure,
AB = DC, AC = DB
Then, ∆ABC = ∆DCB (c)
Question 13.
The two triangles shown in the given figure are:
(a) congruent by AAS rule
(b) congruent by ASA rule
(c) congruent by SAS rule
(d) not congruent.
In the given two triangles are not congruent.
In first triangle, AAS are given while in second ASA are given. (d)
Question 14.
In .the given figure, ∆ABC = ∆PQR. The values of x and y are:
(a) x = 63, y = 35
(b) x = 77, y = 35
(c) x = 35, y = 77
(d) x = 63, y = 40
In the given figure,
∆ABC = ∆PQR
∠A = ∠P and ∠B = ∠Q
Now x – 7 = 70°
⇒ x = 70° + 7 = 77°
and 2y + 5 = 75
⇒ 2y = 75° – 5 = 70°
⇒ y = 35°
x = 77°, y = 35° (b)
Higher Order Thinking Skills (HOTS)
Question 1.
If all the three altitudes of a triangle are equal, then prove that it is an equilateral triangle.
Given: In ∆ABC,
AD, BE and CF are altitudes of the triangle
and AD = BE = CF.
To prove: ∆ABC is an equilateral.
Proof: In ∆ABD and ∆CFB
AD = CF (Given)
∠D = ∠F (Each = 90°)
∠B = ∠B (Common)
∆ABD = ∆CFB (AAS criterion)
AB = BC …….(i)
Similarly in ∆BEC and ∆ADC
BE = AD (Given)
∠C = ∠C (Common)
∠E = ∠D (Each = 90°)
∆BEC = ∆ADC (AAS criterion)
BC = AC ………(ii)
From (i) and (ii)
AB = BC = AC
∆ABC is an equilateral triangle.
Question 2.
In the given fig., if BA || RP, QP || BC and AQ = CR, then prove that ∆ABC = ∆RPQ.
In the given figure, BA || RP
QP || BC and AQ = CR
To prove : ∆ABC = ∆RPQ
Proof: AQ = CR
Adding CQ to both sides
AQ + CQ = CR + CQ
⇒ AC = RQ
Now in ∆ABC and ∆RPQ
∠A = ∠R (Alternate angles)
∠C = ∠Q (Alternate angles)
AC = RQ (Proved)
∆ABC = ∆RPQ (ASA criterion)
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Solving the Equation (x+4)(x-2)=0
The equation (x+4)(x-2) = 0 is a simple quadratic equation that can be solved using the Zero Product Property. This property states that if the product of two or more factors is zero, then at least
one of the factors must be zero.
Here's how to solve the equation:
1. Set each factor equal to zero:
2. Solve for x in each equation:
Therefore, the solutions to the equation (x+4)(x-2) = 0 are x = -4 and x = 2.
Understanding the Zero Product Property
The Zero Product Property is a fundamental concept in algebra. It allows us to solve equations where we have a product of factors equal to zero. By setting each factor equal to zero, we can find the
individual values of the variable that make the entire equation true.
Visualizing the Solutions
We can visualize the solutions of this equation by plotting the graph of the quadratic function represented by the equation. The graph will intersect the x-axis at the points where the function
equals zero. In this case, the graph intersects the x-axis at x = -4 and x = 2. These points represent the solutions to the equation.
The equation (x+4)(x-2) = 0 is a simple example of how the Zero Product Property can be used to solve quadratic equations. By understanding this property, we can easily find the solutions to such
equations and gain a deeper understanding of the relationship between factors and roots in algebra.
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MS 8 IGNOU MBA Assignment July – Dec 2013
1. “Statistical unit is necessary not only for the collection of data, but also for the interpretation and presentation”. Explain the statement.
2. Find the standard deviation and coefficient of skewness for the following distribution
│Variable │0-5│5-10│10-15│15-20│20-25│25-30│30-35│35-40│
│Frequency │2 │5 │7 │13 │21 │16 │8 │3 │
3. A salesman has a 60% chance of making a sale to any one customer. The behaviour of successive customers is independent. If two customers A and B enter, what is the probability that the salesman
will make a sale to A or B.
4. To verify whether a course in Research Methodology improved performance, a similar test was given to 12 participants before and after the course. The original marks and after the course marks are
given below:
│Original Marks │44│40│61│52│32│44│70│41│67│72│53│72│
│Marks after the course │53│38│69│57│46│39│73│48│73│74│60│78│
Was the course useful? Consider these 12 participants as a sample from a population.
5. Write short notes on
a) Bernoulli Trials
b) Standard Normal distribution
c) Central Limit theorem
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C program to calculate the wage of labor on a daily basis
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C program to calculate the wage of labor on a daily basis
In this post, we will learn how to create a program in C that will calculate and print the total daily wage of labor. Wage means the salary or money that has to be paid to the worker. Labor is the
man who worked for you. The money that has to be paid to the labor will be paid on a daily basis as per the following wage structure:
Hours Worked Rate Applicable
Until the first eight hours 50.00
For the next four hours 10.00 per hour additional
For the next four hours 20.00 per hour additional
For the next four hours 25.00 per hour additional
For the next four hours 40.00 per hour additional
Find and Print Labor Wages in C
The question is: write a program in C to compute the wage of labor working on a daily basis as per the wage structure provided in the above table. And the result should be as follows:
Enter Name of Employee: XXXXXXXX
Enter total hours worked: 21
Total Wage: 310
The program given below is the answer to the above question:
int main()
float initWage=50, hours, tempHour, tempWage, totalWage;
char name[20];
printf("Enter Name of Employee: \t");
printf("Enter total hours worked: \t");
scanf("%f", &hours);
totalWage = initWage;
else if(hours>8 && hours<=12)
tempHour = hours-8;
tempWage = tempHour*10;
totalWage = tempWage + initWage;
else if(hours>12 && hours<=16)
tempHour = hours-12;
tempWage = 4*10;
totalWage = initWage + tempWage + (tempHour*20);
else if(hours>16 && hours<=20)
tempHour = hours-16;
tempWage = (4*10) + (4*20);
totalWage = initWage + tempWage + (tempHour*25);
else if(hours>20 && hours<=24)
tempHour = hours-20;
tempWage = (4*10) + (4*20) + (4*25);
totalWage = initWage + tempWage + (tempHour*40);
printf("A single day only has 24 hours.");
return 0;
printf("Total Wage: \t\t\t%0.2f", totalWage);
return 0;
As the program was written in the Code::Blocks IDE, here is the sample run after a successful build and run:
Now provide the name of the laborer, say codescracker, and the total number of hours worked by him, say 21. Press the ENTER key to see the wage of labor as shown in the second snapshot of the sample
run given here:
Here is another sample run. In this case, the laborer has worked for all the day (24 hours). Let's see what the labor earnings will be for one full day based on the above pay scale:
Here are some of the main steps used in the above program:
• Ask the user to enter his name.
• Again, ask him to enter how many hours he has worked for any particular date (or for today).
• Never forget to initialize a variable, say initWage with 50 as its initial value at the start of the program. Because according to the pre-defined wage structure given above, the employer has to
pay $50 to the employee for his first eight hours of work. No matter whether he has worked only for 1 hours or a total of 8 hours.
• Now check whether the hour worked is less than or equal to 8 or not.
• If it is, then just initialize the value of initWage to the variable totalWage, which will hold up the total wage of the labor at the end of the program.
• If the worked hour is not less than or equal to eight, determine whether it is greater than eight and less than or equal to twelve.
• If it is, then add the rate given for the next 4 hours after the initial 8 hours worked by the labor, i.e., 10 rupees per hour is the extra rate for the next 4 hours after starting with 8 hours,
which means we have to minus the given hour by 8 and then multiply the remaining hour value with 10, and then add it up with 50 to initialize it to the totalWage of labor.
• In this way, continue checking and calculating for the given number of hours.
• For example, if labor has worked 23 hours in a day, then the wage that has to be paid to labor will be calculated as follows:
□ Because the user specified 23 as the total number of hours worked, 23 will be set as the hours variable.
□ As 23 is greater than 20 and less than or equal to 24, therefore, the program flow goes inside the last else if block where the applied condition is:
else if(hours>20 && hours<=24)
As the rate for the first 8 hours is 50 rupees, the rate for the next 4 hours is $10/hour additional, the rate for the next 4 hours is $20/hour additional, the rate for the next 4 hours is
$25/hour additional, and the rate for the next and last 4 hours is $40/hour additional.
□ As a result, we must initialize the variable totalWage with 50 + (4*10) + (4*20) + (4*25) + ((hours-20)*40), 50 + 80 + 100 + ((23-20) *40), 230 + (3*40), 230 + 120, or 350. totalWage will
hold the total wage in this program.
• Finally, print the value of totalWage as output.
« Previous Program Next Program »
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Till now we were discussing the various concepts and equations such as continuity equation, Euler equation, Bernoulli’s equation and momentum equation for incompressible fluid flow. In same way we
have also discussed above equations for compressible fluid flow.
We have already seen the derivation of continuity equation, Bernoulli’s equation and momentum equation for compressible fluid flow in our previous posts. We will start here our discussion about the
compressible fluid flow with the derivation of expression for velocity of sound in an isothermal process.
Expression for velocity of sound in isothermal process
Before understanding the process to derive the expression for velocity of sound in isothermal process, we must have to study our previous post which shows the derivation of velocity of sound wave in
a fluid and velocity of sound in terms of bulk modulus.
For an isothermal process, temperature must be constant.
As we know the following equation, as mentioned here, we will use this equation to derive the velocity of sound in an isothermal process.
PV = mRT
PV/m = RT
P/ρ = RT
As we are discussing here the case of an isothermal process and therefore the term RT will be constant and hence we can write the above equation as mentioned here.
P/ρ = Constant = C[1]
P ρ^-1= C[1 ]
Let us differentiate the above equation and we will have following equation as mentioned here.
d (P ρ^-1) = 0
- P ρ^-2d ρ + ρ^-1dP = 0
We will now divide the above equation with ρ^-1 and we will have
- P ρ^-1d ρ + dP = 0
P ρ^-1d ρ = dP
P/ ρ = dP /d ρ
dP /d ρ = RT
Where, C is the velocity of sound
Therefore we will have following equation, as mentioned here, which shows the expression for velocity of sound in isothermal process.
Do you have any suggestions? Please write in comment box.
Fluid mechanics, By R. K. Bansal
Image courtesy: Google
Also read
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Hypothesis Testing: An Introduction
You must be familiar with the phrase hypothesis testing, but, might not have a very clear notion regarding what hypothesis testing is all about. So, basically the term refers to testing a new theory
against an old theory. But, you need to delve deeper to gain in-depth knowledge.
Hypothesis are tentative explanations of a principal operating in nature. Hypothesis testing is a statistical method which helps you prove or disapprove a pre-existing theory.
Hypothesis testing can be done to check whether the average salary of all the employees has increased or not based on the previous year’s data, testing can be done to check if the percentage of
passengers increased or not in the business class due to introduction of a new service and testing can also be done to check the differences in the productivity varied land.
There are two key concepts in testing of hypothesis:-
Null Hypothesis:- It means the old theory is correct, nothing new is happening, the system is in control, old standard is correct etc. This is the theory you want to check if is true or not. For
example if a ice-cream factory owner says that their ice-cream contains 90% milk, this can be written as:-
Alternative Hypothesis:- It means new theory is correct, something is happening, system is out of control, there are new standards etc. This is the theory you check against the null hypothesis. For
example you say that ice-cream does not contain 90% milk, this can be written as:-
Two-tailed, right tailed and left tailed test
Two-tailed test:- When the test can take any value greater or less than 90% in the alternative it is called two-tailed test ( H190%) i.e. you do not care if the alternative is more or less all you
want to know is if it is equal to 90% or no.
Right tailed test:-When your test can take any value greater than 90% (H1>90%) in the alternative hypothesis it is called right tailed test.
Left tailed test:-When your test can take any value less than 90% (H1<90%) in the alternative hypothesis it is called left tailed test.
Type I error and Type II error
->When we reject the null hypothesis when it is true we are committing type I error. It is also called significance level.
->When we accept the null hypothesis when it is false we are committing type II error.
Steps involved in hypothesis testing
1. Build a hypothesis.
2. Collect data
3. Select significance level i.e. probability of committing type I error
4. Select testing method i.e. testing of mean, proportion or variance
5. Based on the significance level find the critical value which is nothing but the value which divides the acceptance region from the rejection region
6. Based on the hypothesis build a two-tailed or one-tailed (right or left) test graph
7. Apply the statistical formula
8. Check if the statistical test falls in the acceptance region or the rejection region and then accept or reject the null hypothesis
Example:- Suppose the average annual salary of the employees in a company in 2018 was 74,914. Now you want to check whether the average salary of the employees has increased or not in 2019. So, a
sample of 112 people were taken and it was found out that the average annual salary of the employees in 2019 is 78,795. σ=14.530.
We will apply hypothesis testing of mean when known with 5% of significance level.
The test result shows that 2.75 falls beyond the critical value of 1.9 we reject the null hypothesis which basically means that the average salary has increased significantly in 2019 compared to
So, now that we have reached at the end of the discussion, you must have grasped the fundamentals of hypothesis testing. Check out the video attached below for more information. You can find
informative posts on Data Science course, on Dexlab Analytics blog.
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Divide Paper into Fifths
How to Divide Paper into Fifths
While you could divide a paper by measuring and then dividing it, there's also another way that's based on geometry. The math and origami masters have figured it out. We don't get into the gritty
math details here. We just show you how to fold it!
Divide Square Paper into Fifths Step 1: Start with a 6 inch x 6 inch (15cm x 15cm) square paper.
Fold paper into half on the horizontal axis. Crease well and unfold.
Divide Square Paper into Fifths Step 2: Make a diagonal fold from the corner to the center crease. Use a ruler to guide you if needed. Be as precise as possible. Crease well.
Divide Square Paper into Fifths Step 3: We need to mark the spot where the tip touches. Make a slight horizontal and vertical crease on that spot. Once again, use a ruler if you need to.
closer look...
Divide Square Paper into Fifths Step 4: Unfold Step 2.
Divide Square Paper into Fifths Step 5: Go ahead and extend those partial creases you made in Step 3. Fold, crease well and unfold.
Divide Square Paper into Fifths Step 6: What has happened is that by completing Steps 2 to 5, we've already divided the paper into fifths.
The math and origami masters have figured by making those folds, the top horizontal portion is now 1/5 of the paper.
And the right vertical portion is now 2/5 of the paper.
With this info, we can now proceed to divide the rest of the paper up into fifths.
Divide Square Paper into Fifths Step 7: We'll divide the horizontal portions first. The photos may look confusing but it's actually pretty simple. Think of it this way....we need to divide the area
A-B-C-D into 4 portions. We do this all the time right?
Fold A-B to C-D. Crease well and unfold.
Divide Square Paper into Fifths Step 8: Fold A-B to E-F.
Divide Square Paper into Fifths Step 9: Fold G-H to I-J. Crease well and unfold.
We've completed dividing the paper into fifths on the horizontal side!
Divide Square Paper into Fifths Step 10: Let's work on the vertical side.
Fold U-V to S-T. Crease well and unfold.
As mentioned in Step 6, the area S-T-U-V is 2/5 of the paper.
So, U-V-W-X and S-T-U-V are now 1/5 each of the paper.
Divide Square Paper into Fifths Step 11: The next steps are to divide the area
Q-R-X-W into 4 portions. Think about it before you look at the photos below.
Fold Q-R to W-X. Crease well and unfold.
Divide Square Paper into Fifths Step 12: Finally, fold Q-R to Y-Z. Crease well and unfold.
and you've completed dividing your paper into fifths!
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Difference Between Exponent and Power
| Difference Between Exponent and Power
Difference Between Exponent and Power
May 7, 2023
Exponent and power are different because an exponent represents the number of times a base should be multiplied by itself in a mathematical notation, while power is a number expressed using an
What is Exponent?
An exponent is a mathematical notation that represents the number of times a base should be multiplied by itself. It is usually written as a superscript number on the right side of the base.
Example of Exponent
• In the expression 2^3, 2 is the base, and 3 is the exponent. It means that 2 should be multiplied by itself three times, resulting in the value of 8.
What is Power?
A power, on the other hand, is a number that is expressed using an exponent. It is the result of multiplying a base by itself multiple times, as specified by the exponent.
Example of Power
• In the expression 2^3, 8 is the power. It means that base 2 has been multiplied by itself three times, resulting in the power of 8.
Relationship between Exponents and Powers
Exponents and powers are closely related because they are used to represent the same mathematical operation of repeated multiplication. The exponent represents the number of times a base should be
multiplied by itself, while the power is the result of that multiplication. For example, in the expression 2^3 = 8, 3 is the exponent, 2 is the base, and 8 is the power.
Difference between Exponent and Power
The differences between exponent and Power are given below:
Exponent Power
A number that represents the number of times a base should be multiplied by itself The result of that multiplication
Written as a superscript after the base Written as a number or expression after the base
Example: 2^3 means 2 multiplied by itself 3 times Example: 2³ means the result of 2 multiplied by itself 3 times
Used to simplify expressions and represent large or small numbers Used to perform calculations and represent physical quantities
Can be negative or fractional Can be positive or negative, but not fractional
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If P=[232−12123],A=[1011] and Q=PAPT, then PT(Q2005)P... | Filo
If and , then is equal to
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Question Text If and , then is equal to
Updated On Apr 26, 2023
Topic Matrices
Subject Mathematics
Class Class 12
Answer Type Text solution:1 Video solution: 9
Upvotes 958
Avg. Video Duration 5 min
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For Crypto Whales: When Less is More Elm Partners
December 14, 2021
Investment Theory
For Crypto Whales: When Less is More
By Victor Haghani and James White ^1
In general, the more optimistic we are on the prospects of an investment, the more of it we’ll want to own. However, at extreme levels of bullishness, the normal relationship can be turned on its
head and it can make sense to own less of an asset the more we like it. It’s hard to think of everyday examples that work like this, so this poses something of a puzzle. It’s a problem which gets
little attention in mainstream finance, because we rarely witness high enough forecasts of investment quality to observe this effect in the wild.^2 We can thank the digital-asset revolution and its
band of optimistic crypto-asset enthusiasts for bringing this problem into focus, which also gives us some valuable insights that apply in other domains of financial decision-making.
We’ll assume a representative Investor with a relatively moderate level of risk-aversion.^3 For those familiar with the Kelly Criterion, we’re assuming an investor with twice the risk-aversion of a
Kelly Bettor.^4 Many individuals find that while “full” Kelly may be appropriate for cash management in blackjack or poker, it calls for too much risk when applied to total wealth. In gambling
circles, our Base-Case investor would be called a “half-Kelly bettor”, and would find himself in the company of quite a few famous investors who also size their risks in line with this level of
risk-aversion. More concretely, such an investor would be indifferent to a 50/50 coin flip which could increase his wealth by 50% or decrease it by 25%.^5
Crypto Risk and Return
It is hard to know how to accurately model the price behavior of digital assets, but most would agree that they do not follow the continuous Geometric Brownian motion of finance textbooks, and their
returns are far from being well-described by the standard Normal distribution. Financial assets in general (and digital assets in particular) experience price jumps and fat tails, and their
variability and expected returns are difficult to estimate and can change dramatically over time. Additionally in the case of digital assets, many investors recognize some risk of losing their
investment through hacking, hard forks, loss of private keys, etc – more like seeing one’s house burn down rather than experiencing a bad run in the market. To cut through all the uncertainty of
crypto return distributions, we’re going to radically simplify and assume that to some chosen horizon there’s a 50% chance the asset goes to 0, and a 50% chance it goes up by a factor of P, the
“payoff ratio”.
A Puzzling Result
The chart below shows the optimal amount our Investor should allocate given a range of payoff ratios.^6 As we increase the payoff ratio from 1:1 to 2048:1, the expected return and risk of the asset
goes up – and crucially, the ratio of return-to-risk, the Sharpe Ratio^7, is also going up. That’s what we mean when we say that the quality of the investment is getting better and better.
When the expected payoff ratio is between 4:1 and 8:1, the optimal allocation reaches its peak at about 17%. Then – and this is the whole point of this note – at higher payoff ratios, the optimal bet
size declines. For very optimistic investors (and believe us, there are some really optimistic ones out there^8), an allocation potentially well under 10% may be optimal.
Explaining the Hump
An intuitive explanation for this hump is this:
• It starts at zero: At the 1:1 ratio at the far left of the chart, since the upside and downside are equally likely and equal in size, the optimal allocation starts at zero since the investor
shouldn’t take risk without some expected reward.
• Then it goes up: As we increase the payoff ratio by moving to the right, the investment opportunity warrants some allocation of capital.
• Then it eventually goes back down to zero again: At some point (rarely seen in practice), when an asset is sufficiently great, holding even a small amount of it will make us fabulously rich in
the good outcome – so there’s no reason to hold a ton of it and risk the bad outcome on a large fraction of wealth. Put another way, since we can get as much cake as we can ever eat for a
pittance, why spend a penny more?! This effect takes the optimal allocation back down again towards zero, giving us the hump shape.
While the circumstances that give us this result are something of an oddity, a closer look at what’s going on gives us insights about wealth and risk that are more broadly applicable.
A Different Perspective on Wealth and Risk
Normally, we think of our financial wealth as the sum of the current market values of the assets we own.^9 This works well enough in most circumstances, but when an investor feels he has come across
an outstanding gem of an investment, using the market price for that asset rather than a value that reflects the higher intrinsic risk-adjusted value can lead to suboptimal decision-making.
Encountering an asset – a digital asset, in this case – that the investor believes has a 50/50 chance of delivering a 100:1 payoff ratio makes him effectively wealthier than a standard mark-to-market
accounting treatment would indicate. If he really believes in the attractiveness of the investment, he would need a substantial compensating payment to forego investing in it. We use the term
Certainty-Equivalent Wealth to refer to the level of wealth that he would be equally happy to possess with absolute certainty instead of his current wealth plus the opportunity to invest in the
highly-attractive asset.
To illustrate, say our investor decides to invest 17% of his wealth in a crypto-asset that has a 50/50 chance of going up eight-fold or down to zero. The expected return of the asset is 300%, and the
investor’s expected wealth is 150% higher than his starting wealth – but his Certainty-Equivalent Wealth is that level of wealth that he’d be just as happy having for sure but without the ability to
buy the attractive crypto-asset. Using our Base-Case investor’s preferences, we can calculate that his Certainty-Equivalent Wealth should be about 125% of starting wealth.
We now turn to the question of risk: how much risk is the investor taking in the above illustration? Normally, one might say that his downside is losing 17% of starting wealth, and that is his risk –
but that ignores that his “true” wealth, his Certainty-Equivalent Wealth, is 125% of his nominal starting wealth because he bought this great investment that sports a 300% expected return. If that’s
his relevant starting wealth, now we see that his downside is much higher, at 34% (the loss from his wealth going from 1.25 to 0.83) if the asset’s downside case is realized. Just like we’d expect,
as the investment gets more attractive the investor is indeed taking more downside risk, measured against his Certainty-Equivalent Wealth.
“All models are wrong, but some are useful.”
– George E.P. Box
The assumptions we’ve made in this analysis have been chosen for simplicity and illustration. In particular, we recognize that modeling outcomes of digital assets in a binary manner is not realistic,
though it does capture a certain kind of view that digital assets will either go to the moon or fade away. But the general effect we describe, that the optimal holding of an asset at some point goes
down as its attractiveness goes up, holds over a pretty broad range of assumptions about distributions of outcomes and investor risk preferences.^10
Moreover, the insight that we should view our base wealth as inclusive of the value provided by attractive investment opportunities is important and applies in other situations. For example, a hedge
fund or private equity manager might be prone to over-investing in the fund he manages if he underestimates the value and risk associated with his ownership interest in his fund management business.
If you think you have an investment opportunity that might benefit from this kind of analysis, we’d love to discuss it with you.
Further Reading and References
• Black, Fischer. “Noise”. Journal of Finance (1986).
• Haghani, Victor and James White. “Measuring the Fabric of Felicity”. SSRN (2018).
• Kelly, John, L. “A New Interpretation of Information Rate”. Bell System Technical Journal (1956).
• Merton, Robert, C. “Lifetime Portfolio Selection under Uncertainty: the Continuous-Time Case”. The Review of Economics and Statistics (1969).
• Thorp, Edward, O. “Fortune’s Formula: The Game of Blackjack”. American Mathematical Society (1961).
1. This not is not an offer or solicitation to invest, nor should this be construed in any way as tax advice. Our thanks to Steve Mobbs for his input on this note. Past returns are not indicative of
future performance.
2. For example, in his 1986 Presidential address to the AFA titled “Noise”, Fischer Black stated:
“…We might define an efficient market as one in which price is within a factor of 2 of value, i.e., the price is more than half of value and less than twice value…By this definition, I think
almost all markets are efficient almost all of the time…”
3. As per a survey we conducted in 2018 of thirty financially sophisticated investors and described in “Measuring the Fabric of Felicity”, we assume our Base-Case investor is in the bottom quartile
of risk-aversion.
4. We assume the investor exhibits Constant Relative Risk Aversion (CRRA), with a coefficient of risk aversion, γ , of 2. CRRA Utility can be written as:U(W) = (1 – W^(1 – γ)) / (γ – 1) for γ <> 1 ,
U(W) = ln(W) for γ = 1 . γ = 1 gives us the Kelly Criterion, and γ = 2 is referred to as “half-Kelly”.
5. Feel free to get in touch with us if you’d like some guidance on calibrating your personal level of risk-aversion.
6. The optimal allocation k^* is that which maximizes the investor’s Expected Utility. Given a payoff ratio P upside probability π and Constant Relative Risk-Aversion coefficient g ,
k^* = (P – π P)^1/g – π^1 / g (P – π P)^1 / g + π^1 / g P
We are assuming this is the only investment opportunity available.
7. One example of a highly optimistic investor is Michael Saylor, CEO and founder of MicroStrategy (MSTR), an owner of several billion dollars of digital-assets. On August 18th, 2021, he stated here
that he expected Bitcoin to become “a $100 Trillion asset.” Given the price at which Bitcoin was trading at the time of his statement, it implied a hundred-and-twenty-fold increase in the price
of Bitcoin.
8. Investors in private, illiquid assets often think of them at their cost basis, or somewhere between cost and an estimate of fair market value.
9. But not all whales are of the humpback variety. Two notable cases where it may not hold are: 1) if the asset follows a continuous random walk and the investor can rebalance his portfolio
continuously without frictions, or 2) for an investor with risk-tolerance equal to or greater than a full Kelly bettor, i.e. whose utility function is at least as risk-tolerant as U(W) = ln(W) .
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|
6.3 Basics of ggplot | An Introduction to Data Analysis
6.3 Basics of ggplot
In this section, we will work towards a first plot with ggplot. It will be a scatter plot (more on different kinds of plots in Section 6.4) for the avocado price data. Check out the ggplot cheat
sheet for a quick overview of the nuts and bolts of ggplot.
The following paragraphs introduce the key concepts of ggplot:
• incremental composition: adding elements or changing attributes of a plot incrementally
• convenience functions & defaults: a closer look at high-level convenience functions (like geom_point) and what they actually do
• layers: seeing how layers are stacked when we call, e.g. different geom_ functions in sequence
• grouping: what happens when we use grouping information (e.g., for color, shape or in facets)
The section finishes with a first full example of a plot that has different layers, uses grouping, and customizes a few other things.
To get started, let’s first load the (preprocessed) avocado data set used for plotting:
6.3.1 Incremental composition of a plot
The “gg” in the package name ggplot is short for “grammar of graphs”. It provides functions for describing scientific data plots in a compositional manner, i.e., for dealing with different recurrent
elements in a plot in an additive way. As a result of this approach, we will use the symbol + to add more and more elements (or to override the implicit defaults in previously evoked elements) to
build a plot. For example, we can obtain a scatter plot for the avocado price data simply by first calling the function ggplot, which just creates an empty plot:
The plot stored in variable incrementally_built_plot is very boring. Take a look:
As you can see, you do not see anything except a (white) canvas. But we can add some stuff. Don’t get hung up on the details right now, just notice that we use + to add stuff to our plot:^29
incrementally_built_plot +
# add a geom of type `point` (=> scatter plot)
# what data to use
data = avocado_data,
# supply a mapping (in the form of an 'aesthetic' (see below))
mapping = aes(
# which variable to map onto the x-axis
x = total_volume_sold,
# which variable to map onto the y-axis
y = average_price
You see that the function geom_point is what makes the points appear. You tell it which data to use and which mapping of variables from the data set to elements in the plot you like. That’s it, at
least to begin with.
We can also supply the information about the data to use and the aesthetic mapping in the ggplot function call. Doing so will make this information the default for any subsequently added layer.
Notice also that the data argument in function ggplot is the first argument, so we will frequently make use of piping, like in the following code which is equivalent to the previous in terms of
6.3.2 Elements in the layered grammar of graphs
Let’s take a step back. Actually, the function geom_point is a convenience function that does a lot of things automatically for us. It helps to understand subsequent code if we peek under the hood at
least for a brief moment initially, if only to just realize where some of the terminology in and around the “grammar of graphs” comes from.
The ggplot package defines a layered grammar of graphs (Wickham 2010). This is a structured description language for plots (relevant for data science). It uses a smart system of defaults so that it
suffices to often just call a convenience wrapper like geom_point. But underneath, there is the possibility of tinkering with (almost?) all of the (layered) elements and changing the defaults if need
The process of mapping data onto a visualization essentially follows this route:
data -> statistical transformation -> geom. object -> aesthetics
You supply (tidy) data. The data is then transformed (e.g., by computing a summary statistic) in some way or another. This could just be an “identity map” in which case you will visualize the data
exactly as it is. The resulting data representation is mapped onto some spatial (geometric) appearance, like a line, a dot, or a geometric shape. Finally, there is room to alter the specific
aesthetics of this mapping from data to visual object, like adjusting the size or the color of a geometric object, possibly depending on some other properties it has (e.g., whether it is an
observation for a conventional or an organically grown avocado).
To make explicit the steps which are implicitly carried out by geom_point in the example above, here is a fully verbose but output-equivalent sequence of commands that builds the same plot by
defining all the basic components manually:
avocado_data %>%
ggplot() +
# plot consists of layers (more on this soon)
# how to map columns onto ingredients in the plot
mapping = aes(x = total_volume_sold, y = average_price),
# what statistical transformation should be used? - here: none
stat = "identity",
# how should the transformed data be visually represented? - here: as points
geom = "point",
# should we tinker in any other way with the positioning of each element?
# - here: no, thank you!
position = "identity"
) +
# x and y axes are non-transformed continuous
scale_x_continuous() +
scale_y_continuous() +
# we use a cartesian coordinate system (not a polar or a geographical map)
In this explicit call, we still need to specify the data and the mapping (which variable to map onto which axis). But we need to specify much more. We tell ggplot that we want standard (e.g., not
log-transformed) axes. We also tell it that our axes are continuous, that the data should not be transformed and that the visual shape (= geom) to which the data is to be mapped is a point (hence the
name geom_point).
It is not important to understand all of these components right now. It is important to have seen them once, and to understand that geom_point is a wrapper around this call which assumes reasonable
defaults (such as non-transformed axes, points for representation etc.).
6.3.3 Layers and groups
ggplot is the “grammar of layered graphs”. Plots are compositionally built by combining different layers, if need be. For example, we can use another function from the geom_ family of functions to
display a different visualization derived from the same data on top of our previous scatter plot.^30
avocado_data %>%
mapping = aes(
# notice that we use the log (try without it to understand why)
x = log(total_volume_sold),
y = average_price
) +
# add a scatter plot
geom_point() +
# add a linear regression line
geom_smooth(method = "lm")
Notice that layering is really sequential. To see this, just check what happens when we reverse the calls of the geom_ functions in the previous example:
avocado_data %>%
mapping = aes(
# notice that we use the log (try without it to understand why)
x = log(total_volume_sold),
y = average_price
) +
# FIRST: add a linear regression line
geom_smooth(method = "lm") +
# THEN: add a scatter plot
If you want lower layers to be visible behind layers added later, one possibility is to tinker with opacity, via the alpha parameter. Notice that the example below also changes the colors. The result
is quite toxic, but at least you see the line underneath the semi-transparent points.
avocado_data %>%
mapping = aes(
# notice that we use the log (try without it to understand why)
x = log(total_volume_sold),
y = average_price
) +
# FIRST: add a linear regression line
geom_smooth(method = "lm", color = "darkgreen") +
# THEN: add a scatter plot
geom_point(alpha = 0.1, color = "orange")
The aesthetics defined in the initial call to ggplot are global defaults for all layers to follow, unless they are overwritten. This also holds for the data supplied to ggplot. For example, we can
create a second layer using another call to geom_point from a second data set (e.g., with a summary statistic), like so:
# create a small tibble with the means of both
# variables of interest
avocado_data_means <-
avocado_data %>%
mean_volume = mean(log(total_volume_sold)),
mean_price = mean(average_price)
## # A tibble: 1 × 2
## mean_volume mean_price
## <dbl> <dbl>
## 1 11.3 1.41
avocado_data %>%
aes(x = log(total_volume_sold),
y = average_price)
) +
# first layer uses globally declared data & mapping
geom_point() +
# second layer uses different data set & mapping
data = avocado_data_means,
mapping = aes(
x = mean_volume,
y = mean_price
# change shape of element to display (see below)
shape = 9,
# change size of element to display
size = 12,
color = "skyblue"
6.3.4 Grouping
Categorical distinction is frequently important in data analysis. Just think of the different combinations of factor levels in a factorial design, or the difference between conventionally grown and
organically grown avocados. ggplot understands grouping very well and acts on appropriately, if you tell it to in the right way.
Grouping can be relevant for different aspects of a plot: the color of points or lines, their shape, or even whether to plot everything together or separately. For instance, we might want to display
different types of avocados in a different color. We can do this like so:
avocado_data %>%
x = log(total_volume_sold),
y = average_price,
# use a different color for each type of avocado
color = type
) +
Notice that we added the grouping information inside of aes to the call of ggplot. This way the grouping is the global default for the whole plot. Check what happens when we then add another layer,
like geom_smooth:
avocado_data %>%
x = log(total_volume_sold),
y = average_price,
# use a different color for each type of avocado
color = type
) +
geom_point() +
geom_smooth(method = "lm")
The regression lines will also be shown in the colors of the underlying scatter plot. We can change this by overwriting the color attribute locally, but then we lose the grouping information:
avocado_data %>%
x = log(total_volume_sold),
y = average_price,
# use a different color for each type of avocado
color = type
) +
geom_point() +
geom_smooth(method = "lm", color = "black")
To retrieve the grouping information, we can change the explicit keyword group (which just treats data from the relevant factor levels differently without directly changing their appearance):
avocado_data %>%
x = log(total_volume_sold),
y = average_price,
# use a different color for each type of avocado
color = type
) +
geom_point() +
# tell the smoother to deal with avocados types separately
aes(group = type),
method = "lm",
color = "black"
Finally, we see that the lines are not uniquely associable with the avocado type, so we can also change the regression line’s shape attribute conditional on avocado type:
avocado_data %>%
x = log(total_volume_sold),
y = average_price,
# use a different color for each type of avocado
color = type
) +
geom_point() +
# tell the smoother to deal with avocados types separately
aes(group = type, linetype = type),
method = "lm",
color = "black"
6.3.5 Example of a customized plot
If done with the proper mind and heart, plots intended to share (and to communicate a point, following the idea of hypothesis-driven visualization) will usually require a lot of tweaking. We will
cover some of the most frequently relevant tweaks in Section 6.6.
To nevertheless get a feeling of where the journey is going, at least roughly, here is an example of a plot of the avocado data which is much more tweaked and honed. No claim is intended regarding
the false idea that this plot is in any sense optimal. There is not even a clear hypothesis or point to communicate. This just showcases some functionality. Notice, for instance, that this plot uses
two layers, invoked by geom_point which shows the scatter plot of points and geom_smooth which layers on top the point cloud regression lines (one for each level in the grouping variable).
# pipe data set into function `ggplot`
avocado_data %>%
# reverse factor level so that horizontal legend entries align with
# the majority of observations of each group in the plot
type = fct_rev(type)
) %>%
# initialize the plot
# defined mapping
mapping = aes(
# which variable goes on the x-axis
x = total_volume_sold,
# which variable goes on the y-axis
y = average_price,
# which groups of variables to distinguish
group = type,
# color and fill to change by grouping variable
fill = type,
linetype = type,
color = type
) +
# declare that we want a scatter plot
# set low opacity for each point
alpha = 0.1
) +
# add a linear model fit (for each group)
color = "black",
method = "lm"
) +
# change the default (normal) of x-axis to log-scale
scale_x_log10() +
# add dollar signs to y-axis labels
scale_y_continuous(labels = scales::dollar) +
# change axis labels and plot title & subtitle
x = 'Total volume sold (on a log scale)',
y = 'Average price',
title = "Avocado prices against amount sold",
subtitle = "With linear regression lines"
Exercise 6.1: Find the match
Determine which graph was created with which code:
Code 1:
code_1 <- ggplot(avocado_data,
mapping = aes(
x = average_price,
y = log(total_volume_sold),
color = type
) +
geom_point() +
geom_smooth(method = "lm")
Code 2:
code_2 <- ggplot(avocado_data,
mapping = aes(
x = log(total_volume_sold),
y = average_price,
color = type
) +
geom_point() +
geom_smooth(method = "lm")
Code 3:
code_3 <- ggplot(avocado_data,
mapping = aes(
x = log(total_volume_sold),
y = average_price
) +
geom_smooth(method = "lm", color = "black") +
geom_point(alpha = 0.1, color = "blue") +
x = 'Total volume sold (on a log scale)',
y = 'Average price',
title = "Avocado prices against amount sold"
Code 4:
code_4 <- ggplot(avocado_data,
mapping = aes(
x = log(total_volume_sold),
y = average_price,
linetype = type
) +
geom_smooth(method = "lm", color = "black") +
geom_point(alpha = 0.1, color = "blue") +
x = 'Total volume sold (on a log scale)',
y = 'Average price',
title = "Avocado prices against amount sold"
Plot 1:
Plot 2:
Plot 3:
Plot 1: Code 4
Plot 2: Code 1
Plot 3: Code 2
Wickham, Hadley. 2010. “A Layered Grammar of Graphics.” Journal of Computational and Graphical Statistics 19 (1): 3–28.
29. If you run this code for yourself, the output is likely to look different from what is shown here. This is because this web-book uses a default theme for all of its plots. We will come back to
customization with themes later.↩︎
30. Notice that, as soon as we add the linear regression line, it makes sense to use the logarithm of total_volume_sold because otherwise, the fit is quite ridiculous. The logarithm helps to spread
out the large number of data points where total_volume_sold is very low, and to “bring back to the flock” the data points where total_volume_sold is outliery high. It can be quite useful to use
such transformations, if they are well understood. It is controversial whether such transformations should precede statistical analyses, but that is not important right now.↩︎
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Mathematical Logic
The course is not on the list Without time-table
Code Completion Credits Range Language
BIE-MLO Z,ZK 5 2P+2C English
It is not possible to register for the course BIE-MLO if the student is concurrently registered for or has already completed the course BIE-DML.21 (mutually exclusive courses).
It is not possible to register for the course BIE-MLO if the student is concurrently registered for or has already completed the course BIE-LOG.21 (mutually exclusive courses).
It is not possible to register for the course BIE-MLO if the student is concurrently registered for or has previously completed the course BIE-DML.21 (mutually exclusive courses).
It is not possible to register for the course BIE-MLO if the student is concurrently registered for or has previously completed the course BIE-LOG.21 (mutually exclusive courses).
Course guarantor:
An introduction to propositional and predicate logic.
Elementary arithmetics, basic understanding of formal languages.
Syllabus of lectures:
1. Introduction. Propositional logic. Truth tables.
2. Satisfiability, tautology, contradiction. Logical equivalence. Basic laws of propositional logic. Complete systems of connectives.
3. Logical consequence. Disjunctive and conjunctive normal form. Full normal forms.
4. Theory and its logical consequences. Semantic trees. Resolution method.
5. Karnaugh maps. Compactness theorem. P vs. NP problem.
6. Predicate logic. Language, terms, formulas. Formalization of natural language.
7. Interpretation of the language. Logical truth, satisfiability, contradiction. Logical consequence and equivalence.
8. Semantic trees. Basic laws of predicate logic. The problem of decidability.
9. Prenex normal forms. Theories and its models. Isomorphism and elementary equivalence.
10. Examples of the first-order theories.
11. Boolean algebra. Models of Boolean algebra.
12. The isomorphism theorem. Correctness, completeness and consistenc
Syllabus of tutorials:
1. Formalization. Truth tables.
2. Satisfiability, tautology, contradiction. Logical equivalence. Universal systems of connectives.
3. Disjunctive and conjunctive normal forms. Full normal forms.
4. Logical consequence. Semantic trees. Satisfiable theories.
5. Resolution method. Karnaugh maps.
6. Predicate logic. Language, terms, formulas.
7. Interpretations. Logical truth, satisfiability, contradiction.
8. Logical consequence and equivalence.
9. Semantic trees. Logical consequence of a theory.
10. Theories and their models, equivalence, ordering, group theory.
11. Boolean algebras.
12. Repetition.
Study Objective:
Predicate logic is a formal language of mathematics. The goal of a course is to learn students to formalize their thoughts and assertions in predicate logic, to deal correctly with formulas,
theories and their models.
Study materials:
Mendelson, E., Introduction to Mathematical Logic, Chapman and Hall, 1997.
Bergmann, M., Moor, J., Nelson, The Logic Book, McGraw-Hill, 2008.
Copi, I.M., Symbolic Logic, The Macmilian Company, London, 1967.
Smullyan, R., What is the Name of this Book?
Demlová, M., Mathematical Logic, ČVUT, Praha: Kernberg Publishing, 2008.
Starý, J., lecture notes (in progress).
Smith, N.J.J., Logic: The Laws of Truth, Princeton University Press, 2012.
Smith, N.J.J., Cusbert J., Logic: The Drill, http://www-personal.usyd.edu.au/~njjsmith/lawsoftruth/
Further information:
No time-table has been prepared for this course
The course is a part of the following study plans:
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|
2022-08-19 13:31:57 +02:00
.github/workflows 2022-08-02 12:34:51 +02:00
el 2022-08-19 13:31:57 +02:00
HelpSource/Classes 2019-12-22 23:31:55 +01:00
sc/scide_scel 2021-08-19 20:54:46 -04:00
.dir-locals.el 2022-08-17 09:19:50 +02:00
.gitignore 2021-08-09 11:57:27 -04:00
CHANGELOG.md 2021-08-10 21:04:10 -04:00
CMakeLists.txt 2021-08-19 20:54:46 -04:00
README.md 2022-08-02 12:48:02 +02:00
scel.quark 2021-07-25 19:54:35 -04:00
scel - sclang-mode for emacs
SuperCollider/Emacs interface
There are 3 options for installation:
1. Using SuperCollider Quarks (recommended)
2. Using an Emacs package manager
3. From debian package supercollider-emacs
4. From source
Option #1 is the best cross-platform option, and is recommended. Whatever option you choose, make sure not to mix installation methods. In particular, do not install the Quark if you already have the
supercollider-emacs package or if you compiled SuperCollider with the -DSC_EL=ON option. Otherwise you will get an error from SuperCollider about duplicated classes.
Install Option 1: SuperCollider's own package manager
The repository contains two subprojects. /el contains the emacs-lisp implementation. /sc contains the SuperCollider code required to implement the Emacs interface. SuperCollider has its own package
system called Quarks, which we can use to install both halves.
Evaluate this code in the SuperCollider GUI by pasting it and pressing shift+enter:
The scel repository will be downloaded to your local file system and the path will be added to your currently used sclang_conf.yaml file. (You can find its location by evaluating
Next, find out where scel was installed. You will use this install-path in your emacs config.
// -> /Users/<username>/Library/Application Support/SuperCollider/downloaded-quarks
Now in your emacs config, add the /el subdirectory to your load path
;; in ~/.emacs
;; Paste path from above, appending "/scel/el"
(add-to-list 'load-path "/Users/<username>/Library/Application Support/SuperCollider/downloaded-quarks/scel/el")
(require 'sclang)
On macOS
If sclang executable is not on your path, you may need to add it to your exec-path.
;; in ~/.emacs
(setq exec-path (append exec-path '("/Applications/SuperCollider.app/Contents/MacOS/")))
Install Option 2: Emacs package manager
The sclang package can be installed from MELPA and configured with use-package.
It's possible to install with straight.el, use-package, doom, etc. Instructions for doing so are beyond the scope of this README, but note that autoloads are implemented for entry-point functions so
if you like to have a speedy start-up time you can use the :defer t option.
Install Option 3: Debian package
There is a debian package which provides emacs integration called supercollider-emacs. Option #1 will likely be more recent, but if you prefer you can install the package with:
sudo apt install supercollider-emacs
Install Option 4: Installing from source
If you are building SuperCollider from source, you can optionally compile and install this library along with it. The cmake -DSC_EL flag controls whether scel will be compiled. On Linux machines
-DSC_EL=ON by default. See the supercollider README files for more info.
;; in ~/.emacs
(add-to-list 'load-path "/usr/local/share/emacs/site-lisp/SuperCollider/") ;; path will depend on your compilation settings
(require 'sclang)
Optional Installation Requirements
There are two options for SuperCollider help files. They can be opened in the help browser that ships with SuperCollider, or if you prefer an emacs-only workflow they can be opened using the w3m
browser. The browse-in-emacs option requires an additional dependency.
;; in ~/.emacs
(require 'w3m)
The main function which starts interacting with the sclang interpreter is sclang-start. You can execute that anywhere with M-x sclang-start, or from within a .scd buffer by pressing C-c C-o.
If you know you want to launch sclang when you start emacs you can use the -f option to execute that function right away:
# in your terminal
emacs -f sclang-start
To fine-tune the installation from within emacs' graphical customization interface, type:
M-x sclang-customize
NOTE: If you use an sclang configuration file different from the default sclang_conf.yaml, you need to specify it in scel by customizing the sclang-library-configuration-file variable. Otherwise,
even after installing the Quark in SuperCollider, you won't be able to run sclang code in emacs.
Getting help
Inside an sclang-mode buffer (e.g. by editing a .sc file), execute
C-h m
and a window with key bindings in sclang-mode will pop up.
C-x C-h lets you search for a help file
C-M-h opens or switches to the Help browser (if no Help file has been opened, the default Help file will be opened).
E copies the buffer, puts it in text mode and sclang-minor-mode, to enable you to edit the code parts to try out variations of the provided code in the help file. With C-M-h you can then return to
the Help browser and browse further from the Help file.
C-c C-e allows you to edit the source of the HTML file, for example if you want to improve it and commit it to the repository.
To enable moving around in the help file with arrow keys add the following in your ~/.emacs:
(eval-after-load "w3m"
(define-key w3m-mode-map [left] 'backward-char)
(define-key w3m-mode-map [right] 'forward-char)
(define-key w3m-mode-map [up] 'previous-line)
(define-key w3m-mode-map [down] 'next-line)))
This ensures that the arrow keys are just for moving through the document, and not from hyperlink to hyperlink, which is the default in w3m-mode.
Server control
In the post buffer window, right-click on the server name; by default the two servers internal and localhost are available. You will get a menu with common server control operations.
To select another server, step through the server list by left-clicking on the server name.
Servers instantiated from the language will automatically be available in the mode line.
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The Great Rhombicuboctahedron
The great rhombicuboctahedron is a 3D uniform polyhedron bounded by 26 polygons (8 hexagons, 12 squares, and 6 octagons), 72 edges, and 48 vertices. It may be constructed by radially expanding the
octagonal faces of the truncated cube outwards, or equivalently, radially expanding the hexagonal faces of the truncated octahedron, or the non-axial square faces of the rhombicuboctahedron.
The great rhombicuboctahedron is also known as the truncated cuboctahedron; however, this is a misnomer. Truncating the cuboctahedron does not yield a uniform polyhedron, only a non-uniform
topological equivalent of the great rhombicuboctahedron. The correct derivation is as described above.
The dual of the great rhombicuboctahedron is the disdyakis dodecahedron, a Catalan solid.
In order to be able to identify the great rhombicuboctahedron in various projections of 4D objects, it is useful to know how it appears from various viewpoints. The following are some of the
commonly-encountered views:
Projection Envelope Description
Octagon Parallel projection centered on an octagonal face.
Dodecagon Parallel projection centered on a hexagonal face.
Octagon Parallel projection centered on a square face.
The Cartesian coordinates of the great rhombicuboctahedron, centered on the origin and having edge length 2, are all permutations of coordinates and changes of sign of:
The great rhombicuboctahedron appears as cells in the following 4D uniform polytopes:
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Type Two Theory of Effectivity
All right, let’s have computable function (analysis), eventually. Have added the disambiguation now at partial recursive function.
BTW, in that entry and maybe elsewhere, “Church-Turing thesis” should eventually hyperlink to somewhere…
Okay, I see. If in computable analysis, a computable function has domain $\mathbb{R}$ (for instance), then the answer would have to be ’no’. In that case, I think it makes sense to write an article
titled, e.g., computable function (analysis). The Wikipedia article that had been linked to in the earlier article you wrote up gives the notion involving partial recursive functions whose domain is
a subset of $\mathbb{N}^k$, so I assumed that was meant, hence the merge.
Does “computable function” mean the same in computable analysis? Does it matter to distinguish between “number realizability” and “function realizability”?
Well, no, what I think I’d rather do (instead of “filling in”) is merge into partial recursive function. So I’ll do that.
Todd, there is essentially nothing in that entry. You should go and fill in whatever you deem appropriate.
Ah, I don’t have the energy to merge the entries now, and you would be more expert than me to do so anyway. All I did was add that survey and cross-link constructive analysis and computable analysis.
This was quick.
Actually, I should merge with exact analysis, then. Give me just a minute…
Quick comment: We wrote an overview article some time ago. The page should be merged with computable analysis.
For computable function, I understand this to be a synonym for partial recursive function; the trend seems to be to use “computable” more in modern texts and “partial recursive” in older ones.
Anyway, one might consider a renaming or redirect or something.
happened to need Type Two Theory of Effectivity
Todd, looking at p. 4 of Andrej Bauer’s lecture notes (pdf) makes me feel that we should have a standalone entry “computable function” after all, with some general discussion along such lines and
then pointing to the various special incarnations.
Would you object?
Urs, that seems sensible to me.
Okay, please check out computable function now. Please edit as you see the need.
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756109BJ2 Downside Variance | US756109BJ21 Bond
756109BJ2 91.47 0.26 0.28%
756109BJ2 downside-variance technical analysis lookup allows you to check this and other technical indicators for US756109BJ21 or any other equities. You can select from a set of available technical
indicators by clicking on the link to the right. Please note, not all equities are covered by this module due to inconsistencies in global equity categorizations and data normalization technicques.
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US756109BJ21 has current Downside Variance of 5.63. Downside Variance (or DV) is measured by target semi-variance and is termed downside volatility. It is expressed in percentages and therefore
allows for rankings in the same way as variance. One way to view downside volatility is the annualized variance of returns below the target.
SUM(RET DEV)^2
Downside Variance = = 5.63
SUM = Summation notation
RET DEV = Actual returns deviation over selected period
N(ER) = Number of points with returns less than expected return for the period
756109BJ2 Downside Variance Peers Comparison
756109BJ2 Downside Variance Relative To Other Indicators
US756109BJ21 cannot be rated in Downside Variance category at this point. It cannot be rated in Maximum Drawdown category at this point. reporting about
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Downside Variance is the probability-weighted squared below-target returns. The squaring of the below-target returns has the effect of penalizing failures at an exponential rate. This is consistent
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Compare 756109BJ2 to Peers Predict 756109BJ2
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I Am Not Charlie Hebdo
New York Times
David Brooks
The journalists at Charlie Hebdo are now rightly being celebrated as martyrs on behalf of freedom of expression, but let’s face it: If they had tried to publish their satirical newspaper on any
American university campus over the last two decades it wouldn’t have lasted 30 seconds. Student and faculty groups would have accused them of hate speech. The administration would have cut financing
and shut them down.
Public reaction to the attack in Paris has revealed that there are a lot of people who are quick to lionize those who offend the views of Islamist terrorists in France but who are a lot less tolerant
toward those who offend their own views at home.
Just look at all the people who have overreacted to campus micro-aggressions. The University of Illinois fired a professor who taught the Roman Catholic view on homosexuality. The University of
Kansas suspended a professor for writing a harsh tweet against the N.R.A. Vanderbilt University derecognized a Christian group that insisted that it be led by Christians.
Americans may laud Charlie Hebdo for being brave enough to publish cartoons ridiculing the Prophet Muhammad, but, if Ayaan Hirsi Ali is invited to campus, there are often calls to deny her a podium.
So this might be a teachable moment. As we are mortified by the slaughter of those writers and editors in Paris, it’s a good time to come up with a less hypocritical approach to our own controversial
figures, provocateurs and satirists.
The first thing to say, I suppose, is that whatever you might have put on your Facebook page yesterday, it is inaccurate for most of us to claim, Je Suis Charlie Hebdo, or I Am Charlie Hebdo. Most of
us don’t actually engage in the sort of deliberately offensive humor that that newspaper specializes in.
We might have started out that way. When you are 13, it seems daring and provocative to “épater la bourgeoisie,” to stick a finger in the eye of authority, to ridicule other people’s religious
But after a while that seems puerile. Most of us move toward more complicated views of reality and more forgiving views of others. (Ridicule becomes less fun as you become more aware of your own
frequent ridiculousness.) Most of us do try to show a modicum of respect for people of different creeds and faiths. We do try to open conversations with listening rather than insult.
Yet, at the same time, most of us know that provocateurs and other outlandish figures serve useful public roles. Satirists and ridiculers expose our weakness and vanity when we are feeling proud.
They puncture the self-puffery of the successful. They level social inequality by bringing the mighty low. When they are effective they help us address our foibles communally, since laughter is one
of the ultimate bonding experiences.
Moreover, provocateurs and ridiculers expose the stupidity of the fundamentalists. Fundamentalists are people who take everything literally. They are incapable of multiple viewpoints. They are
incapable of seeing that while their religion may be worthy of the deepest reverence, it is also true that most religions are kind of weird. Satirists expose those who are incapable of laughing at
themselves and teach the rest of us that we probably should.
If you try to pull off this delicate balance with law, speech codes and banned speakers, you’ll end up with crude censorship and a strangled conversation. It’s almost always wrong to try to suppress
speech, erect speech codes and disinvite speakers.
Fortunately, social manners are more malleable and supple than laws and codes. Most societies have successfully maintained standards of civility and respect while keeping open avenues for those who
are funny, uncivil and offensive.
In most societies, there’s the adults’ table and there’s the kids’ table. The people who read Le Monde or the establishment organs are at the adults’ table. The jesters, the holy fools and people
like Ann Coulter and Bill Maher are at the kids’ table. They’re not granted complete respectability, but they are heard because in their unguided missile manner, they sometimes say necessary things
that no one else is saying.
Healthy societies, in other words, don’t suppress speech, but they do grant different standing to different sorts of people. Wise and considerate scholars are heard with high respect. Satirists are
heard with bemused semirespect. Racists and anti-Semites are heard through a filter of opprobrium and disrespect. People who want to be heard attentively have to earn it through their conduct.
The massacre at Charlie Hebdo should be an occasion to end speech codes. And it should remind us to be legally tolerant toward offensive voices, even as we are socially discriminating.
^^ A hijabed pregnant woman lost her kid because idiots beat her up in response to the shootings. Did she get what she deserved?
By the way, if your God is incapable of defunding his religion and needs you to go around shooting people to do so, you should rethink something's.
By the way, if your God is incapable of defunding his religion and needs you to go around shooting people to do so, you should rethink something's.
Somalee is not thinking at all, considering he seems to be under the impression that Charlie Hebdo is a person.
^^ A hijabed pregnant woman lost her kid because idiots beat her up in response to the shootings. Did she get what she deserved?
By the way, if your God is incapable of defunding his religion and needs you to go around shooting people to do so, you should rethink something's.
With all due respect, your input here isn't very necessary....and your attempts to use this incident as a hammer to bash Muslims is especially offensive
With all due respect, your input here isn't very necessary....and your attempts to use this incident as a hammer to bash Muslims is especially offensive
You're more offended by Naxar's post than Somalee's post justifying the killings?
You're more offended by Naxar's post than Somalee's post justifying the killings?
I find it a little strange that you condemn Somalee's post but yet you ignore what Naxar Nugaleed said! Talk about double standards here.
What happened in Paris was obviously a crime, and should be roundly condemned. But that doesn't mean we should allow opportunistic Non-Muslims like Bill Maher and Naxar Nugaleed to use this incident
to bash us.
You really need to be more balanced.
I find it a little strange that you condemn Somalee's post but yet you ignore what Naxar Nugaleed said! Talk about double standards here.
What happened in Paris was obviously a crime, and should be roundly condemned. But that doesn't mean we should allow opportunistic Non-Muslims like Bill Maher and Naxar Nugaleed to use this incident
to bash us.
You really need to be more balanced.
There's no "us" being bashed, the comment was specifically directed at somalee, who represents a particular view that justifies the killings for religious reasons (feeling disrespected by the
cartoons in his mind makes murder legitimate). And Naxar Nugaleed is right, if somalee thinks God needs the murder of cartoonists to defend religion, he DOES need to rethink things.
Killing people is always wrong , people do not deserve to be killed. And every one must condemn this act against the people of France. Though i agree that the world press the west in particular tries
to show one perspective of the whole issue. Though its an honer to defend the Prophet of Islam but killing and shooting is not one of them or trying to kill cartoonist. You havent done islam a great
honer nor the prophet nor Humanity. Every single person will be judged by God we are not here to judge people nor to send them to their grave.
Somalee is not thinking at all, considering he seems to be under the impression that Charlie Hebdo is a person.
Safferz, lol, good one.
Hahahaha@@@the Robin Hood line, that's classic.
The video of the gardheer will not take the focus of Kenney's Islamist leaning self.
Yarta, be honest with yourself. Come out of the closet.
LayZie G.
Safferz, lol, good one.
Hahahaha@@@the Robin Hood line, that's classic.
The video of the gardheer will not take the focus of Kenney's Islamist leaning self.
Yarta, be honest with yourself. Come out of the closet.
LayZie G.
I don't think it's exactly a secret that I'm "Islamist leaning"....read my posts and you'll see it for yourself. The opinion of Yasir Qadhi and Nouman Ali Khan are the opinions which I hold. And I do
not appreciate opportunistic Kaffirs to take this incident in Paris and use it as a sledgehammer against us. And I sure as hell don't appreciate seeing Muslims apologize for this attack in Paris, as
if we were in any way involved in this crime.
It goes both ways saaxib. You don't see me demanding that some random Buddhist guys apologize for the atrocities being committed against Muslims by Burmese Buddhist Monks right? I mean right now,
Muslims are being killed/oppressed in Burma but you'll NEVER see me blame the Buddhists for this. This isn't their fault.
Similarly, a Muslim who lives in Somalia or the United States shouldn't have to be harassed or shamed because some murderous thugs in France killed an entire newspaper staff. Both actions are
undoubtedly wrong.
Should you bother to really ask me and I would tell you I don't like bill maher but then again what can we expect from simpletons. A normal person would take my condemnation of senseless murder as a
defense of of Islam rather then an attack of Islam. Either way please do all of us a favor and move to the mountains of Afghanistan already.
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How to Apply A Function to A Nested List Of Strings In Haskell?
To apply a function to a nested list of strings in Haskell, you can use recursion and pattern matching. Here is an example of how it can be done:
1 applyToNestedList :: (String -> String) -> [[String]] -> [[String]]
2 applyToNestedList _ [] = [] -- base case: if the list is empty, return an empty list
3 applyToNestedList f (x:xs) = (applyToEach f x) : (applyToNestedList f xs) -- apply the function to the head of the list and recursively process the tail
5 applyToEach :: (String -> String) -> [String] -> [String]
6 applyToEach _ [] = [] -- base case: if the list is empty, return an empty list
7 applyToEach f (x:xs) = (f x) : (applyToEach f xs) -- apply the function to the head of the list and recursively process the tail
In the applyToNestedList function, we first define a base case when the input list is empty, we return an empty list. Otherwise, we apply the applyToEach function to the head of the list (x) using
the given function (f), and recursively process the tail of the list (xs).
In the applyToEach function, we define a similar base case for an empty list. Otherwise, we apply the given function f to the head of the list (x) and recursively process the tail of the list (xs).
By using these two functions together, you can apply a function to each string in a nested list of strings in Haskell.
What is the list comprehension syntax in Haskell?
The syntax for list comprehension in Haskell is as follows:
1 [expression | binding, condition]
Here, "expression" represents the result or transformation applied to each element in the list. "binding" refers to the element(s) that are drawn from a given list. "condition" is an optional
predicate that filters the elements based on a specified condition.
Here's an example to illustrate the syntax:
1 squares :: [Int]
2 squares = [x * x | x <- [1..10]]
In this example, the list comprehension x <- [1..10] binds each value of x in the range [1..10]. The expression x * x is then applied to each bound value, resulting in a list of squares from 1 to
What are applicative functors in Haskell?
In Haskell, an applicative functor is a typeclass that represents functors that can be applied to a value inside the functor. It extends the functionality of regular functors.
The Applicative typeclass is defined as follows:
1 class Functor f => Applicative f where
2 pure :: a -> f a
3 (<*>) :: f (a -> b) -> f a -> f b
The pure function takes a value and wraps it in an applicative functor. It produces an applicative functor with the given value inside it.
The <*> function takes an applicative functor containing a function and applies it to an applicative functor containing a value. It combines the two functors to produce a new functor with the result.
For example, the Maybe datatype is an applicative functor. We can use the pure function to wrap a value in a Just constructor:
1 pure 42 :: Maybe Int -- Just 42
We can use the <*> function to apply a function from one Maybe value to another Maybe value:
1 Just (+1) <*> Just 42 -- Just 43
Applicative functors are useful for working with computations that may or may not have a value, such as optional values or computations that can fail. They provide a way to combine computations and
handle the absence of values in a convenient and expressive way. They are particularly useful when chaining multiple computations together.
What is the lambda function in Haskell?
In Haskell, a lambda function is an anonymous function that can be defined inline without giving it a name. It is created using the lambda symbol "" followed by the parameters and a "->" arrow to
separate the parameters from the function body.
Here is the general syntax for a lambda function:
\parameter1 parameter2 ... -> function body
Here is an example of a lambda function that adds two numbers:
\ x y -> x + y
This lambda function takes two parameters (x and y) and returns their sum (x + y).
Lambda functions are commonly used in higher-order functions, where functions can be passed as arguments or returned as results. They are a concise way to define simple functions without explicitly
naming them.
What is the traverse function in Haskell?
In Haskell, the traverse function is a higher-order function that combines mapping and sequencing operations over a data structure. It is part of the Traversable type class and has the following type
1 traverse :: (Traversable t, Applicative f) => (a -> f b) -> t a -> f (t b)
The function takes two arguments: a function f that maps each element of type a to an action of type f b, and a traversable data structure t containing elements of type a. The traverse function
applies the given function to each element of the data structure, resulting in a sequence of actions of type f b. It then uses the Applicative instance of f to combine these actions into a single
action that produces a new traversable data structure t b.
In other words, traverse allows you to apply a function to each element of a data structure, while accumulating the results in an applicative context. It is often used for operations such as mapping
over lists, where each element is transformed by a function that may have effects or return values wrapped in an applicative functor.
What are monads in Haskell?
In Haskell, a monad is a type class that represents a computational context, which allows sequential composition of computations and handles effects such as state, input/output, and exceptions in a
controlled and predictable manner.
A monad consists of two main components:
1. A type constructor (usually referred to as the monad itself), which is used to wrap a value or a computation.
2. A set of operations that define the behavior of the monad, such as return (to wrap a value into the monadic context) and >>= (pronounced as "bind", to sequentially compose computations).
The purpose of monads is to encapsulate side effects in a type-safe and composable way, while providing a clear and predictable sequencing of computations. This allows for more modular, readable, and
maintainable code.
Some common monads in Haskell include:
• Maybe monad, which represents computations with possible absence of a value.
• List monad, which represents non-deterministic computations that produce multiple results.
• State monad, which encapsulates computations that carry around a state that can be modified.
• IO monad, which represents computations that interact with the outside world.
Monads in Haskell enable the use of do notation, which syntactically simplifies working with monadic values by allowing imperative-style programming in a pure functional language.
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Problem statement
A message containing letters from A-Z can be encoded into numbers using the following mapping:
'A' -> "1"
'B' -> "2"
'Z' -> "26"
To decode an encoded message, all the digits must be grouped then mapped back into letters using the reverse of the mapping above (there may be multiple ways).
Given a string ‘S’ containing only digits, return the number of ways to decode it.
Input: ‘S’ = "11106"
Output: 2
The possible ways are:-
(1 1 10 6),
(11 10 6)
Note that the grouping (1 11 06) is invalid because "06" cannot be mapped into 'F' since "6" is different from "06".
Input Format :
The first line contains ‘T’, denoting the number of test cases.
Each test case's first and only line contains the string ‘S’.
Output format :
Return the number of ways to decode the string ‘S’.
Note :
You don't need to print anything. It has already been taken care of. Just implement the given function.
Constraints :
1 <= T <= 10
1 <= | S | <= 100
Time Limit: 1 sec
Sample Input 1 :
Sample Output 1 :
Explanation Of Sample Input 1 :
For the first test case:-
"12" could be decoded as "AB" (1 2) or "L" (12).
For the second test case:-
"226" could be decoded as "BZ" (2 26), "VF" (22 6), or "BBF" (2 2 6).
Sample Input 2 :
Sample Output 2 :
Think of the possible choices you might make and try to solve them with the help of recursion.
Function numDecodingsUtil( string S, int i, int N )
1. First, write the base cases:
□ if i<’N’ && S[i]==’0’, return 0.
□ If i>= ’N’, return 1.
2. Then, declare and initialize a variable ‘ways’ to 0.
□ Go for option 1. Call the numDecodingsUtil function for index i+1 again and add the returned value to ‘ways’.
□ For option 2, check if we can take (i+1)th character. For that check if ((i+1)<n && ((S[i] == '1' && S[i] <= '9') || (S[i]=='2' && S[i+1] < '7'))), i.e., if it lies inside the string and also
in the range [10, 26]. If yes, go for option 2, call numDecodingsUtil for index i+2 again and add the returned value to ‘ways’.
3. At last, return ‘ways’.
Function numDecodings(string S):
1. call numDecodingsUtil with index as 0 and length of ‘S’.
Time Complexity
O(2^N), where ‘N’ is the length of the string ‘S’.
In the worst case, for each index i, we can maximum make 2 recursion calls for each i. Thus the complexity will be exponential and equal to O(2^N).
Hence, the time complexity is O(2^N).
Space Complexity
O( N ), where ‘N’ is the length of the string ‘S’.
In the worst case, the extra space used by the recursion stack can go up to a maximum depth of ‘N’. Hence the space complexity is O(N).
Hence the space complexity is O( N ).
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Thermal Expansion Calculator
Last updated: Dec 16, 2022
Welcome to our thermal expansion calculator, where you'll be able to calculate the thermal expansion of steel, aluminum, and other common materials.
From the thermal expansion equation, you'll note that to calculate the thermal expansion, you only need to know:
• The thermal expansion coefficient (aka CTE).
• The initial dimension (length for linear expansion and volume for volumetric expansion).
• The temperature change.
Additionally, you can use this tool to calculate the CTE as long as you know the initial dimension and the temperature and dimensional changes.
What is thermal expansion?
1. When we increase the temperature of some material, we're supplying energy to its molecules (the amount of energy required depends on the specific heat of the material).
2. That energy supply causes an increase in the kinetic energy and speed of the molecules.
3. The more these molecules move, the further away they need to stay from each other.
4. This molecular separation is what causes the material to expand (and change its density slightly)
Linear expansion
Linear expansion refers to one-dimensional expansion, and we typically observe it in objects whose length is much higher than the width, for example, resistors. Check the to learn more about
Volumetric expansion
On the other hand, this is a three-dimensional expansion. A real-life example is opening a closed glass jar with a metal lid. It might be difficult, but it gives way more easily after pouring some
hot water on the lid. It happens because the latter expands much faster than glass.
Thermal expansion equation
• Linear thermal expansion equation: $\Delta L = aL_1\Delta T$, where:
□ $\Delta L$ — Change in object's length;
□ $L_1$ — Initial length;
□ $a$ — Linear expansion coefficient;
• Volumetric thermal expansion equation: $\Delta V = bV_1\Delta T$, where:
□ $\Delta V$ — Change in object's volume;
□ $V_1$ — Initial volume; and
□ $b$ — Volumetric expansion coefficient.
$\Delta T$ refers to the temperature change, and it's simply the difference between the final and the initial temperatures ($T_2$ and $T_1$, respectively):
$\Delta T = T_2 - T_1$
Coefficient of thermal expansion equation
From the previous equations, we can solve for $a$ and $b$ and obtain the coefficient of thermal expansion equations:
• Linear coefficient of thermal expansion formula: $a = \frac{\Delta L/L_1}{\Delta T}$
• Volumetric coefficient of thermal expansion formula: $b = \frac{\Delta V/V_1}{\Delta T}$
Coefficient of thermal expansion of various materials
You can use the following values of CTE to calculate the thermal expansion of steel and other solid materials:
CTE (K^-1 or (°C)^-1)
Linear Volumetric
Aluminum 2.4 × 10^-5 7.2 × 10^-5
Brass 2.0 × 10^-5 6.0 × 10^-5
Copper 1.7 × 10^-5 5.1 × 10^-5
Glass 0.4-0.9 × 10^-5 1.2-2.7 × 10^-5
Invar 0.09 × 10^-5 0.27 × 10^-5
Quartz (fuzed) 0.04 × 10^-5 0.12 × 10^-5
Steel 1.2 × 10^-5 3.6 × 10^-5
For liquids, only volumetric expansion has physical meaning:
• Ethanol: 75 × 10^-5 K^-1
• Carbon disulfide: 115 × 10^-5 K^-1
• Glycerin: 49 × 10^-5 K^-1
• Mercury: 18 × 10^-5 K^-1
Linear expansion
Linear expansion coefficient
Volumetric expansion
Volumetric expansion coefficient
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Solve returns the variable to be solved for as a dependent variable
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1 Reply
1 Total Likes
Solve returns the variable to be solved for as a dependent variable
I have the following code where I want to solve for lam1R, lam2R and lam3R. However, the Solve command gives me these three results as functions of lam1R, i.e. lam1R is on the right-hand side of the
solutions for lam1R, lam2R and lam3R. No warning is issued. What is happening here?
Thank you,
e1R = 1/Ah (-Sqrt[2] ky kz lam1R - Sqrt[2] kx kz lam2R -
kx ky lam3R);
e4R = 1/As (-Sqrt[6] kx^2 lam1R + Sqrt[6] kx ky lam2R +
Sqrt[3] kx kz lam3R);
e5R = 1/As (Sqrt[6] kx ky lam1R\:ffff - Sqrt[6] ky^2 lam2R +
Sqrt[3] ky kz lam3R);
e6R = 1/As (Sqrt[6] kx kz lam1R + Sqrt[6] ky kz lam2R -
Sqrt[3] kz^2 lam3R);
finc1R =
e1R Sqrt[2] ky kz + e2R Sqrt[3] ky kz + e3R ky kz +
e4R Sqrt[6] kx^2 - e5R Sqrt[6] kx ky - e6R Sqrt[6] kx kz;
finc2R =
e1R Sqrt[2] kx kz - e2R Sqrt[3] kx kz + e3R kx kz -
e4R Sqrt[6] kx ky + e5R Sqrt[6] ky^2 - e6R Sqrt[6] ky kz;
finc3R =
e1R kx ky - e3R Sqrt[2] kx ky - e4R Sqrt[3] kx kz -
e5R Sqrt[3] ky kz + e6R Sqrt[3] kz^2;
sol = Solve[{finc1R == 0, finc2R == 0, finc3R == 0}, {lam1R, lam2R,
1 Reply
Okay, I can answer this myself. When I look at the code that I posted, there is "lam1R\:ffff" in e5R. There is presumably some extra character after lam1R which is not visible in the Mathematica
notebook. This is not lam1R but some other variable that is treated as independent. In the output, the part with "\:ffff" is again not visible and thus it looks like lam1R depends on lam1R. In fact,
it is that lam1R is a function of lam1R\:ffff. I have never seen this before and it is rather dangerous that Mathematica does not warn me that there is some extra character after lam1R that is
treated as a part of the variable name.
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Similarity (geometry)
Informally, two objects are similar if they are similar in every aspect except possibly size or orientation. For example, a globe and the surface of the earth are, in theory, similar.
More formally, we say two objects are congruent if they are the same up to translation, rotation and reflection (rigid motions). We say two objects are similar if they are congruent up to a dilation.
Determining Similarity
• All circles are similar.
• There are three ways of determining if two triangles are similar.
□ If two of the triangles' corresponding angles are the same, the triangles are similar by AA Similarity. Note that by the Triangle Angle Theorem, the third corresponding angle is also the same
from the two triangles.
□ Two triangles are similar if all their corresponding sides are in equal ratios by SSS Similarity.
□ If two of the triangles' corresponding sides are in equal ratio and the corresponding angle between the two sides are the same the triangles are similar by SAS Similarity.
• Two polygons are similar if their corresponding angles are equal and corresponding sides are in a fixed ratio. Note that for polygons with 4 or more sides, both of these conditions are necessary.
For instance, all rectangles have the same angles, but not all rectangles are similar.
Applications to Similarity
Once two figures are determined to be similar, the corresponding sides are proportional and the corresponding angles are congruent.
Similar figures (especially triangles) can be usually found in figures that contain many pairs of equal angles.
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Tento text není v aktuálním jazyce dostupný. Zobrazuje se verze "en".
In the Colored Bin Packing problem a sequence of items of sizes up to 1 arrives to be packed into bins of unit capacity. Each item has one of at least two colors and an additional constraint is that
we cannot pack two items of the same color next to each other in the same bin.
The objective is to minimize the number of bins. In the important special case when all items have size zero, we characterize the optimal value to be equal to color discrepancy.
As our main result, we give an (asymptotically) 1.5-competitive algorithm which is optimal. In fact, the algorithm always uses at most bins and we can force any deterministic online algorithm to use
at least bins while the offline optimum is for any value of.
In particular, the absolute competitive ratio of our algorithm is 5 / 3 and this is optimal. For items of arbitrary size we give a lower bound of 2.5 on the asymptotic competitive ratio of any online
algorithm and an absolutely 3.5-competitive algorithm.
When the items have sizes of at most 1 / d for a real the asymptotic competitive ratio of our algorithm is. We also show that classical algorithms First Fit, Best Fit and Worst Fit are not constant
competitive, which holds already for three colors and small items.
In the case of two colors-the Black and White Bin Packing problem-we give a lower bound of 2 on the asymptotic competitive ratio of any online algorithm when items have arbitrary size. We also prove
that all Any Fit algorithms have the absolute competitive ratio 3.
When the items have sizes of at most 1 / d for a real we show that the Worst Fit algorithm is absolutely -competitive.
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For this problem, perform the required simulations using “MIT Atomic... on the nanoHUB. Select the “SIESTA” tool from the menu.... 3.021 Quantum Modeling
3.021 Quantum Modeling
Problem Set 6
1. Basic calculations of a solid
For this problem, perform the required simulations using “MIT Atomic Scale Modeling Toolkit”
on the nanoHUB. Select the “SIESTA” tool from the menu. In all simulations, use GGA/PBE for
“XC functional” and DZP for “Basis”. Also, take 100 for “Mesh cutoff'”.
(a) Using the Si diamond structure, find the equilibrium lattice constant and verify that your
value is converged with respect to k-point density (note: this may not be the default lattice
(b) Using the equilibrium lattice constant found in (a), plot the band structure.
(c) Perform the same calculations as in (a) and (b) for Zincblende(GaAs). Discuss how GaAs is
different than Silicon. In particular what are the differences between the two band structures?
How might these differences be relevant to solar cells?
(d) Use the same tool to compute the binding energies of each material. Compare your values
with experiments. You’ll need to have “spin polarized” selected for calculating the energies of
the atoms. Be sure to specify what your convergence settings were – namely your k-point mesh
and basis set.
(e) Calculate the bulk modulus (in GPa) for both Si and GaAs and verify which of these two
materials is harder. Be sure your computed values are converged with respect to k-points.
Compare your results with the experimental data. Note that the bulk modulus (B) is defined as:
d 2 E "
da %
2 4 d 2 E 8k
B =
$ ' =
da 2 #
dV &
9a da 2 9a where k is the quadratic coefficient and a is the lattice constant.
2. Efficiency of photovoltaic materials
For this problem use the same tool and setup as for problem #1.
(a) For many applications, such as next-generation computer chips, solar cells or
thermoelectrics, we would like to be able to control the mobility of a material – that is,
the drift velocity of electrons and holes in response to an applied electric field. Starting
from your converged calculations in part 1, compress and stretch the Si unit cell. You can
do so by changing the lattice constant. How does this pressure (or negative pressure in the
case of stretching) affect the mobility of charge carriers in Si? Discuss your findings for
both positive and negative carriers.
(b) Can you think of other ways to change the mobility in silicon? Try at least one such
“materials design” idea out (apart from applying pressure) using the simulation tool and
show and discuss your findings.
(c) Just as is the case for solar thermal fuels, the band gap of a material is a critical
component for both light absorption and energy conversion in photovoltaics. Using the
same solar spectrum from problem set #5, calculate the fraction of energy of the solar
spectrum that both Si and GaAs could absorb, assuming sufficiently thick layers
(hundreds of microns). [Use a scissor shift of 0.5 eV for Si and 0.7 eV for GaAs].
(d) Using what you know about the meaning of the band structure of a material, what is the
maximum energy you could extract from a single photon excitation in each material and
how would this relate to the voltage a PV cell could produce? Combine this with your
work from part (c) to present a calculation of the maximum theoretical efficiency of a
solar cell made of each material.
MIT OpenCourseWare
3.021J / 1.021J / 10.333J / 18.361J / 22.00J Introduction to Modeling and Simulation
Spring 2012
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
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½ Vulgar fraction a half copy ⋆ Copy & Paste!
½ Vulgar fraction a half copy
You can copy Vulgar fraction a half by pressing the copy button below. This sign is probably the most widely used fraction. Fraction a half represents a half, 50% or 0.5 of something. Here, the
numerator is the number one and at the bottom is the denominator with the number two. If one multiplies this fraction by two, then 1 comes out. The exact same result is obtained when the fraction is
summed up with itself. Imagine buying a bar of chocolate with your friend. You then split them exactly in the middle, so that you have two equal parts. Each of you will now have ½ of the chocolate.
An application example would be: “I bought ½ bread.” You want to copy the fraction a half? You can easily do that by using the copy button below.
Copy & Paste
Unicode: U+00BD
Hex NCRs: ½
Rate ½ Vulgar fraction a half copy
More emojis:
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Exploration 29.5
Exploration 29.5: Self-Inductance
Please wait for the animation to completely load.
This animation shows a cross section of a solenoid (think of a long tube cut lengthwise down the cylinder and then looking at the edge) so that the black dots represent the current-carrying wires
coming into and out of the screen. Restart. The arrows show the direction and magnitude of the magnetic field. You can drag the black dot around to measure the field in different spots (position is
given in centimeters, the magnetic field strength is given in millitesla, 10^-3 T, and current is given in amperes). You can either change field by varying the current in the wires with the slider or
you can choose to change the current linearly as a function of time.
Faraday's law tells us that when a loop is in a changing magnetic field, an induced emf in the loop will result. But what if the loop itself has a changing current? With a changing current, the loop
has a changing magnetic field. Wouldn't it make sense, then, for there to be an induced emf and an induced current to oppose the changing flux? The answer is that there are: If the current is changed
in a current loop, there is a self-induced back emf. The measure of the back emf produced when a current is changed in a loop is called its self-inductance, or simply inductance, represented by L and
measured in henries, H (1 H = 1 T·m^2/A). From Faraday's law, emf = - dΦ/dt, the self-inductance is the back emf = - L (dI/dt).
Run the change field by varying the current in the wires with the slider. Instead of considering a loop, we will look at a solenoid (it is easier to calculate the magnetic field inside a long
1. For the solenoid above, adjust the current with the slider and determine how the magnetic field varies with current.
2. For this solenoid (given the value of the magnetic field at the current chosen), how many loops per meter are there?
Run change the current linearly as a function of time.
3. What is the emf?
4. Using the equation above, what is the inductance, L?
5. Using Faraday's law and the equation above, show that L = (Φ/I) N for an inductor with N loops.
6. Therefore, show that the inductance, L, of a solenoid is μ[0]N^2A/(length), where N is the number of loops, A is the cross-sectional area and length is the length of the solenoid (so that N/
length is the number of loops per meter).
7. If this solenoid is 2 m long, calculate the inductance and compare it to your answer in (d) above.
Exploration authored by Anne J. Cox.
Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.
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Amar sells goods to Bhola for र 10,000 plus CGST and SGST @ 9 % each. He receives the GST amount in cash and draws upon Bhola a bill for the balance amount payable 3 months after date. The bill is accepted by Bhola. Amar discounts the bill with his bank at a discount of 150 inclusive of all charges. Bhola fails to meet this bill on maturity. Amar pays off his bank and his expenses amounting to र 100 . Bhola gives a fresh bill of 2 months' date to Amar for र 10,250 , which he meets at maturity. Show necessary Journal entries in Amar's books.
Amar sells goods to Bhola for ₹ 10,000 plus CGST and SGST @ 9% each. He receives the GST amount in cash and draws upon Bhola a bill for the balance amount payable 3 months after date. The bill is
accepted by Bhola. Amar discounts the bill with his bank at a discount of ₹ 150 inclusive of all charges. Bhola fails to meet this bill on maturity. Amar pays off his bank and his expenses amounting
to ₹ 100. Bhola gives a fresh bill of 2 months' date to Amar for ₹ 10,250, which he meets at maturity. Show necessary Journal entries in Amar's books.
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Railway - math word problem (2013)
Railway line had on 5.8 km segment climb nine permille. How many meters does the track ascent?
Correct answer:
Did you find an error or inaccuracy? Feel free to
write us
. Thank you!
You need to know the following knowledge to solve this word math problem:
Units of physical quantities:
Grade of the word problem:
We encourage you to watch this tutorial video on this math problem:
Related math problems and questions:
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Calculate the Average Percentage of Marks in Excel
Excel is a perfect tool for all mathematical operations and visual presentation of data. It can be used to combine the two, as well.
In the example below, we will show how can you use Excel to calculate the average percentage of marks.
Calculate the Average Percentage of Marks
For our example, we will suppose that we had four groups of students, each group containing 15 students, and their marks from the exam, ranging from 1% to 100%:
We now need to calculate the average of our percentages for every group, and we will do so by inserting the AVERAGE formula at the bottom of our table:
Now we need to calculate the averages of our four groups. We need to consider that every group has a different number of students (for example, we have 15 students in group A, but only 11 students in
group C).
To encapsulate this, we need to use the COUNT formula. We will place it beneath the averages:
To calculate the average percentage of all marks, we will use the SUMPRODUCT formula, including averages and counts of records. Our formula will be as follows:
1 =SUMPRODUCT(B17:E17,B18:E18)/SUM(B18:E18)
This is what the formula looks like in the sheet:
And our result will be 49.40%.
To verify this result we calculate results for every group (multiplying AVERAGE and COUNTA for every group):
Then we sum all these numbers and divide them by the sum of the total students. We will get the same number:
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The garden - math word problem (39701)
The garden
The garden has the shape of an isosceles trapezoid whose bases are 64 m and 24 m long. The height is 25 m. In what garden area is it possible to grow vegetables if a fifth of the area is occupied by
a cottage, lawn, and path?
Correct answer:
Did you find an error or inaccuracy? Feel free to
write us
. Thank you!
Tips for related online calculators
Need help calculating sum, simplifying, or multiplying fractions? Try our
fraction calculator
You need to know the following knowledge to solve this word math problem:
Units of physical quantities:
Grade of the word problem:
We encourage you to watch this tutorial video on this math problem:
Related math problems and questions:
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