content stringlengths 86 994k | meta stringlengths 288 619 |
|---|---|
Back Reaction of 4D Conformal Fields on Static Geometry
In classical mechanics, a black hole is described by a vacuum solution with the horizon of the Einstein equation. For spherical case, it is the Schwarzschild metric, and the location of the horizon
is given by the Schwarzschild radius. (Note that the Schwarzschild radius can also be defined even for a star without horizon.) In quantum mechanics, a black hole evaporates and information inside it
seems to be lost, which is contradict to the principle of quantum mechanics. An effective way to address this problem is to consider again “What is the black hole in quantum mechanics?” In this
paper, we examined how robust the use of the Schwarzschild metric to represent a black hole is in quantum mechanics. We consider conformal matters (e.g. electromagnetic field) and introduce the
quantum effect (4D conformal anomaly) into the Einstein equation, which necessarily makes the equation non-vacuum. We start from the Schwarzschild metric, add the quantum effect perturbatively, and
solve the Einstein equation in a self-consistent manner. Then, we showed that the quantum effect can play a crucial role in shaping the static geometry near the Schwarzschild radius. The geometry
depends on a parameter corresponding to a boundary condition, and the existence of the horizon requires the fine-tuning. Therefore, in quantum mechanics, a typical static spherical solution does not
have a horizon.
Pei-Ming Ho, Hikaru Kawai, Yoshinori Matsuo, Yuki Yokokura
"Back Reaction of 4D Conformal Fields on Static Geometry"
doi: 10.1007/JHEP11(2018)056
arXiv: 1807.11352 | {"url":"https://ithems.riken.jp/en/news/back-reaction-of-4d-conformal-fields-on-static-geometry","timestamp":"2024-11-14T08:47:47Z","content_type":"text/html","content_length":"36945","record_id":"<urn:uuid:5341bd10-3d46-445d-8410-278413254593>","cc-path":"CC-MAIN-2024-46/segments/1730477028545.2/warc/CC-MAIN-20241114062951-20241114092951-00612.warc.gz"} |
Author content
All content in this area was uploaded by Cristian Mihail Păuna on Jan 10, 2020
Content may be subject to copyright.
Author content
All content in this area was uploaded by Cristian Mihail Păuna on Nov 01, 2019
Content may be subject to copyright.
“Management Strategies for High Performance”
31st October – 1st November, 2019, BUCHAREST, ROMANIA
Cristian PĂUNA a
a The Bucharest University of Economic Studies, Bucharest, Romania
Capital investment, trading, or any business, all are activities involving risk. A proper capital
management strategy to ensure long-term profitability is valuable nowadays. High price volatility
in the stock markets, unpredicted or unusual economic and geopolitical news, or just hard to
manage rare resources or human factors, all of these are instability reasons which can decrease
capital efficiency or even cancel the profit over time. To manage the involved risk in any economic
activity is a key factor for any manager today. Whatever the risk is estimated, the basic idea is
always the same. To ensure long-term profitability, the investor has to save a part of the profit and
to reinvest the rest to obtain a stable capital grow in time. The question this paper will answer is
how much profit to save and how much to reinvest to produce stable capital growth and sustainable
capital efficiency? The Logarithmic Risk Distribution will be presented, a practical method to size
the risk level depending on the invested capital, on the used capital exposure level, and on the profit
already made in the current business. It was found that the risk level can depend only on these three
factors through a function that will provide an exponential capital grow even if the risk is higher
than the realized profit. This paper will also include examples to prove the efficiency and simplicity
of the presented method. The Logarithmic Risk Distribution is simple and easy to be applied in any
business or investment.
KEYWORDS: business management, capital investment, logarithmic risk distribution, trading.
To make a profit is not enough today. For a sustainable activity, for long-run business development,
any manager has to provide long-term profitability. It is well known that any capital investment,
any trading activity, and in fact, any business is involving a risk. High price volatility in the stock
markets, financial crisis, unpredicted economic or geopolitical news, or only hard to manage rare
resources or human factors, all of these are instability reasons which can decrease capital efficiency
or even can cancel the business profit over a significant period of time. No matter how the risk is
measured, a proper capital and risk management strategy can ensure stable business growth in time.
The problem analyzed in this paper is how much to save from the obtained profit and how much to
reinvest in order to build a stable profit growth over time. Sustained capital management is a crucial
factor in any economic activity. A common problem for any manager today is to find the proper
profit and risk distribution. The methods of how to measure the risk involved in the current
economic activity are not a subject of this paper. In this paper, we will consider those methods to be
known, and the risk can be accurately established at any moment in our considered activity.
In those activities where the profit is higher than the involved risk, the risk distribution is easy to be
set by empirical or experimental models. Formulas, as to save half of the profit or save two-thirds or
Corresponding author. E-mail address: cristian.pauna@ie.ase.ro
“Management Strategies for High Performance”
31st October – 1st November, 2019, BUCHAREST, ROMANIA
three quarters and reinvest the rest, are well tested before for hundreds of years by our predecessors.
These cases will not be a subject of this paper. A more important problem is emitted for those cases
when the profit level is lower than the involved risk in a specified period of time. It is well known
that in tremendously higher activity domains, the risk involved today is much higher than the profit
obtained. This fact is not because of a lack of experience, or because of inadequate capital
management, but due to the specificityof the considered domain. Capital investment on shares,
short-time financial trading, real estate investments, huge allocated resources businesses, are only a
few examples of cases in which the risk distribution becomes more significant today. A substantial
loss in these cases can delete the profit for an extended period of time, and can even conduct to
bankruptcy in that activity. The risk distribution presented in this article is designed especially for
these cases when the risk level is higher than the recorded profit in a specified period.
This paper will present the Logarithmic Risk Distribution to answer to the enounced problem. It
was found that, in any business case, the current risk level can depend only on the initial invested
capital, on the capital exposure level used, and on the current profit obtained in the economic
activity. The Logarithmic Risk Distribution willprovide the risk percentage for each moment of
time in order to produce an exponential capital growth for the next period. The specificity of the
business is not essential; the presented risk distribution can be applied for any economic activity, as
we will see in this article. The presented capital management formula was specially designed for
those cases when the risk involved is higher than the recorded profit. The presented distribution can
also be used for the cases when the profit is higher than the risk, as we can see later in the paper.
The Logarithmic Risk Distribution presented in this article is a straightforward money management
strategy. It can be adapted to any economic activity once the risk can be estimated. Anyone can
compute the presented method with small resources in order to manage any economic activity
involving a capital risk. The model permits capital and risk adjustment over time in order to ensure
the adaptability for different cases or situations. The Logarithmic Risk Distribution can be applied
in any capital investment to manage any business or trading activity. It can be used even to build a
stable gambling money management strategy. This paper will include some examples to prove the
model’s simplicity and efficacy.
As it was mentioned before, the problem discussed in this paper is the profit distribution.
Considering we have a stable and profitable economic activity, involving a measurable risk level,
we ask how much from the realized profit we have to save, and how much we have to reinvest in
the current activity, in order to build a sustained capital growth over the time. The money
management and risk aversion problems are a high-interest subject for hundreds of years. There are
well known Bernoulli’s empirical solutions for the risk assessment and risk distribution (Eeckhoudt,
Gollier & Schlesinger, 2005) even from the eighteenth century. Splitting the income or the profit in
more parts with different risk allocation are methods tested before by our predecessors. Save half,
save two-thirds or save three-quarters and reinvest the rest are empirical methods for we have not a
specific author. These are functional models, especially when the income or profit is much higher
than the risk. When the risk is higher than the income, these models are failing when a significant
loss is met. For these cases, we need a stable methodology for the risk distribution.
Over time more money management strategies and risk distribution functions or methods have been
imagined depending on the specificity of each activity. Different working models and original
approach for money management strategies can be found in the literature. One of the most active
domains that substantially contribute to the money management strategy development is the capital
trading and investment domain. The high-risk involved in this field imposes significant attention on
the money management steps in order to conserve the invested capital. Over time more significant
methodologies for the money and risk management were developed. Especially for capital
“Management Strategies for High Performance”
31st October – 1st November, 2019, BUCHAREST, ROMANIA
investment activity, substantial considerations about money and risk management strategies can be
found in (Dormeier, 2011), (Farley, 2010), (Chan, 2009), (Bland, Meisler & Archer, 2009),
(Dologa, 2008), (Corcoran, 2007), (Mac, 2006), (Mun, 2006), (Weissman, 2005), (Elder, 2002),
(Connors & Radchke, 1995), and (Elder, 1993). Because taking the risk has a significant
psychological impact factor, and because individuals may have different risk attitudes (Hillson &
Murray-Webster, 2007), the risk assertion and the risk aversion are factors that must be taken into
consideration on a general risk distribution. From the psychological point of view, several authors
have a substantial contribution as (Ward, 2009), (Kiev, 2008), or (Pring, 1992).
The second one domain participating significantly in the risk and capital management strategy
development is the corporate finance domain, in which the profit distribution is usually made
depending on the specificity of the current activity. Significant approaches and models can be found
in (Basak & Makarov, 2014), (Saks & Maringer, 2009), (Armstrong & Murlis, 2007), (Basak,
Pavlova & Shapiro, 2007), (Power, 2004), (Stultz, 1996), or (Vince, 1992). None of these strategies
are generally applicable. Some of them are not functioning when the risk is higher than the realized
profit. This is a gap that will be filled by this paper.
In this paper, we want to present a riskdistribution, a mathematical formula defining the risk level,
which will be imposed by the manager on each step of the economic activity involved. In this chapter,
we will define the hypotheses we will use to build this function, and the variables used.
As we already affirmed, comparing the risk and the profit level, the economic activities can be
divided into two major parts. The first part includesthose activities in which the considered risk is
lower than the profit made into a specified time. An interesting example related to the capital trading
activity is one of using an investment strategywiththe risk and reward ratio lowerthan one. In this
case, the profit is higher than the assumed risk. Foreach one dollar risked, the strategy will produce
more than one dollar profit. This case is a happy one when a loss will preserve the initial capital, once
the number of the winning trades is higher than the number of the losing trades on a specified period.
Such as strategies are rare, and can be implemented in limited market conditions.
In the majority of cases, the riskis much higher than the realized profit. This is our first hypothesis.
This case is the real one, the situation of the most capital investment strategies, the majorityof any
trading activity, the case of all real-estate investments, and the situation in almost all businesses in the
first step of implementation. Usual to set a business, initial capitalis involved,an initial amount of
resources is set in order to organize the business activity, to hire the first employees, and to produce
the first profit stakes. It is well known that any important investment will be covered by the realized
profit in the next years, meaning that the realized profit per year is much lower than the capital
involved and the resources used.
The second hypothesisis related to the phases in which the risk level is changed or not. We will
consider our economic activity is carried out through two different phases. In the first one, the
implementation phase, the initial risk involved is kept unchanged until a significant profit is made. In
the second phase, the risk will be changed by the manager, through the risk distribution function we
build, depending on the activity results, in order to improve and to increase the capitalization. We will
call this second phase to be the maturity phase of our business.
In the implementation phase, an initial capital (C) is involved, an initial riskedcapital (
) is
allocated in order to realize an initial profit stake (
). The measure r is the risk rate, and pis
the profit rate, in order to define all the measure depending on the initial capital. By hypothesis, until
P is not achieved, the risk R remains unchanged. In the implementation phase, the safe capital (S) is
defined by the difference between the initial capital and the risked capital:
“Management Strategies for High Performance”
31st October – 1st November, 2019, BUCHAREST, ROMANIA
On a simple example, an initial capital C = 1,000,000 $ is invested in an economic activity with a risk
rate of
. The risked capital is
and the safe capital
. In the
implementation phase,by example, a profit rate
of the initialcapital will be obtained at
some point in time. To avoid confusion, we have to mention that we are still in the case in which the
profitis lower than the risk involved in a specified period of time.In the current example, the profit
rate pmentioned above defines the implementation phase. This phasecan include several years of
activity, in each year, the realized profit being lower than the risk rate r. For example, is the profit rate
per year is 5%, the implementation phase in our example will include6 years of activity. The cases
when the profit rate is higher than the profit rate per year can be easily included in the same algorithm.
Anyway, by the initial business plan, in this period, the capital risk rate r is set as fixed, as we have
presumed. At the end of the implementationphase, once the profit P is achieved,the total available
capital will be given by:
The third hypothesis in our model is related to the maturityphase.In this phase, the initial business
plan was achieved; the activity proved that it could produce a profit rate p with a capital risk rate r in a
specified period of time. Once the realized profit in the implementation phase is much higher than the
risk involved, even the yearly profit rate is lower than the risk rate, from this moment, it can be
considered that the risk can be increasedin order to improve the results for the next periods and to
speed up the business.
A common mistake in the second phase is to multiply the risk rate with a high number. Even a new
risk rate equal
for the second period is a bad idea; it can cancel the profit for four years of activity
in our example if a significant loss is recorded. In this case, the capital will decrease significantly, a
longerperiod of time being required to recover that loss. A better idea is to increase the risk with a
very small value. The new risk level will be close to the initial risk level included in the initial
business plan, a more stable functionality of all economic processes being expected.
Also, by hypothesis, the maturity period will be divided into small time intervals. On each time
interval, the risk will be increased by a small
risk gradient. In time, each interval will be defined
until a small profit
is obtained. When
are small, the number of the time intervals into
the maturity period of our business is high. When these measures tend towards zero, we want to know
a distribution function to define the risk level at any time moment. This is actually the problem of the
manager in the maturity interval: to know how much to set the risk level. The answer will be logically
deducted in the next chapter.
As was mentioned before, the maturity period is divided into small time intervals defined in time by
achieving the
profit. For each time interval the risk rate is increased with
. Noting with (i) the
time interval index, we can write the general formula for the considered risk rate for each interval:
By definition, each time interval last until a
profit rate is achieved,
being applied to the initial
capital for each time interval. In this case, we will have the capital at the end of each interval defined
“Management Strategies for High Performance”
31st October – 1st November, 2019, BUCHAREST, ROMANIA
2for 1
111 ipCCrCC iiii
is defined by the formula (2). Solving the recurrent formula (4), it can be simplified in:
1for 11 1-i ippCCi
In formula (5), C, p, and
are known terms. This fact permits to have a relation between the current
capital (which can be measured by the manager at anytime) and the risk involved in any time interval
in the maturity phase of the economic activity. Using the natural logarithm function and some simple
transformations, we can find the (i) interval for each capital amount given by:
In this way, using formula (3), we will find the Logarithmic Risk Distribution which will define the
risk associated with each capital level:
rrr i
Formula (7) isstill hard to be applied; the current risk level
is expressed as afunction of the
which is the capital at the end of the time interval. Usually, the manager can measure the
capital at the beginning of each time interval. Using formula (4), we can obtain a match more
convenient form of the Logarithmic Risk Distribution:
rrr i
in which the term
is completely excluded. In practice, it is more convenient to work with
instead of
, once the time interval is defined until
is achieved. Usually, there is a direct
correlation between these two terms. The manager can set, for example, to increase the risk with 1%
each time when the capital was increased with 10%. This is only an example. To generalize for any
other numbers, we can have a direct linear dependence defined by:
In this particular case, the Logarithmic Risk Distribution will be defined by:
prr i
The risk
for each time interval will be modified depending on the initial capital C, on the initial
risk rate r used to make the initial profit p, all of these terms being established by the initial business
plan. The term ξ, the relation between the risk increment and the realized profit is defined by the
“Management Strategies for High Performance”
31st October – 1st November, 2019, BUCHAREST, ROMANIA
business plan set for the maturity period of our activity. Having all of these, each capital amount,
which is perfectly measurable, will define the proper risk level by formula (10).
The most important advantage introduced by the Logarithmic Risk Distribution is the fact that the
capital is evolving in the maturity phase through an exponential function. This fact is revealed by
applying the exponential function to all terms of the relation (7). After some common operations,
we will obtain:
relation in whom the terms in front of the exponential function are constant once the business plan
is set. Considering relation (3) the term
can be excluded and we will obtain much simpler:
1for 11 1 ieppCC i
formula confirmed by the first term. For i=1 we have the capital at the end of the first time interval
in the maturity phase defined by
, in perfect accordance with our model and all
considered hypothesis.
5. RESULTS
In this chapter, we will see the results of applying the Logarithmic Risk Distribution in real cases.
The first example is the one we have already considered. In figure 1, is presented the capital
evolution in time. It can be observer the constant evolution in the implementation phase and the
exponential evolution realized in the maturity phase because of the risk increase.
Figure 1. Capital evolution due to the Logarithmic Risk Distribution
An important observation is regarding of axis of the abscissae. This must not be confused with the
time axes. By our hypothesis, a time period on the maturity phase is defined by recording the p
profit rate. Due to the business characteristics, the time consumed can be different from a period to
another. Usually, once the capital is increased, the time spending for each phase can be higher.
“Management Strategies for High Performance”
31st October – 1st November, 2019, BUCHAREST, ROMANIA
Another important observation is regarding safe capital. Even the capital is importantly increased in
the maturity phase, the risk is higher from one interval to another. This means the safe capital
expressed as a percentage is decreasing once the risk is increased. This is figured in figure 2.
Figure 2. Risk evolution and safe capital evolution
In the example above, it was considered acase in which the risk was increased in the maturity
phase, with 1% each time when a 10% profit stake was recorded. This can be a typical case of any
stable business in which the losses are quickly recovered and have a lower impact on capital
evolution. In these cases, the x-axis can be in a direct correlation tithe the time spent.
A different situation is used in those cases when a loss decreases the involved capital significantly
in the current business. In the capital investment activity, after a loss, the capital decreases with that
loss. If the risk is high, the loss is important, and the time consumed to recover can be significant. In
cases like this, the risk level is lower, and the risk gradient in the maturity phase is also lower. After
each loss, the formula (10) will provide the new lower risk level, with some intervals back on the x-
axis. The risk will be increased again after some profit stakes will be recorded, following the same
risk distribution.
Figure 3. Risk comparison for different risk gradients
For the capital investment and financial trading activities, the Logarithmic Risk Distribution can be
successfully combined with the „Global Stop Loss” methodology (Pauna, 2018). Especially for the
automatic trading and investment systems, the risk calibration needs a distribution function in order
“Management Strategies for High Performance”
31st October – 1st November, 2019, BUCHAREST, ROMANIA
to set the risk automatically depending on the results obtained. The risk distribution presented in
this paper is adaptable by the results obtained in each moment of time, can be programmed, is
simple, and can be computed in real-time. The Logarithmic Risk Distribution, together with the
Global Stop Loss methodology, builds together a dependable risk management procedure for any
automated trading software. The steps to be considered in order to implement this methodology
package are the next:
a) Set an initial capital (C) together with an initial global risk level (r) and the implementation profit
level (p). With all of these, considering that the automated trading system has a positive expectancy
strategy, the system will trade the capital until the profit (P) is achieved. In all this period, the risk
level is set to be constant at (r) no matter the capital evolution is achieved.
b) Once the implementation phase is ready, and the profit P is collected, the maturity phase can
start. For this, the software designers will set the risk gradient
and the profit gradient
or the
link between these tow factors measured by the ξ coefficient.
c) Inevery moment of time, when the capital managementprocedure is called, the available capital
will define the risk level using formula (10). If the capital is increased or decreased by the last capital
trades, the formula (10) will provide the proper risk calibration according tothe money management
strategy set by the functional parameters used.
d) Optimizations for the gradient measures
can be made. The values can depend on the
software specificity, on the trading frequency, and, more importantly, on the expectancy and risk to
reward ratio assured by the investment capital strategies included in the automated trading software
used.This optimization is one of the most important factors in long-term efficiency. A significant
numberof big losses can decrease the profit ratio drastically. Meanwhile, a small number of loss
tradesstrategycan improve the value for the risk gradient, which can contribute significantly in the
capital efficiency on the long-term.
A significant number of capital investors and traders are still using the individual stop-loss protection
for each trade. The Logarithmic Risk Distribution can also be used in these cases after each trade. The
risk can be set anytime, depending on the current capital level. For this purpose, an automated trading
system is a right solution.
The real-estate domain is anotherexample of large investments with high running costs and lower
profitrates. The Logarithmic Risk Distribution can be used in order to set the expenditure level for
each moment of time, depending on the liquidities. In the risk distribution formula, the capital can be
substituted by two factors: the investedcapital (CI) and the liquid capital(CL). While the invested
capital is almost constant in real estate, the liquid capital is variable and depends on the incomes, on
the current expenses, which can be assimilated with a risk. Form this substitution, the current
expenditure level can be computed depending on the incomes.
6. CONCLUSIONS
The Logarithmic Risk Distribution is a reliable function which permits to set the risk level
depending on the current capital involved in any business. The model was developed by splitting
the business scenario into two different phases. The first one is designed for the business
implementation period. The business plan is applied until a specific profit level is recorded using a
constant risk level. The second phase, called the maturity phase, is the period when the risk is
increased with small gradients in order to speed up the business and to increase capital efficiency.
The model can be applied both for businesses with the profit ratio higher or lower the risk ratio.
For the maturity phase, the risk is increased with small gradients each time when a small
profitability level is obtained. The dependency between the risk level and the available capital is a
logarithmic one. This function produces an exponential capital evolution in the maturity phase, the
main advantage instead of the linear capital evolution recorded in the implementation phase.
“Management Strategies for High Performance”
31st October – 1st November, 2019, BUCHAREST, ROMANIA
The risk model proposed in this paper can be applied in a large number of economic activities
starting with the capital investment, any trading activity, in the real-estate domain, and in any
business in which the capital and the risk involved can be measurable. The variables in the
Logarithmic Risk Distribution formula are usually included in every business plan, even from the
business analysis step. The model has the advantage that is entirely functional for both, the
economic activities in which the capital is continuously increasing, but even in those cases in which
losses can decrease the capital from time to time. The Logarithmic Risk Distribution will redefine
the risk level in the maturity phase for each capital level, assuring a continuous business
management activity.
One of the most important advantages of the risk function presented in this paper is simplicity. The
Logarithmic Risk Distribution can be computed by anyone for any economic activity using a simple
pocket calculator. More than that, the risk function presented can be programmed in advanced
business software systems in order to assist the business intelligence procedures in making
automated decisions regarding the risk level.
The Logarithmic Risk Distribution is a reliable formula that can be included in any economic and
business model which permits to manage a risk increase depending on the available capital.
Armstrong, M. & Murlis, H. (2007).Reward Management: A Handbook of Remuneration Strategy
and Practice. Revised eddition. HayGroup. ISBN: 978-0749449865
Basak, S. & Makarov, D. (2014). Strategic Asset Allocation in Money Management. The Journal of
American Finance Association. 69, (1) doi: 10.1111/jofi.12106
Basak, S., Pavlova, A. & Shapiro, A. (2007). Optimal Asset Allocation and Risk Shifting in Money
Management. The Review of Financial Studies, 20, (5). 1583-1621. doi: 10.1093/rfs/hhm026
Bland, J.M., Meisler, J.M. & Archer, M.D. (2009). Forex essentials in 15 trades. New Jersey:John
Wiley & Sons. ISBN: 978-0-470-29263-1
Chan, E.P. (2009). Quantitative trading. How to build your own algorithmic trading business. John
Wiley & Sons. ISBN: 978-0-470-28488-9
Connors, A.L. & Raschke, L.B. (1995). Street smart. High probability short term trading strategies.
Malibu, California: M. Gordon Publishing Group. ISBN: 0-9650461-0-9
Corcoran, C.M. (2007). Long/short market dynamics. John Wiley & Sons. ISBN: 978-047005728-5
Dologa, M. (2008). Integrated Pitchfork Analysis. John wiley & Sons. ISBN: 978-0-470-69434-3
Dormeier, B.P. (2011). Investing with volume analysis. New Jersey:Pearson Education. ISBN: 978-
Eeckhoudt, L., Gollier, C. & Schlesinger, H. (2005). Meconomic and Financial Decisions under
Risk. US: Princeton University Press. ISBN: 978-0691122151
Elder, A. (1993). Trading for a living. Canada: John Wiley & Sons. ISBN: 9780471592259
Elder, A. (2002). Come into my trading room. US:John Wiley & Sons. ISBN: 0-471-22534-7
Farley, A.S. (2010). The master swing trader toolkit. US: McGraw Hill. ISBN: 978-0-07-175955-7
Hillson, D. & Murray-Webster, R. (2007). Understanding and Managing Risk Attitude. Gower
Publishing. ISBN 978-0-566-08798-1
Kiev, A. (2008). Mastering Trading Stress. John Wiley & Sons. ISBN: 978-0-470-18168-3
Mac, D.K. (2006). Mathematical techniques in financial market trading. World Scientific. ISBN:
“Management Strategies for High Performance”
31st October – 1st November, 2019, BUCHAREST, ROMANIA
Mun, J. (2006). Modeling risk. John wiley & Sons. ISBN: 978-0-471-78900-0
Power, M. (2004). The risk management of everything. Journal of Risk Finance, 5, (3), 58-65 doi::
Pauna, C. (2018). Capital and risk management for automated trading systems. Proceeding of the
17thInternational Conference on Informatics in Economy, Iasi, Romania. Retrived September,
20,019: https://pauna.biz/ideas
Pring, M.J. (1992). Investment psychology explained. John Wiley & Sons. ISBN: 9780471557210
Vince, R. (1992). The Mathematics of Money Management: Risk Analysis Techniques for Traders.
John Wiley & Sons. ISBN: 0-471-54738-7
Saks, P. & Maringer, D. (2009). Evolutionary Money Management. Applications of Evolutionary
Computing. EvoWorkshops 2009. Lecture Notes in Computer Science, Springer, Berlin,
Heidelberg. doi:10.1007/978-3-642-01129-0_20
Stultz, M.R. (1996). Rethinking Risk Management. Journal of Applied Corporate Finance. 9, (3).
8-24, doi: j.1745-6622.1996.tb00295.x
Ward, S. (2009). High performance trading. 35 practical strategies and techniques to enhance your
trading psychology and performance. Harriman House. ISBN: 978-1-905641-61-1
Weissman, R.L. (2005). Mechanical Trading Systems. John Wiley & Sons. ISBN: 0-471-65435-3. | {"url":"https://www.researchgate.net/publication/336937800_LOGARITHMIC_RISK_DISTRIBUTION_TO_BUILD_A_STABLE_CAPITAL_GROWTH_FOR_ANY_BUSINESS_OR_INVESTMENT","timestamp":"2024-11-02T08:41:59Z","content_type":"text/html","content_length":"562765","record_id":"<urn:uuid:81a4fe48-02d8-43a5-a175-e3349d2c6d6e>","cc-path":"CC-MAIN-2024-46/segments/1730477027709.8/warc/CC-MAIN-20241102071948-20241102101948-00578.warc.gz"} |
How to Prevent Matplotlib From Dropping Points?
To prevent Matplotlib from dropping points, you can consider the following guidelines:
1. Increase the figure size: One common reason for dropped points is the insufficient figure size. By increasing the size of the figure, more space will be available to display the points without
2. Adjust the marker size: If the points are too small, they might appear as dropped. You can increase the marker size using the markersize parameter to make them more prominent.
3. Set appropriate axis limits: If points are outside the axis limits, Matplotlib might drop them to fit the plot within the given bounds. Ensure that the axis limits are set correctly using the
xlim and ylim functions to include all the desired data points.
4. Disable the default marker clipping behavior: By default, Matplotlib clips markers outside the data limits. You can disable it using the clip_on parameter and set it to False when plotting the
5. Adjust plot margins: Sometimes, Matplotlib crops the points if they are close to the plot edges. You can adjust the margins using the subplots_adjust function to increase the space around the
plot area.
6. Use the scatter plot instead of the line plot: If you are plotting individual points using a line plot, it might result in dropped points due to the connection between them. Using the scatter
plot instead will visualize all points separately.
By implementing these suggestions, you can prevent Matplotlib from dropping points and ensure that all your data is correctly displayed in the plot.
How to handle missing or dropped points while plotting using Matplotlib?
When plotting using Matplotlib in Python, you might come across situations where there are missing or dropped points in your data. These missing or dropped points can create gaps or jumps in your
plotted data, which might affect the overall visualization.
Here are a few ways to handle missing or dropped points while plotting with Matplotlib:
1. Connect the points: By default, Matplotlib draws lines between consecutive points in the data. So, if there are missing points in the data, you can control how Matplotlib handles them by
specifying the line style. For example, you can use the '-' line style to connect the points with straight lines or use '.' to plot only the available points without connecting them.
1 import matplotlib.pyplot as plt
3 x = [1, 2, 4, 5] # Missing point at x=3
4 y = [2, 4, 8, 10]
6 plt.plot(x, y, '-o') # Connect points with lines and add markers
7 plt.show()
1. Handle missing values explicitly: If your data contains missing values or NaN (not a number) values, you can handle them explicitly by removing or replacing them before plotting the data. For
example, you can use the numpy library to handle missing values or NaN values in your data.
1 import numpy as np
2 import matplotlib.pyplot as plt
4 x = [1, 2, None, 4, 5] # Missing value at index 2
5 y = [2, 4, 5, 8, 10]
7 x = np.array(x)
8 y = np.array(y)
10 x = x[~np.isnan(x)] # Remove NaN values
11 y = y[~np.isnan(y)]
13 plt.plot(x, y, '-o') # Connect points with lines and add markers
14 plt.show()
1. Interpolate missing points: If you want to fill the gaps in your data by estimating values for the missing points, you can use interpolation techniques. Matplotlib supports various interpolation
methods, such as linear, polynomial, and spline interpolation. The scipy library provides functions for interpolation that you can use in combination with Matplotlib.
1 import numpy as np
2 import matplotlib.pyplot as plt
3 from scipy.interpolate import interp1d
5 x = [1, 2, None, 4, 5] # Missing value at index 2
6 y = [2, 4, 5, 8, 10]
8 x = np.array(x)
9 y = np.array(y)
11 mask = ~np.isnan(x) & ~np.isnan(y) # Mask to handle NaN values
12 interpolation = interp1d(x[mask], y[mask], kind='linear')
14 x_interp = np.linspace(np.nanmin(x), np.nanmax(x), 100) # Generate new interpolated points
15 y_interp = interpolation(x_interp)
17 plt.plot(x_interp, y_interp) # Connect interpolated points with lines
18 plt.scatter(x[mask], y[mask], c='r', label='Existing Points') # Plot existing points
19 plt.legend()
20 plt.show()
By implementing these techniques, you can handle missing or dropped points while plotting with Matplotlib and ensure a proper visualization of your data.
How to avoid gaps in plotted data points with Matplotlib?
To avoid gaps in plotted data points with Matplotlib, you can make use of the plt.plot() function in combination with the plt.fill_between() function. Here's a step-by-step guide:
1. Import the necessary libraries:
1 import matplotlib.pyplot as plt
2 import numpy as np
1. Generate your data points. In this example, we'll create some random data:
1 x = np.linspace(0, 10, 100)
2 y = np.random.randn(100)
1. Plot the data points using plt.plot():
1. Create a mask to identify the missing data points. Here, we'll assume that any data point with a value less than zero is missing:
1. Use plt.fill_between() to fill in the gaps:
1 plt.fill_between(x, y, where=~mask, interpolate=True, color='gray')
Setting interpolate=True ensures that the edges of the filled gap follow the lines of adjacent points.
1. Finally, show the plot using plt.show():
By following these steps, you should be able to avoid gaps in your plotted data points in Matplotlib.
How to adjust the chart size to minimize the chances of dropped points in Matplotlib?
To minimize the chances of dropped points in a Matplotlib chart, you can adjust the chart size using the figsize parameter.
By increasing the size of the chart, you allow more space for the points to be plotted without overlapping or being cut off. Here is an example:
1 import matplotlib.pyplot as plt
3 # Sample data
4 x = [1, 2, 3, 4, 5]
5 y = [6, 7, 10, 8, 9]
7 # Create a figure and axis with adjusted size
8 fig, ax = plt.subplots(figsize=(8, 6))
10 # Plot the data
11 ax.plot(x, y, 'o')
13 # Display the chart
14 plt.show()
In the example above, figsize=(8, 6) sets the width and height of the chart to 8 and 6 inches, respectively. Adjust these values according to your requirements.
By increasing the size, the chart will have more space to fit all the points without any being dropped.
How to deal with NaN values causing dropped points in Matplotlib?
To deal with NaN values causing dropped points in Matplotlib, you can follow these steps:
1. Import the necessary libraries:
1 import matplotlib.pyplot as plt
2 import numpy as np
1. Generate some random data with NaN values:
1 x = np.linspace(0, 10, 100)
2 y = np.sin(x) + np.random.normal(0, 0.2, 100)
3 y[20] = np.nan
4 y[40] = np.nan
1. Create a mask to identify the NaN values:
1. Plot the data using the mask to exclude NaN values:
1 plt.plot(x[mask], y[mask], 'o')
2 plt.show()
By applying the mask, the NaN values are excluded from the plot, and only the valid data points are visualized.
How to adjust the spacing between points to prevent dropping in Matplotlib?
To adjust the spacing between points in Matplotlib and prevent dropping, you can use the plt.subplots_adjust() function to modify the subplot's parameters. Here's an example of how you can adjust the
1 import matplotlib.pyplot as plt
3 # Create a figure and axis
4 fig, ax = plt.subplots()
6 # Plot your data
7 x = [1, 2, 3, 4, 5]
8 y = [1, 4, 3, 7, 6]
9 plt.plot(x, y, marker='o')
11 # Adjust the spacing between points
12 plt.subplots_adjust(bottom=0.1, top=0.9) # Adjust the bottom and top margins as needed
14 # Show the plot
15 plt.show()
In the example above, the plt.subplots_adjust() function is used to adjust the bottom and top margins of the plot. By modifying the bottom and top parameters, you can control the amount of space
between points and the plot's edges.
Feel free to adjust the values of bottom and top to achieve the desired spacing for your plot. | {"url":"https://topminisite.com/blog/how-to-prevent-matplotlib-from-dropping-points","timestamp":"2024-11-06T14:39:18Z","content_type":"text/html","content_length":"428651","record_id":"<urn:uuid:d40eb4e8-256f-4a86-af06-2f15e7f2c439>","cc-path":"CC-MAIN-2024-46/segments/1730477027932.70/warc/CC-MAIN-20241106132104-20241106162104-00615.warc.gz"} |
Greedy Algorithms: A Deep Dive
Learn what greedy algorithms are and when to use them.
Greedy algorithms
Greedy is an algorithmic paradigm in which the solution is built piece by piece. The next piece that offers the most obvious and immediate benefit is chosen. The greedy approach will always make the
choice that will maximize the profit and minimize the cost at any given point. It means that a locally optimal choice is made in the hope that it will lead to a globally optimal solution.
A real life example
Suppose you just got a new piggy bank to save some money for your college admission. The bank is small and can only contain a fixed weight. Each item can only be added once. You’ve got to be smart
and choose the maximum value vs. weight ratio for putting anything into it.
This is also called the fractional knapsack problem. The local optimal strategy is to choose the item with the maximum value vs. weight ratio. This strategy also leads to a globally optimal solution
because we are allowed to take fractions of an item.
Level up your interview prep. Join Educative to access 80+ hands-on prep courses. | {"url":"https://www.educative.io/courses/algorithms-for-coding-interviews-in-csharp/greedy-algorithms-a-deep-dive","timestamp":"2024-11-14T15:29:16Z","content_type":"text/html","content_length":"776127","record_id":"<urn:uuid:84daaa29-3298-4087-91f0-c17fbaf9a89f>","cc-path":"CC-MAIN-2024-46/segments/1730477028657.76/warc/CC-MAIN-20241114130448-20241114160448-00191.warc.gz"} |
How does Simulink determine step size?
If the model specifies one or more periodic sample times, Simulink chooses a step size equal to the greatest common divisor of the specified sample times. This step size, known as the fundamental
sample time of the model, ensures that the solver will take a step at every sample time defined by the model.
How does Matlab calculate step size?
Determine Step Size
1. To open the reference model, at the MATLAB® command prompt, enter:
2. Simulate the model:
3. Create a semilogarithmic plot that shows how the step size for the solver varies during the simulation.
4. To see different post-zero-crossing behaviors, zoom to the region in the red box at time (t) = ~1 second.
What is the difference between fixed step size and sample time?
A fixed-step solver sets the simulation step size equal to the fundamental sample time of the discrete system. In contrast, a variable-step solver varies the step size to equal the distance between
actual sample time hits. The following diagram illustrates the difference between a fixed-step and a variable-step solver.
What is sample time in Simulink?
In engineering, sample time refers to the rate at which a discrete system samples its inputs. Simulink allows you to model single-rate and multirate discrete systems and hybrid continuous-discrete
systems through the appropriate setting of block sample times that control the rate of block execution (calculations).
What happens if step size is too small?
However, if the step size is too small, the simulation can take too long time. In many cases, too small step size implies that the model has some problem in it, so solver stops the simulation and
reports this error.
What is used to calculate the step size?
The quantization step size is calculated as. Δ = 5 − − 5 2 3 − 1 = 1.43 V . e q = x q − x = − 4.28 − − 3.6 = − 0.69 V . e q = 0 − 0.5 = − 0.5 V .
What is step size in numerical methods?
In mathematics numerical analysis, an adaptive step size is used in some methods for the numerical solution of ordinary differential equations (including the special case of numerical integration) in
order to control the errors of the method and to ensure stability properties such as A-stability.
What is a normal step length?
An average person has a stride length of approximately 2.1 to 2.5 feet.
How does Simulink® calculate the maximum step size of a model?
If the stop time equals the start time or is inf, Simulink ® chooses 0.2 seconds as the maximum step size. Otherwise, it sets the maximum step size to. For Sine and Signal Generator source blocks,
Simulink calculates the max step size using this heuristic: where is the maximum frequency (Hz) of these blocks in the model.
How do I run a Simulink model from a MATLAB M-file?
Tutorial: Running Simulink from a MATLAB M-file Getting started Set up a Simulink file to solve the ODE given by 1.5y&+y =3u, where y(0) = −2 and u(t) is a unit step input. Save the model under the
filename first_order.mdl. Your simulation file should look like: Every time you make a change to a MATLAB M-file or a Simulink model file,
How to run Simulink simulation for time interval 0 ≤ T ≤ 20?
In the M-file, add a new argument to the sim command. The bracketed expression [0 20] tells Simulink to run the simulation for the time interval 0 ≤ t ≤ 20. The M-file should now look like: % M-file
to run Simulink file clear; y0 = -3; tau = 2; A = 4; sim(‘first_order’,[0 20]); % last line The solution should look as follows.
What is the maximum step size (tsmax) for a simulation?
The maximum step size ( Tsmax ) for obtaining accurate real-time results for the original model is approximately 1e-2 seconds. For information on determining Tsmax , see Determine Step Size. Plot the
simulation results. | {"url":"https://www.bloodraynebetrayal.com/suzanna-escobar/articles/how-does-simulink-determine-step-size/","timestamp":"2024-11-02T15:26:40Z","content_type":"text/html","content_length":"100556","record_id":"<urn:uuid:5f6faa72-8ab8-4ea1-b94a-1e542aa9b5fb>","cc-path":"CC-MAIN-2024-46/segments/1730477027714.37/warc/CC-MAIN-20241102133748-20241102163748-00110.warc.gz"} |
I know that a lot of very knowledgeable people read this blog. And, just because I disagree with some readers/commentors doesn't mean that I don't think they aren't knowledgeable. (How's that for a
triple negative?)
In any event, I'd like to know what you think are decent standardized tests for academic subjects such as reading and math. I'm especially interested in hearing your opinions on testing the various
aspects of reading ability.
What tests are good for measuring the mechanics of reading, such as decoding ability, vocabulary knowledge and fluency? Are there any reliable tests. how about the end-product of reading instruction
-- reading comprehension?
What about math? What's a good test for skills students should possess at the end of elementary school and/or to see if they are ready for algebra?
What about tests for history, geography, science?
Be sure to list the tests' weaknesses along with the advantages.
10 comments:
As a private math tutor, I do not create tests. I create problems to gauge the imagination and creativity of my students. Can they "see through a problem" rather than simply attempt to apply the
formulas and equations they have been taught to memorize in dull, dull school? Can they find a solution by looking at the problem from different angles? Can they combine observation, logic and
math to find a path to the soultion?
Here is one of my favorites: Given a strip of paper about one inch wide and precisely 12 inches long. Using nothing but a pair of scissors, cut a length that is exactly 7.5 inches long. Remember,
you cannot use any other device or tool except for the scissors. No guessing or estimating allowed.
I'll post the answer later if you or your readers get stuck.
Fold the paper in half 3 times. Count 5 folds. Cut.
How would you get them to solve a problem like "The positions of a particle and a thin (treat it as being as thin as a line) rocket of length 0.280 m are specified by means of Cartesian
coordinates. At time 0 the particle is at the origin and is moving on a horizontal surface at 23.0 m/s at 51.0°. It has a constant acceleration of 2.43 m/s2 in the +y direction. At time 0 the
rocket is at rest and it extends from (−.280 m, 50.0 m) to (0, 50.0 m), but, it has a constant acceleration in the +x direction. What must the acceleration of the rocket be in order for the
particle to hit the rocket?" whchis more along the lines of what they'll be doing in any half-decent physics class.
There are many reliable standardized achievement tests, but the underlying theory by which the tests are developed (Item Response Theory) precludes their instructional sensitivity. IRT is complex
statistically, but the logic is simple;it derives from the
days of yesteryear when psychologists viewed matters in terms of “traits and factors.” IRT is a means of generating a scale that reflects a “latent trait.” The “trait” is defined only by the
test. The scale can be “chopped up” into “grade levels” and into chunks termed degrees of “proficiency,” but the “grade levels” are ungrounded and the degrees of “proficiency” are nothing more
than cut-scores on what has been forced into a normal distribution.
The thing is,instruction isn’t a matter of “latent traits.” it’s a matter of effecting specified performance capabilities. Prior to instruction, the student “can’t do it;” “scores” pile up at the
bottom. Effective instruction enables specified capability; “scores” pile up at the top. IRT precludes either distribution, because items that students flunk and items that students ace are both
thrown out. The “normal curve” inherent to IRT is operationally a function of what students have had an opportunity to learn. That gets you up to the mean of the normal distribution. The downward
slope of the bell-shaped curve is a function of what only some students have had an opportunity to learn. The test is sensitive to socioeconomic status, but not to effective instruction.
So what’s the alternative? In reading, the aspired aspiration is for a student to read any English text with understanding equal to that were the communication spoken. When this has been
accomplished, no further formal instruction in reading per se is required. The student can then use the capability to acquire other capabilities—“read to learn.” Aggregate children entering
school have a more-than-adequate spoken lexicon to make reading instruction feasible without burdening the task with terms and concepts they don’t understand in spoken communication. Confounding
reading instruction and testing with such terms and concepts (under the banner of “comprehension”)is instuctionally unjustifiable.
It’s a simple matter to determine if a kid can read. Put a text in front of the kid’s face and say: “Read this and tell me what it says.” Instructional and testing matters arise only when the
kiddo can’t read. The instruction, not the kid, should be the focus of the tests involved. This is what we do in every area of life other than “school.” We don’t hold the “end-user” “accountable”
for the effectiveness of a“treatment/product.”
Constructing useful indicators of instructional accomplishments is very straightforward. The relevant literature of “business intelligence,” “key performance indicators,” and “executive
dashboards” is unknown in EdLand, but it is commonplace in the Corporate World. All that’s required is to specify 5-9 successive indicators that mark the trajectory from beginning to end. In the
Corporate World the bottom line is typically a “sale.” In EdLand it’s a specified instructional enablement (or a specified societal service such as feeding kids, providing the first line of
health screening , and such that are important societal benefits but that go unrecognized.)
The 5-9 Key Performance Indicators constitute a Guttman Scale; such scales have a very respectable psychometric lineage extending back to Binet’s “intelligence test.” With Key Performance
Indicators marking the instructional trajectory in hand, dynamic Executive Dashboards that reflect the instructional status of students, aggregated by teacher, school, district, and biosocial
categories of interest are feasible without any artificial or intrusive “testing.” The “results” are transparent and can be verified “with one’s own eyes,” rather than by chasing “numbers in the
air.” Prototype Executive Dashboards for Instructional Accomplishments and for Societal Services can be accessed at www.3RsPlus.net .
The task of generating Key Performance Indicators for Instructional Accomplishments is complicated only by the fact that few instructional “programs” have the structure and substance to deliver
specified aspired instructional aspirations. Fortunately, DI Reading Mastery does have the requisite elements to make Key Performance Indicators and Executive Dashboards a feasible endeavor. All
that is required is a “thinking cap.” As a matter of fact, one could even do the necessary thinking without a cap.
It’s possible that there’s another way to get a handle on instruction, but the route sketched here has proven widely applicable outside of education and appears equally applicable to instruction.
The same logic is applicable to “math” and to other instructional matters. Tests for some “subjects” such as “history,” “geography,” require thinking what about what should reasonably be “in the
kid’s head” and what is reasonable to “look up on demand.” The advent of the Internet changes balance.
The sketch here has gone fast. Googling for any of the technical terms will generate a Wikipedia link and more additional information than anyone will need to follow the logic. The logic is a far
cry from prevailing instructional testing practices, but it is much simpler, unobtrusive, and to the point.
Dick Schutz
Good job, Ken. I hope you saw the subtle features en route to the answer that evade most grade schoolers. From my experience, about one in twenty will solve this problem.
Kids are conditioned to think that rulers are used to measure inches, not fractions of feet. They are conditioned to think rulers are structurally rigid measuring tools and overlook that a
flexible, unmarked strip of paper can be made into a ruler that measures fractions of feet by merely folding it.
But most interestingly, when they examine the uniqueness of the "seven and one half", if it is expressed as a decimal (7.5) they rarely discover that by using complex fractions, it is also 5/8 of
a foot. If the number is expressed as 7 1/2, they are a little more likely (but not much more) to get to the 5/8 since they apparently see that fractional 1/2.
It's a simple, somewhat trivial problem...but it illustrates even at such young tender ages, conventional math instruction gets kids locked into one way of thinking about things thereby causing
them to lose the flexibility they need to solve problems.
I agree that flexibilty of knowledge is what is needed and I think that most elementary school children lack this flexibility, not necessarily due to what or how they are tuaght, but rather that
they have not practiced math sufficiently yet to gain that flexibility.
I probably could not have solved this problem as a child, and certainly not in the five seconds it took me as an adult. As an adult having gone through the rigors of engineering school I have a
certain amount of flexibility in basic math up to algebra one, because I was forced to use that math in solving thousands of math problems from age 5 to 23.
As a private math tutor, I do not create tests. I create problems to gauge the imagination and creativity of my students.
This is appropriate if you want to test the imagination and creativity of your students.
However, if you want to test something else, like have they learnt a specific technique, then a different sort of test is needed. For example, if you want to know if they have learnt the Order of
Operations correctly, then testing their imagination and creativity won't help.
Now...about that physics problem.
For starters, I would get the student to recast the problem in terms they could understand. In this case. drawing a Cartesian co-ordinate grahical diagram would be very helpful.
At time zero, the "particle" is at the origin (0,0). The "rocket" is 50.0 meters above the "particle" with its nose at the coordintes (0, 50.0 meters) and its tail at (-.280 meters, 50.0 meters).
(By the way, a rocket 0.280 meters long? An 11-inch long rocket?
And by the way #2...a "thin line"? A line has no thickness. It is a path of points. Only our pencils give it thickness.)
At the same moment, 1)the "rocket" begins to move horizontally at an unknown but constant acceleration and 2)the "particle" is launched on a 51 degree trajectory at a velocity of 23.0 meters per
second whose vertical component of acceleration is a constant 2.43 meters per second per second.
Next, I would have the student rephrase the question in terms that they understand.
In this case, what must the acceleration of the "rocket" be so that its nose and the "particle" occupy the same co-ordinates (the "rocket" hits the "particle")at the same time?
We already know the y-coordinate of both the "rocket" and the "particle" at impact is 50 meters.
So the question reduces itself to what must be the acceleration of the "rocket" so that its nose and the "particle" have the same coordinates (unknown but same number of meters,50.0 meters)at the
same time?
Lastly, I'm afraid I'm not much of a physicist. So the student would be on his own to use the applicable relationships of velocity and acceleration to solve the problem.
But the initial strategy I described...re-phrase the problem and re-state the question...both in understandable terms...I believe would go a long way in helping the student solve the problem.
Good start.
The only physics you need to know is the distance formula (distance = initial distance + initial velocity x time + 0.5 x acceleration x time^2) and how to decompe a vector into xa nd y
components, which I think is taught in algebra.
The rest is algebra I, trig, and basic math.
Here's a post I did on this problem back in 2006.
Tracy...what you say is quite true. If a student doesn't know the Order of Operations, no amount of imagination will replace teaching it and then checking to see if the student learned it.
However, because I have the luxury of one-to-one relationships with my kids (not one-to-twenty like in a classroom), I can not only teach math, more importantly, I can show them how to
think...how to combine observation, logic and math tools to solve problems. This is where that "paper strip" problem fits in.
At least, this is what I try to do. It doesn't always work out, but when it does...it's something to behold.
However, because I have the luxury of one-to-one relationships with my kids (not one-to-twenty like in a classroom), I can not only teach math, more importantly, I can show them how to
think...how to combine observation, logic and math tools to solve problems.
I don't think that this sort of teaching is confined to one-to-one teaching relationships. I went through engineering school, where we were taught this en masse.
The course consisted of a combination of lectures, labs and assignments, cumulating in a year-long project in the final year (we also had standard courses and exams then). The lectures taught us
the basic skills and conventions, and also had some explicit teaching in problem-solving techniques, such as how to design a testing programme, likely sources of faults, how to design a product
process, etc. The labs and assignments got more and more complicated.
Of course a lot of the work was learning solutions that had been previously developed. But once those solutions are in your head, you can then apply them to new situations. | {"url":"https://d-edreckoning.blogspot.com/2008/04/tests.html?showComment=1208360520000","timestamp":"2024-11-13T08:35:25Z","content_type":"text/html","content_length":"95120","record_id":"<urn:uuid:2f4a0982-1f0a-47ef-b327-ce334d787011>","cc-path":"CC-MAIN-2024-46/segments/1730477028342.51/warc/CC-MAIN-20241113071746-20241113101746-00163.warc.gz"} |
Step 5: Solution
These instructions are for FLUENT 6.3.26. Click here for instructions for FLUENT 12.
Now we will set the solve settings for this problem and then iterate through and actually solve it.
Solve > Control > Solution
We'll just use the defaults. Note that a second-order discretization scheme will be used. Click OK.
Set Initial Guess
Main Menu > Solve > Initialize > Initialize...
As you may recall from the previous tutorials, this is where we set the initial guess values for the iterative solution. We'll set these values to be the ones at the inlet. Select inlet under Compute
Click Init. The above values of pressure, velocity and temperature are now assigned to each cell in the grid. This completes the initialization. Close the window.
Set Convergence Criteria
FLUENT reports a residual for each governing equation being solved. The residual is a measure of how well the current solution satisfies the discrete form of each governing equation. We'll iterate
the solution until the residual for each equation falls below 1e-6.
Main Menu > Solve > Monitors > Residual...
Change the residual under Convergence Criterion for continuity, x-velocity, y-velocity and energy to 1e-6.
Also, under Options, select Plot. This will plot the residuals in the graphics window as they are calculated.
Click OK.
Iterate Until Convergence
Main Menu > Solve > Iterate...
In the Iterate Window that comes up, change the Number of Iterations to 500. Click Iterate.
The residuals for each iteration is printed out as well as plotted in the graphics window as they are calculated.
Save case and data after you have obtained a converged solution.
Go to Step 6: Results
See and rate the complete Learning Module | {"url":"https://confluence.cornell.edu/pages/diffpagesbyversion.action?pageId=90741048&selectedPageVersions=22&selectedPageVersions=23","timestamp":"2024-11-05T05:54:16Z","content_type":"text/html","content_length":"68869","record_id":"<urn:uuid:4e40d5a4-a30d-412a-a109-47f59c06bff9>","cc-path":"CC-MAIN-2024-46/segments/1730477027871.46/warc/CC-MAIN-20241105052136-20241105082136-00207.warc.gz"} |
Postulates in Geometry
Learn Basic Postulates in Geometry with Our Experts
Recent questions in Postulates
Learning the basic postulates of Geometry is something that you will have to return to, especially if you’re dealing with design and engineering disciplines. Since most of these questions are learned
at school, it is helpful when you are looking through the equations, graphs, coordination systems, and more. If you need a more complex postulates geometry explanation, you have to proceed with the
simple answers first and then choose something more specific. It’s the safest way to learn more complex things when you know the main postulates first. Start with the equations, look at the graphs,
and you’ll get it. | {"url":"https://plainmath.org/secondary/geometry/elementary-geometry/postulates","timestamp":"2024-11-04T11:15:29Z","content_type":"text/html","content_length":"230460","record_id":"<urn:uuid:13de9250-e426-43ae-9bff-3ad4979e99ff>","cc-path":"CC-MAIN-2024-46/segments/1730477027821.39/warc/CC-MAIN-20241104100555-20241104130555-00615.warc.gz"} |
Parallel Circuit (Meaning and Explanation)
Parallel Circuit
We explain what a parallel circuit is and the formulas it uses. Also, some examples and what a series circuit is.
Parallel circuits are used in the electrical network of all homes.
What is a parallel circuit?
When we talk about a parallel circuit or a parallel connection, we refer to a connection of electrical devices (such as coils, generators, resistors, capacitors, etc.) placed in such a way that both
the input terminals or terminals of each one, and their output terminals, coincide each other.
The parallel circuit is the model used in the electrical network of all homes so that all loads have the same voltage. If we understand it using the metaphor of a water pipe, we would have two liquid
tanks that are filled simultaneously from a common inlet, and emptied in the same way through a shared drain.
This type of circuits allow one connection or device to be repaired without affecting the others, and also maintains the exact same voltage between all devices despite the fact that the more devices
there are, the more current the electrical source must generate. Furthermore, the resistance obtained in this way is less than the sum of the resistances of the complete circuit: the more receptors,
the less resistance.
The great advantage of parallel circuits is this: the independence of each station in the network, whose possible failure would not alter in any way the potential difference at the ends of the
circuit. This is its main difference in use with series circuits.
Formulas for a parallel circuit
The total values of a parallel circuit are obtained by simple addition. The formulas for this are the following:
• Intensity It = I1 + I2 + I3 … +In
• Resistances. 1/RT = 1/R1 + 1/R2 + 1/ R3… +1/ Rn
• Capacitors. Ct = C1 + C2 + C3 … + Cn
Parallel circuit example
Each bulb has its own power supply line.
A perfect example of a parallel circuit is a lamp that has several bulbs on at the same time. In the event that one of these bulbs burns out and stops operating, the electrical flow will not be
interrupted to the other bulbs, which will continue to shine. This is because each one has its own parallel power supply line.
The same thing happens with the electrical wiring in our homes: that's why we can have a damaged socket and use the next one on the wall, or have a burned-out lamp in the living room and be able to
turn on the one in the bedroom, for example.
series circuit
Series circuits have a single path for electricity.
Unlike parallel circuits, designed to maintain flow upon device failure, Series circuits present a single path for electricity to and from the source so a failure in the transmission chain would lead
to the interruption of the electrical flow. Of course: at any point in the circuit the current will always be the same, but the resistance increases with each additional device connected to the | {"url":"https://meaningss.com/parallel-circuit/","timestamp":"2024-11-13T11:24:33Z","content_type":"text/html","content_length":"86990","record_id":"<urn:uuid:2edf1cb3-d169-459f-b5bb-82db45e038b8>","cc-path":"CC-MAIN-2024-46/segments/1730477028347.28/warc/CC-MAIN-20241113103539-20241113133539-00677.warc.gz"} |
The most interesting schemes of knitting the pattern "Wave"
Knitting patterns for the pattern “Wave” and detailed progress of work
Knitting patterns for the pattern “Wave” and detailed progress of work
Not all knitted items need to have a bottomdecorated with an elastic band. In such cases, you want to find a pattern that would not only look beautiful inside the item, but also design the edge in an
original and logical way. A wavy knitting pattern is ideal for such products. In fact, there are many variations of waves; let’s look at the drawing in detail, and several more schemes with similar
Relief Wave
This delicate ornament is ideal forAny product: from stole to cardigan. Most effectively, such waves "fall" from mohair yarn. The thing turns out very warm, but weightless and airy. Also, knitting
can be done from any thin or medium thickness of the thread, for example, cotton or half wool.
To delicate patterns read more clearly, you can take the needles one-and-a-half the size of what is recommended for the selected yarn.
Rapport is the number of loops that is a multiple of 11+ 2 edges, 14 rows high. For the sample, we will cast on 24 loops on the knitting needles. In the first, and in all subsequent rows, we knit the
first edge knit, the last one purl. Next, two loops (further in the text the designation P is introduced) together behind the back wall, or with an inclination to the left side, then there are 3
front loops (further designated LP), yarn over (further designated N), 1 LP, N, again 3 LP , the rapport is completed by two Ps together behind the front wall, that is, with an inclination to the
right side.
This is what rapport looks like.
Continue knitting rapport first with two P with a slope to the left and continue in the same way to the edgeband. The second knit with the wrong loops (symbol PI).
We knit R 3, 5, 7, 9 in the same way as the first. R 2, 4, 6, 8, 10 as the second. In the eleventh row, after the front edge, we knit only IP. 12 R – only medicinal products. 13 R – IP. 14 R – LP.
We continue the drawing from the first P, alternating openwork and relief elements.
Two-color waves with loops
This wavy pattern can be made with knitting needles of the same color, but more effectively it looks from yarn of contrasting colors.
The rapport consists of 10 loops + 6 for the symmetry of the pattern + 2 edges. In order to get a sample, we will dial 28 loops.
Performing any patterns, it is recommended to startFrom the sample to correctly calculate the number of loops and see how the ornament will look in the finished product. In the first R. we will bind
P faceplates. In the same way we will bind the second R.
In the third R.we knit: remove the edge, then 6 LP, N, LP, now two yarn overs, again LP, 3 yarn overs, LP, 2 N, LP, N, LP, 5 LP. In the fourth R. we will knit only the LP, bypassing the yarn overs,
that is, we insert the knitting needle only into the loops of the previous row. At the same time, we also lower the yarn overs from the knitting needle.
When we stretch the fabric a little, we get this wave. The fifth and sixth R. again LP. We switch to a thread of a contrasting color, or continue knitting with the same yarn. Let's knit two rows of
And now we repeat the third and fourth R.
Wavy patterns
I propose some more schemes on which the openwork waves are shown. So, the scheme 1:
This is a very simple ornament, which even beginner needlewomen can perform. The rapport of this wave is thirteen loops and six rows in height:
• 1 P - At the beginning of the first P. We do a broach (hereinafter we introduce the notation of the prostate), now nine LPs, and two II simultaneously. When we are tying two eyelets together in
each row one above the other, the product begins to acquire the desired "wavy" relief;
• 2 R - PI;
• 3 P - We start again from the broach, then 7 LP, two at the same time LP;
• 4 R - IP;
• 5 Р - ПЖ, after alternating ЛП and Н, at the end of rapport again we knit two together ЛП;
• 6 Р - we finish the rapport of the drawing next to the LP. Continue to follow the pattern, from the very beginning, to the desired height.
The next pattern is fantasy; the pattern for this interesting ornament is a little more complicated. To avoid confusion, let's look at it in more detail. So, scheme 2:
• 1-4 Р - we knit the LP;
• 5 Р - begin R. With LP, after we make H, after 3 LP, three P vm. (We remove 2 П on the right knitting needle, we leave a thread behind a cloth, third Вяжем ЛП, and we "throw" the first two П on
the knitted), again we will make 3 LP, N, we finish LP;
• 6 Р - from the beginning there are 2 ИП, then Н, again 2 ИП, three Пмм. IP (we interchange the first two P, and then we knit all three of them IP), we will bind 2 IP, N, at the end again 2 IP;
• 7 Р - 3 ЛП, then Н, 1 ЛП, three вм., As in the fifth Р., 1 more ЛП, we do Н, we finish with three LP;
• 8 Р - in the beginning two ИП, 2 LP, we do Н, 3 вм., As in the sixth Р, Н, 2 LP, at the end of 2 IP;
• 9 Р - 1 ЛП, after Н, now we will make a broach, 1 ИП, Н, 3-и simultaneously, Н, ИП, two вм. LP, H, we finish 1 LP;
• 10 Р - begin with 3 purl П, ЛП, 3 more ИП, again ЛП, 3 ИП;
• 11 Р - two LPs, then Н, we make one ПЖ, Н, 3 вм., Н, 2 вм., Again we will make Н, in the end 2 ЛП .;
• 12 Р - only loops on the right;
• 13 Р - we will connect two ЛП, ИП, then a face loop, Н, 3 вм., We will make Н, ЛП, 1 ИП, 2 LP;
• 14 Р - 2 ИП, we make 1 ЛП, then five ИП, 1 ЛП, we will finish with two back loops;
• 15 Р - see 13 Р .;
• 16 Р - see 14 R.
Another scheme to a very original wavy pattern. Such openwork patterns decorate any product.
I would like to note that each of the proposedornaments can be knitted on circular knitting needles, respectively, in a circle. For this type of work, read the diagram in one direction only, from
right to left. In a circle with such waves you can make a hat, pencil skirt, dress and other products that can be knitted without seams according to pattern 3:
• 1 Р-5 Р - Only LP. On empty cells do not pay attention, just knit further according to the scheme. The ornament starts with a simple smooth surface;
• 6 Р - All purl loops;
• 7 P - only facial;
• 8 Р - purl loops. After a small segment of the facial smoothness, we proceed to the drawing of the figure with the waves;
• 9 Р - two П together with LP, then 8 ЛП, we make Н, a face loop, still Н, eight ЛП, we finish with broach;
• 10 Р - 2 П вм., We will fasten 17 ИП, we will finish ПЖ;
• 11 Р - two П Пм., 6 ЛП, we make H, ЛП, again Н, ЛП, one Н, ЛП, Н, six ЛП, we finish ПЖ;
• 12 Р - we knit is identical to 10 Р .;
• 13 Р - we begin with 2 Пмм., Now 4 LP, then we alternate eight накидов with seven LP, now 4 LP, we finish with broaching;
• 14 Р - 2 П вм., 21 ИП, we will make PZH;
• 15 Р-2 П вм., 2 Пмм., Н, once again 2 Пмм., We make накид, 2 П вм., Н, two Пмм., Н, 3 ЛП, Н, drawing, Н, ПЖ, H, P, H, R, and one more RV at the end;
• 16 Р - knitting is identical to 8 Р .;
• 17 Р - all LP;
• 18 Р - again we look at 8 Р .;
• 19 Р - we start by doing stretching, now 2 LP, H, PZ, 2 LP, H, PZ, LP, PZ, H, 2 LP, H, PZ, again two LPs, at the end of H;
• 20 R - see the eighth R .;
• 21 R - LP, H, PZ, two LPs, a cape, a PZ, now three LP, we make H, PZ, 2 LP, H, PZ, again 2 LP, H, PZ, complete facial P;
• 22 Р- and again look at the eighth P.
Carefully follow the diagrams, and everything will turn out. Pleasant needlework!
Video: Ways of knitting a wave pattern with knitting needles
Selection of schemes for knitting the pattern "Wave" | {"url":"https://handmadebase.com/schema-for-knitting-pattern-and-wave-undermining/","timestamp":"2024-11-04T14:21:53Z","content_type":"text/html","content_length":"74188","record_id":"<urn:uuid:92ff2245-8bec-40ab-85c1-0e9523976b5e>","cc-path":"CC-MAIN-2024-46/segments/1730477027829.31/warc/CC-MAIN-20241104131715-20241104161715-00112.warc.gz"} |
Fuzzy independence and extended conditional probability
In many applications, the use of Bayesian probability theory is problematical. Information needed to feasibility calculate is unavailable. There are different methodologies for dealing with this
problem, e.g., maximal entropy and Dempster-Shafer Theory. If one can make independence assumptions, many of the problems disappear, and in fact, this is often the method of choice even when it is
obviously, incorrect. The notion of independence is a 0-1 concept, which implies that human guesses about its validity will not lead to robust systems. In this paper, we propose a fuzzy formulation
of this concept. It should lend itself to probabilistic updating formulas by allowing heuristic estimation of the "degree of independence." We show how this can be applied to compute a new notion of
conditional probability (we call this "extended conditional probability"). Given information, one typically has the choice of full conditioning (standard dependence) or ignoring the information
(standard independence). We list some desiderata for the extension of this to allowing degree of conditioning. We then show how our formulation of degree of independence leads to a formula fulfilling
these desiderata. After describing this formula, we show how this compares with other possible formulations of parameterized independence. In particular, we compare it to a linear interpolant, a
higher power of a linear interpolant, and to a notion originally presented by Hummel and Manevitz [Tenth Int. Joint Conf. on Artificial Intelligence, 1987]. Interestingly, it turns out that a
transformation of the Hummel-Manevitz method and our "fuzzy" method are close approximations of each other. Two examples illustrate how fuzzy independence and extended conditional probability might
be applied. The first shows how linguistic probabilities result from treating fuzzy independence as a linguistic variable. The second is an industrial example of troubleshooting on the shop floor.
ASJC Scopus subject areas
• Software
• Control and Systems Engineering
• Theoretical Computer Science
• Computer Science Applications
• Information Systems and Management
• Artificial Intelligence
Dive into the research topics of 'Fuzzy independence and extended conditional probability'. Together they form a unique fingerprint. | {"url":"https://cris.haifa.ac.il/en/publications/fuzzy-independence-and-extended-conditional-probability-2","timestamp":"2024-11-01T23:15:09Z","content_type":"text/html","content_length":"56775","record_id":"<urn:uuid:dd7035eb-5a67-42ca-ade1-e1749bcca3d3>","cc-path":"CC-MAIN-2024-46/segments/1730477027599.25/warc/CC-MAIN-20241101215119-20241102005119-00317.warc.gz"} |
Form the Partial differential equation by eliminating the arbitrary function for the equation z = f (x^2 + y^2)
Form the Partial differential equation by eliminating the arbitrary function for the equation z = f (x^2 + y^2)
Partial Differentiation Equation (PDE) – Part I
Partial Differentiation Equation (PDE) – Part II
Partial Differentiation Equation Problems
Share this content | {"url":"https://www.yawin.in/form-the-partial-differential-equation-by-eliminating-the-arbitrary-function-for-the-equation-z-f-x2-y2/","timestamp":"2024-11-04T20:38:01Z","content_type":"text/html","content_length":"86693","record_id":"<urn:uuid:3fdeec04-f015-4eaa-8f1e-6625ecb0064a>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.16/warc/CC-MAIN-20241104194528-20241104224528-00257.warc.gz"} |
Basic Electricity for Beginners
Don’t know your ohm from your elbow?
One thing that e cig beginners have said to me repeatedly is that they don’t understand what ohms and volts and watts are and why it’s useful to know about them. If you’re really not interested, the
best thing you can do is to buy a regulated setup that comes complete with battery and atomiser. It’s only when you start to use separate batteries, mods & atomisers that this stuff starts to be
important and sadly, most of the ‘exploding e-cigs’ stories come down to not understanding this stuff or ignoring battery safety. So, if this really isn’t your thang, then please only use the
charger, batteries & tank that came with your device. When charging batteries, never leave them unattended, take them off charge as soon as they are charged and only carry batteries in a battery box
. If you are interested in finding out a little more, read on.
Ohm’s Law
There are plenty of websites out there where you can learn about the physics & history behind all this if you are interested. As a vaper, you only really need to understand the principles and the
relationship. A commonly used analogy is that of a water system. It’s not perfect but it seems to help most people.
Pressure = Voltage
In a water system you can measure water pressure as the height of the column of water that it would produce. In an electrical system pressure is measured in volts. A typical e-cig battery has a
voltage of 3.7 volts. Electronic circuits are used to either stabilise this level or to increase it to a higher level.
Flow = Current
Cubic feet per second can be used to measure the flow rate of water. The electrical equivalent is Amperes. This is often shortened to ‘amps’ or just ‘A’. One thousandth of an amp is a milliamp (mA).
Capacity or flow over time = milliAmpere hours
With e-cig batteries you’ll see the capacity stated in milliAmpere hours (mAh). For example, a 2000 mAh battery should be able to deliver 2 amps for one hour, one amp for two hours or 200mA for 10
Restriction = Resistance
In a water system, where there is a restriction in a pipe, the flow of water is impeded. The electrical equivalent of this is resistance and it’s measured in ohms. In an atomiser, the coil is
often made from special alloys, such as iron, chromium and aluminium. These produce heat because of their resistance.
Resistance and Ohm’s law
In the picture below, you can see the relationship between current flow & resistance by moving the slider to change resistance in the circuit. With the slider at the right, its resistance is zero and
when its at the left resistance is infinity.
As the resistance of the slider decreases, the flow of current increases & the lamp begins to light-up. As the slider resistance increases, the flow of current becomes lower & the lamp dims. In this
example, the voltage has remained constant and changing the resistance changed the current.
In fact, there is a simple equation that describes the relationship:
Voltage = Current X Resistance and this is usually written as V = I x R
In an e-cig, the resistance is more or less fixed (resistance does actually change a little as the coil heats), so we need to rearrange the formula to make it more use to us as vapers. So
re-arranging it, we get:
Resistance = Voltage divided by Current or R = V/I
Current = Voltage divided by Resistance or I = V/R
So, if we know the voltage and the resistance, we can calculate the current and if we know the voltage and current, we can calculate the resistance.
Suppose our atomiser has a resistance of 2 ohms (this is often marked as 2Ω) and our battery has a voltage of 3.6 volts. We can calculate the current flowing:
3.6/2 = 1.8 Amps
If our atomiser had a resistance of 1Ω and the voltage was 3.6 volts, our current would be:
3.6/1 = 3.6 Amps
We’ve seen the relationship between voltage, current and resistance above but there is another factor that vapers need to understand. That is power. It is measured in watts and is the product of
current and voltage.
Power = Voltage x Current and is usually written as P = I x V
In the picture below, you can alter both the voltage delivered to the circuit and the resistance. Moving the voltage slider to the right increases voltage and moving the resistance slider to the
right increases resistance. You can see the resulting power consumed in watts at the top left.
The power equation (P = I x V) can be re-arranged just like the one for Ohm’s law, so we can derive these formulas from it:
Current = Power divided by Voltage (I = P/V) and
Voltage = Power divided by Current (V = P/I)
Using the same example as above, where our atomiser had a resistance of 2 ohms and our battery had a voltage of 3.6 volts, we calculated the current flowing to be 1.8 Amps.
Now we can calculate the power by using the new formula:
P = I x V or P = 1.8 x 3.6 = 6.48 Watts
Pulling it all together
The two simple equations enable us to solve for each of the components involved and we can also combine them together to produce some more useful formulas. The original equations and those that are
derived are shown below:
P = V² x R I = P/V R = V²/P V = √(P x R) V = I x R R = V/I I = V/R
P = I² x R I = √P/R R = P/I² V = P/I P = I x V I = P/V
How is this useful?
To be fair, understanding this sort of thing isn’t really important until you get beyond basic e-cigs. However, anyone going ‘sub-ohm’ really should have a good grasp of what they’re doing. I saw a
post on a forum some time back where someone was saying that they’d built a coil with a resistance of 0.01 ohms and they were intending to use it in a single battery mechanical mod. Now, that’s all
well and good but a few quick calculations highlight the dangers:
R = 0.01Ω
Lets say voltage = 3.7 Volts & we can calculate the current:
I = V/R so I = 3.7/0.01 = 370 Amps and Power = V x I = 3.7 x 370 = 1369 Watts
That might just lead to a hot vape for a few seconds before the battery goes into thermal runway and then explodes or hopefully, the coil or wiring disintegrates first & it stops working.
Being able to do calculations like these enables you to ensure that the battery that you’re intending to use is actually capable of delivering the current that the atomiser will draw.
I usually use a variable wattage device but if I had to use a mod that was only able to do variable voltage, I could easily and quickly set my desired power by knowing the atomiser resistance and
doing a quick calculation. For example, if my atomiser was 1.8Ω and I wanted to vape at 15 Watts, I could easily calculate the voltage using the formula above:
V = √(P x R) so Voltage = √(15 x 1.8) = 5.196 Volts and 5.2 Volts is near enough for rock n roll
Originally Published by Dave Upton 2015 – Reproduced by ocdz.co.uk with kind permission
[…] Basic Electricity for Beginners […] | {"url":"https://vapers.org.uk/e-cigs-the-facts/basic-electricity-for-beginners/","timestamp":"2024-11-06T05:25:11Z","content_type":"text/html","content_length":"93152","record_id":"<urn:uuid:4d38cc51-cb0e-4afa-9d1f-af6fbc3a58e2>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00690.warc.gz"} |
Dashed line theory | Let's prove Goldbach!
Dashed line theory
Dashed line theory is a new mathematical theory which studies the connection between the sequence of natural numbers and their divisibility relationship. Typical problems are the computation of the
$n$-th natural number divisible by at least one of $k$ fixed numbers, or not divisible by any of them. Due to this nature, the theory is suited for studying prime numbers with a constructive
approach, inspired to the sieve of Eratosthenes...
The birth of the theory was among the school desks, with the aim of creating a useful tool for the proof of the Goldbach's conjecture.
When the maths teacher of Simone, during the third year of high school, told him about the Goldbach’s conjecture, he felt the irresistible desire for understanding it deeply, in order to try to prove
it. Some classmates followed his first reasoning, but their interest didn’t come from the problem itself, but from the one million dollar prize which at that time would have been won by whoever was
able to prove it. For Simone the prize was important too, but not as much as the desire for knowing the mechanisms that conceal themselves under the simple statement of the conjecture. So his
classmates soon lost interest in that matter, while he was busy, in the next years, in developing a new mathematical theory that he believed a useful tool for the proof. He named it dashed line
But why conceiving a new theory, just for solving a specific problem? He thought that, if nobody was able to prove the conjecture yet, a reason could be the lack of the right mathematical tools. So
it was worth the effort to try with a new approach, based on a new theory.
In 2010 the theory was published for the first time in a complete form, in Italian, in the website http://teoriadeitratteggi.webnode.it, but with a very formal language, which leaves little space to
intuition. This aspect has been improved since 2018, with the birth of the Let's prove Goldbach! project, thanks to which the topics of dashed line theory have been explained in a more instructive
way, with the help of images and examples. The result are the posts listed below.
Still as a part of the Let's prove Goldbach! project, the theory was further developed, when looking for the proof of the Goldbach's conjecture. Soon we'll gather most of these developments into a
new section of this site.
As an internal reference to this section of the site, we created a list of the definitions and of the adopted symbols.
One of the open problems of dashed line theory is "characterizing" spaces, i.e. looking for a criterion that tells us when a certain column of a dashed line is a space and when it is not. Certainly,
a first characterization is the definition of space itself, but in our research we have noticed that it is sometimes useful to find alternative criteria.
One of the still open problems of dashed line theory is, given a linear dashed line $T = (p_1, p_2, \ldots p_k)$ of order $k$, finding an expression that is able to represent an upper bound for the
maximum distance between a space and the one immediately preceding it. That is, given two columns $s_1$ and $s_2$ of a dashed line, both spaces, such that $s_1 \lt s_2$, without other spaces between
them, the purpose of this investigation is finding $h$ such that $s_2 - s_1 \leq h$, for each possible pair of consecutive spaces $(s_1, s_2)$ of the dashed…
By now, the formula for calculation of $\mathrm{t\_space}$ for a linear dashed line of any order is not yet known, but, how we have seen in the section about dashed line theory, some partial results
exist, which could bring, once extended, to a general formula.
The function $\mathrm{t\_value}$, by definition, indicates which column of a dashed line a dash belongs to. For this reason, in principle, calculating this function is quite easy, because the
definition itself shows us how to do it.
Our research about Goldbach's Conjecture led us, at one point, to extend the definition of linear dashed line. As we know, a linear dashed line is a function represented by a table with $k$ rows and
infinite numbered columns starting from 1, where, in each row, a dash appears for each column whose number is a multiple of a given fixed positive integer (one of the components of the dashed line).
Sometimes it is necessary to consider tables in which the dashes appear not only in correspondence with the multiples, but also in correspondence with the numbers that have a… | {"url":"http://www.dimostriamogoldbach.it/en/dashed-line-theory-page/page/4/?doing_wp_cron=1685156155.4093561172485351562500","timestamp":"2024-11-05T16:13:17Z","content_type":"text/html","content_length":"268841","record_id":"<urn:uuid:581bed95-f9d9-47fa-9068-0d9a47040368>","cc-path":"CC-MAIN-2024-46/segments/1730477027884.62/warc/CC-MAIN-20241105145721-20241105175721-00263.warc.gz"} |
StatsExamples | One factor ANOVA introduction
ONE FACTOR ANOVA (INTRODUCTION)
Watch this space
Detailed text explanation coming soon. In the meantime, enjoy our video. The text below is a transcript of the video.
Connect with StatsExamples here
Slide 1.
The one factor ANOVA is the most common technique to see if the means of more than two populations are different from each other. In this video we'll look at the concepts behind it and how it works.
There's also a companion video on this channel that works through two step-by-step examples.
Slide 2.
We often want to compare the averages, or means, of different populations. When we have two populations, we typically do a single t-test for the pair. This usually gives us the correct answer, but it
does have a 5% chance of type I error - that is, telling us the populations have different means when they don't.
►When we have more than two populations, four for example, we would have to do six different t tests, one for each pair. These would also usually give us the correct answer, but now the overall
chance of at least one type I error rises to about 28%. This is now a more serious problem and we face a genuine risk of making the wrong conclusion.
►The problem I've illustrated is that multiple separate comparisons inflate the overall probability of type I error. We need a new test with 5% overall probability of type I error.
Slide 3.
As I mentioned, when we have just two populations we use the t-test to decide if the population means differ. When doing a t-test we compare the difference between the sample means to the combined
standard error using the equation shown there.
The bigger the t calculated value, the more likely it is that the population means differ because that indicates cases in which the difference between sample means are large relative to how different
we expect them to be based on the variation within the groups.
For more details about this idea and the t-test, watch our intro to the two sample t-test video.
Slide 4.
With the ANOVA we use the same basic concept as the t-test, comparing the overall variation in the means of the groups to the variation we would expect if it was caused only by whatever causes the
variation within the groups.
For the ANOVA we measure the variations we want to compare using variances, instead of the pure difference in means or standard errors, and then we compare these using an F test. The F calculated
value divides the variance among the groups, the measure of the variation in the means, by the variance within the groups, the measure of the variation or noise within each group.
The bigger the F calculated value, the more likely it is that the population means differ because that indicates cases in which the variance of the sample means is larger than we expect it to be
based on the variances within the groups.
Slide 5.
One aspect of the ANOVA that makes it a bit different from some other statistical tests is that the conceptual hypotheses and the actual tested hypotheses differ somewhat.
Our conceptual null and alternative hypotheses are about the means of the populations - are they all equal or do at least two differ?
But the formal hypotheses, the actual thing we will test, is about the mean sums among, MSA, and mean sums within MSW. The hypotheses ask whether the mean sums among is less than or equal to the mean
sums within or whether the mean sums among is greater than the mean sums within.
Note that while the language of the ANOVA uses the term mean sums, the MSA and MSW are actually variances.
These hypotheses are connected - the decision to reject or fail to reject the formal null hypothesis is equivalent to rejecting or failing to reject the conceptual null hypothesis.
If we accept the null hypothesis, then we lack the evidence to decide that any of the population mean differ from one another.
But if we reject the null hypothesis and decide that one or more of the population means differ, a second question then arises - which ones? We'll come back to this later.
We know we're going to do the ANOVA using an F test of the variances, but let's look at how these variances relate to each other in more detail so we can understand exactly what we'll be doing.
Mean sums are variances based on sums of squares so before we calculate the mean sum, we need to calculate three sets of sums of squares.
Slide 6.
The first sum of squares we will calculate is one using all the data regardless of which population the sample data value is from. We compare each value to the overall mean to calculate a sum of
squares total, SST.
From the figure we can see that this overall variation will be caused by two things.
When the means of the groups are more variable, as shown for the examples on the left, the overall data values will tend to also be more variable. When the means of the groups are less variable, the
overall data values will tend to be less variable.
When the values within each of the groups are more variable, as shown for the top examples, the overall data values will tend to be more variable. When the values within each of the groups are less
variable like in the lower figures, then the overall data values will tend to be less variable.
The sum of squares total value for all our data will therefore be caused by both the differences between the means of the groups and the variation within them.
Slide 7.
Focusing on the variation coming from the means of the groups we could calculate something called the sum of squares among, SSA. This is a sum of squares value that is based on the values of the
group means, compared to the overall mean of everything.
Since each of these means is based on multiple values, we will be weighing this sum of squares value by the number of values in each of the groups.
Slide 8.
Focusing on the total variation coming from the variation within the groups we could calculate something called the sum of squares within, SSW. This is a sum of squares value that is based on the
values for each group, compared to the means for each group, then all added up afterwards.
Slide 9.
Looking at these together we can see visually how the sum of squares total is due to both the sum of squares among and the sum of squares within.
►In fact, there is a mathematical proof that states that if we calculate the sums of squares the way I just described, the numerical value for the sum of squares total will be equal to the sum of the
sum of squares among and sum of squares within.
This useful mathematical property is actually the main reason why so much of statistics is done using sums of squares and variances even when these values can have serious problems as descriptive
statistics for the variation.
Slide 10.
We have a sense of our three sums of squares values and their relationship, now what?
If all the variation was just caused by random noise, then the SSA and SSW would both contribute quite a bit to the sum of squares total. How do we determine whether the differences between the
groups, the "Among" factor is larger than we expect based on the "Within" factor however?
►For this we will convert the sums of squares values into their mean sums, otherwise known as variances using these equations. The mean sum is the sum of squares divided by the degrees of freedom
►Once we have these two variances, we can use an F test to compare them and see if they differ. We could do a two-tailed F test to see if the group means are either more different than we expect or
more similar, but the second question isn't usually what we care about.
We therefore use a one-tailed F test, dividing MSA by MSW, to see whether we have evidence that the variance among the groups is significantly larger than the variance within the groups.
Now we just need the degrees of freedom values so we can do the F test.
Slide 11.
Let's consider a data table such as the one shown to the right with a column for each of "k" groups and rows for the "n" individuals within each groups.
►The degrees of freedom for the among groups variance will be the number of group means we used minus one, this is k-1.
►The degrees of freedom for the within groups variance is the number of values in each group minus one for each of the k groups. This can also be represented by capital N minus k where the capital N
is the total number of data values in the entire data set.
►The degrees of freedom for the entire data set would be capital N minus one.
►The means sums among is therefore SSA divided by k- minus one.
►The means sums within is therefore SSW divided by capital N- minus k.
►The F calculated value for our one-tailed test is MSA divided by MSW. We get this and compare it to the critical values from our F table for alpha equals 0.05 to see if the variances are
significantly different. We can use additional tables to get a more precise range for the p value of our test. A computer with statistical software can give us the exact p value if we have access to
You can watch our intro to the F-test video for more about this test if you're not familiar with it.
That's the idea, let's look at this again to see how we would actually use a data table directly.
Slide 12.
How do we get SST, SSA, and SSW from a data table?
The top figure shows what we're looking for. The rest shows a diagram of the data table, with values for each group arranged in the red columns.
To get SST we calculate the sum of squares for all data values, comparing each value to the overall mean. The purple box around all the data represents this.
This measures the overall variation - how the data values differ depending on which groups they're in, combined with the noise within each group.
You can watch our intro to summary statistics video for more about calculating sums of squares.
Slide 13.
To get SSA we first calculate the mean value for each group, these are the X bar values shown below the data table.
Then we calculate the sum of squares of these group mean values, comparing them to the overall mean, and multiplying these squares by the group sample size, n.
This measures the variation that is associated with the differences in the means of the groups. How much is the data spread out because the means of the groups are spread out?
Slide 14.
To get SSW we calculate the sum of squares values separately for each of the k groups using the group means and sum them.
This measures how much of the variation comes from variation within each of the groups. How much noise is in the data?
Slide 15.
To help keep everything organized and to present it clearly to others, data is usually presented in an ANOVA table.
The table has a column for the source of the variation, the degrees of freedom for each source, the sums of squares and mean sums values, the F calculated value and the p value that corresponds to
By convention, the sources are listed with among group variation first, followed by within group and then total on the third line.
The degrees of freedom values are the ones from before - k minus one for the among, capital N minus k for the within, and capital N minus one for the total.
The sums of squares values are entered in the next column.
The mean sums are then easy to calculate since the two values needed are on the same row already. The MSA is SSA divided by k minus one and the MSW is the SSW divided by the capital N minus k.
The F value is then just the MSA value divided by the MSW value.
Finally the p value from our F test indicates if the variances are different which corresponds to whether any of the means are significantly different.
If p is less than 0.05 then one or more means are significantly different from one or more other means.
If p is larger than 0.05 then we lack evidence to decide that any of the means are different from any of the others, we would typically conclude that they all appear to all be equal.
Note that if we fail to reject the null hypothesis, we don't prove that the means are the same, we decide that they appear equal because we looked for evidence that they differed and didn't find it.
Published tables will often omit the sums of squares column since it is easily figured out from the degrees of freedom and the mean sums columns.
That's all there to doing an ANOVA, calculating variances and doing and F test, but there are a few other things we need to be aware of.
Slide 16.
The first thing to be aware of is that the ANOVA is a homoscedastic test. The ANOVA requires equal variances to prevent one unusually variable group from overwhelming the SSW value as shown in the
For example, the gigantic variance of the red group would overwhelm the SSW term and render our F test nonsignificant even it's obvious that it should tell us there's a difference between the
smallest and largest groups.
Unequal variances can cause type II errors, that is, the failure to detect genuine differences between population means.
►A prerequisite for the ANOVA is therefore a test for equal variances such as the Fmax test. If the variances are equal, then we can do ANOVA, but if not then can't do the ANOVA. If that happens, we
have to transform the data into a new data set that has equal variances or use a less powerful alternative test like the Kruskal-Wallis test.
Slide 17.
Here's the formal procedure for the one factor ANOVA.
►First, we create our null and alternative hypotheses.
The null is that the means of the population are the same, which is equivalent to the mean sums among being less than or equal to the means sum within.
The alternative is that the means of the population are not all the same, which is equivalent to the mean sums among being greater than the means sum within. ►Then we calculate the three sums of
squares values and use the SSA and SSW to calculate the mean sums values MSA and MSW.
►Then we perform a one-tailed F test on the MSA and MSW to test whether the mean sums among is larger than the mean sums within using the F statistic calculation shown.
►We then compare the F calculated value to various F critical values - the most important being the value for an alpha value of 0.05 since that is what we typically use to reject or fail to reject
the null hypothesis of our F test.
►By using multiple tables or a computer we determine the precise p value for our test, that's the probability of seeing an F calculated value as large as we do if the null hypotheses are true.
►Then we decide to "reject the null hypothesis" or "fail to reject the null hypothesis " based on the p value.
If the p value is greater than or equal to 0.05 then we would fail to reject the null hypothesis and decide that we lack evidence to decide that any of the means are different. We would then
generally say that they're all equal. Note that we don't prove this, we're just making an informed decision.
If the p value is less than 0.05 then we would reject the null hypothesis and therefore decide that we do have good evidence to decide that some of these means are different. Again, this isn't proof,
it's an informed decision based on probability.
This procedure doesn't tell us everything that we want to know however - for one thing it doesn't tell us which means are different or not.
Slide 18.
The ANOVA procedure just described is the first step.
If the null hypothesis is accepted, that is when p is not less than 0.05, then we conclude that none of the means are significantly different from any of the others. We are done unless we want to do
a power analysis to estimate the maximum undetectable differences, but honestly this isn't done as often as it should be.
If the null hypothesis is rejected however, when p is less than 0.05, then one or more of the means are significantly different from one or more of the others. The ANOVA doesn't tell us which ones
differ, just than one or more do, but obviously this is information that we are probably really interested in.
There are two options to determine which means differ.
Slide 19.
The first option for determining which means differ is to use Bonferroni corrected t tests.
For this we go back to the original data sets and do all the possible pairwise t-tests, but with a smaller alpha value threshold, one less than 0.05, as the threshold for significance.
This is called the Bonferroni correction for the critical alpha value and we usually use a corrected alpha value equal to 0.05 divided by the number of tests we have to perform.
►For example, if we're comparing three data sets then we would do the three pairwise t-tests, but only reject the null hypothesis of equal means for a pair when the p value is less than 0.05 divided
by 3 which is 0.01666.
►If we're comparing four data sets then we would do the six pairwise t-tests, but only reject the null hypothesis of equal means for a pair when the p value is less than 0.05 divided by 6 which is
Slide 20.
The second option for determining which means differ is to use Tukey-Cramer comparison intervals.
For this we calculate a value called the MSD (minimum significant difference) also known as the HSD (honestly significant difference) and create intervals around each sample mean of 1/2 MSD above and
below their means. Non-overlapping intervals indicate differing means.
The equation to get the MSD or HSD uses a value Q which varies based on the desired alpha value, the number of groups, and the degrees of freedom of the mean sums within. The StatsExamples website
has several tables of Q values like the one shown for alpha equals 0.05.
This Q value is then multiplied by the square root of the mean sums within, divided by the sample size within each group, essentially the average standard error for the groups.
►For example, imagine that we had data which resulted in a minimum significant difference value of 6.
We would then go to each sample and put an interval of plus and minus 3, half of the six, around each mean.
If our sample means were 8, 10, and 15 we would get intervals of 5 to 11, 7 to 13, and 12 to 18.
We then compare these intervals and identify which ones overlap and which ones don't. If the intervals for two groups overlap then their population means are not significantly different, but if the
intervals don't overlap then they are significantly different.
For our example we can see that the means of populations A and B aren't significantly different, the means of populations B and C aren't significantly different, but the means of populations A and C
are significantly different.
Slide 21.
To recap. When we compare multiple groups we have a problem because the overall risk of type I error gets too high when doing multiple comparisons.
The solution is to perform an analysis of variance which is called an ANOVA.
Before we do that, we do have to keep in mind that the ANOVA is homoscedastic, so we have a prerequisite test for the equality of the population variances. Assuming the data passes that test we can
do an ANOVA.
When we do the ANOVA, we have conceptual hypotheses about the means which we test with formal hypotheses about the mean sums among and within.
We do this test by calculating the sums of squares, mean sums, and performing a one-tailed F test to see if the MSA is significantly larger than the MSW.
We typically summarize the results of our test in an ANOVA table and use the p value to reject or fail to reject our null hypothesis. This tells use whether we have evidence that some of the
population means differ or not.
If we reject the null hypothesis then we have two option to figure out which means differ - performing a series of Bonferroni correct t tests or calculating the minimum significant difference and
comparing Tukey-Cramer comparison intervals.
Zoom out.
The ANOVA is often extremely intimidating to students when they first encounter it, but I hope that this video shows that it's not a mysterious black box. Doing an ANOVA doesn't require a computer,
you can do one by hand.
As always, a high-resolution PDF of this screen is available on the StatsExample website and check out our companion video that works through two step-by-step numerical examples.
End screen.
To help others find this video, click like or subscribe.
Connect with StatsExamples here
This information is intended for the greater good; please use statistics responsibly. | {"url":"http://statsexamples.com/topic-ANOVA-one-factor-intro.html","timestamp":"2024-11-12T00:37:58Z","content_type":"text/html","content_length":"30036","record_id":"<urn:uuid:e96280a2-6ae3-4322-b290-65cce1ed5e64>","cc-path":"CC-MAIN-2024-46/segments/1730477028240.82/warc/CC-MAIN-20241111222353-20241112012353-00445.warc.gz"} |
So what are item parameters, anyway?
Item Response Theory (IRT) item parameter estimates play an important role in many of the reports generated in Galileo K-12 Online. In addition to describing item characteristics in the Item
Parameter report, they help to determine student Development Level (DL) scores and to identify the standards that are recommended for re-teaching efforts in the drill-downs from the Risk Assessment
report. But what are they?
The best way to understand what item parameters refer to is to look at an Item Characteristic Curve. On an item characteristic curve, which presents the data for one, specific item, student ability
(based on their performance on the assessment as a whole) is plotted on the horizontal axis, with a mean of 0 and a standard deviation of 1. The probability of answering the item correctly is plotted
on the vertical axis. Typically the probability of answering correctly is relatively low for low ability students and relatively high for students of higher ability.
The first example (Item #4) is an example of a great item as far as the parameters go. The b-value (difficulty) for that item was 0.689, which is a bit on the difficult side, but not too bad. The
important point here is that b-values (item difficulty) are on the same scale as student ability. So what this example is telling us is that students at or above 0.689 standard deviations above the
mean are likely to get the answer correct. Students below that point on the ability scale are more likely to answer incorrectly. The b-parameter is also known as the location parameter, because it
locates the point on the ability scale where students start demonstrating mastery of the concept.
The a-value (discrimination) refers to how well the item discriminates between different ability levels. It’s how steep the rise is in the curve that shows the probability of answering correctly.
Ideally, there is a nice, steep rise in the probability of answering correctly like the one for question 4. That indicates that there is a dramatic change in how likely it is that a student has
mastered the concept that’s pin-pointed within a very narrow range of the ability scale. You can be pretty confident that students above 0.689 standard deviations above the mean “get it” and that
students below that point generally don’t. The discrimination parameter for question 4 is 1.459.
The next example, Item 5, shows an item that doesn’t discriminate quite as well as Item 4. The a-value on that one is 0.53. It’s also a pretty easy item, with a b-value of -1.07. So, on this one,
most students are likely to get it correct, unless they’re more than one standard deviation below the mean of the ability scale.
It’s not necessarily the case that an easy item automatically has poor discrimination. The final example, Item 8, is an easy item that discriminates very well. Although students at most ability
levels are likely to select the correct answer, there is still a dramatic increase in likelihood of answering correctly within a relatively narrow range of the ability scale.
The guessing parameter (the c-value) is the probability of getting the item correct by just guessing. It defines the lower limit of the item characteristic curve. For a multiple choice item with four
answer choices, the guessing parameter should be around 0.25 or, preferably, a bit lower. | {"url":"http://townhallblog.ati-online.com/2010/01/so-what-are-item-parameters-anyway.html","timestamp":"2024-11-13T22:39:36Z","content_type":"text/html","content_length":"94324","record_id":"<urn:uuid:1eb29f93-1644-467c-a834-b6e357559d37>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00774.warc.gz"} |
Math Review 48 Area of Triangles
Find the Area:
Find the Area:
Find the Area:
Find the Area:
Find the Area:
Find the Area:
Find the Area:
Find the Area:
In right triangle ABC,
the length of BC is twice the length of AB.
What is the area of Triangle ABC?
Area of the unshaded part:
Students who took this test also took : | {"url":"https://www.thatquiz.org/tq/preview?c=kzg9oxye&s=paohva","timestamp":"2024-11-06T04:58:26Z","content_type":"text/html","content_length":"15330","record_id":"<urn:uuid:7d1c7ff6-bf51-447b-b81f-98c177126627>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00370.warc.gz"} |
next → ← prev
Derivation of Equations of Motion
Before discussing the equations of motion, we need to understand what is meant by the term 'motion'. Motion is the phenomenon of a change in an object's position with respect to time. In simpler
terms, it refers to the movement or displacement of an object from one place to another.
Motion can occur in various forms, such as linear, circular, periodic, or random, depending on the path the object takes and the forces acting upon it. We witness and partake in motion every day and
every minute of our life. The movement of your hand or arms to pick up something, the object that is picked up and placed somewhere else, walking from one place to another, and driving in a car or
any other vehicle, are all examples of some kind of motion we witness every day.
Motion is prevalent in the universe, from the motion of celestial bodies like planets and stars to the motion of atoms and particles at the subatomic level. Observing and comprehending motion is
essential for many scientific fields, engineering, and everyday life applications. It is a crucial concept for understanding the dynamics of the world around us and has played a central role in the
development of various scientific theories and technological advancements.
The study of motion enables us to understand how objects behave under the influence of forces, allowing us to predict their future positions and velocities based on initial conditions and applied
Newton's Law of Motion:
Newton's laws of motion are three fundamental principles that laid the foundation for classical mechanics and revolutionized our understanding of how objects move. These laws were formulated by Sir
Isaac Newton in his work published in 1687. As the equations of motion are based on Newton's law, it is important first to grasp what the said laws dictate.
Newton's 1st Law of Motion:
The first law, also known as the law of inertia, states that:
An object at rest will remain at rest, and an object in motion will continue to move with a constant velocity in a straight line unless acted upon by an external force.
In simpler terms, an object will maintain its state of motion (whether at rest or moving with a constant speed in a straight line) unless an external force acts on it. This law implies that the
natural tendency of an object is to resist changes in its motion, which is often referred to as inertia.
Newton's 2nd Law of Motion:
The second law states that:
The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
Mathematically, Newton's second law is expressed as F = m*a, where:
• F is the net force acting on the object,
• m is the mass of the object, and
• a is the acceleration of the object.
This law tells us that the force acting on an object is responsible for changing its state of motion. Larger forces cause greater acceleration, while more massive objects require larger forces to
produce the same acceleration.
Newton's 3rd Law of Motion:
The third law of motion states that:
For every action, there is an equal and opposite reaction.
This law states that when two objects interact, the force exerted by one object on the other is matched by an equal but opposite force exerted by the second object on the first. In other words, if
object A exerts a force on object B, object B simultaneously exerts an equal and opposite force on object A.
Newton's laws of motion have had a profound impact on the development of physics and have become the cornerstone of classical mechanics. They are fundamental to understanding and predicting the
motion of objects, from simple everyday situations to complex interactions in celestial mechanics and engineering applications. These laws continue to be taught and applied in various scientific
fields and remain crucial for our understanding of the physical world.
First Equation of Motion:
The equations of motion are crucial principles in classical mechanics that describe the behavior of a particle in response to external forces. In one dimension, these equations establish a
relationship between the particle's position, velocity, and acceleration as functions of time. The first equation states that the velocity of the particle is the time derivative of its position,
representing how quickly the particle's position changes with time.
Let us consider an object with an initial velocity 'u'. After time 't' it accelerates to a final velocity of 'v'. The acceleration is 'a'.
According to the definition of acceleration:
acceleration (a) = Change in velocity/time taken (t)
Now, change in velocity = final velocity (v) - initial velocity (u)
This means:
a = (v - u) / t
Cross multiplying t with a, we get:
a*t = v - u
After rearranging the above equation, we get:
v = u + a*t
This is the first equation of motion.
Second Equation of Motion:
The second equation of motion describes the position of a particle as a function of time when the particle is subjected to constant acceleration. The equation is also known as the "position-time"
equation and is one of the crucial equations of classical mechanics. The equation describes how the position of the particle changes with time when it undergoes constant acceleration. The equation
assumes that the acceleration experienced by the particle remains constant throughout the motion. This means that the acceleration does not change with time and is the same at any given instant.
Mathematically it is represented as:
x = u * t + (1/2) * a * t 2
Let us consider an object with an initial velocity 'u'. After time 't' it accelerates to a final velocity of 'v' and travels 'x' amount of distance. The acceleration is 'a'.
The average velocity for this object would be: (u + v)/2
Now, we know that the distance traveled is the average velocity multiplied by the time taken:
x = [(u + v)/2]*t
From the first equation of motion, we know that:
v = u + a*t
Using this, our equation becomes:
x = [(u + u + a*t)/2]*t
x= (2u*t + a*t2)/2
x = u*t + ½(a*t2)
This is the second equation of motion and is a crucial tool in classical mechanics and plays a significant role in understanding the motion of particles subjected to constant acceleration. It is
widely used in various physics and engineering applications, such as analyzing the motion of projectiles, studying the motion of vehicles, and describing the dynamics of celestial bodies.
Third Equation of Motion:
The third equation of motion shows how the final velocity of the particle (v) is related to its initial velocity (u) when subjected to constant acceleration. The final velocity is obtained by
squaring the initial velocity, adding twice the product of the acceleration and the displacement, and then taking the square root. It is also known as the "velocity-time" equation. Similar to the
first and second equations of motion, the third equation assumes that the acceleration experienced by the particle remains constant throughout the motion.
Mathematically, it is represented as:
v2 - u2 = 2a*x
Using the first equation:
v = u + a*t
v - u = a*t
t = (v-u)/a
Now, substitute this value of t in the second equation of motion: x = u*t + ½(a*t2)
x = u*(v-u)/a +½ [a*(v-u)2]/a2
x = (v*u - u2)/a + (v2 - 2*v*u + u2)/2a
x = (2*u*v - 2*u2 + v2 - 2*u*v + u2)/2a
2ax= v2 - u2
v2 - u2 = 2ax
This is the third equation of motion. The third equation of motion complements the first two equations by providing a way to calculate the final velocity of an object under constant acceleration
given its initial conditions (velocity and displacement). This equation is valuable for understanding the dynamics of moving objects and is used in various physics and engineering applications, such
as calculating the final speed of a vehicle after a certain distance traveled or predicting the velocities of projectiles in projectile motion problems.
The equations of motion are derived from Newton's second law of motion and velocity can be calculated by integrating the acceleration and position can be calculated by integrating the velocity. These
equations provide a mathematical description of the motion of a particle under the influence of external forces. These equations, along with Newton's second law relating force and acceleration,
provide a powerful framework for understanding and predicting the motion of objects in various scenarios, from simple linear motion to more complex dynamics involving multiple dimensions and
Next TopicDoppler Effect
← prev next → | {"url":"https://www.javatpoint.com/derivation-of-equations-of-motion","timestamp":"2024-11-10T01:28:59Z","content_type":"text/html","content_length":"47036","record_id":"<urn:uuid:8d47d058-6c9e-441d-8271-a2dd920ed8a8>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.3/warc/CC-MAIN-20241110005602-20241110035602-00763.warc.gz"} |
Term: Inferential Analysis
Glossary Definition
Last Updated: 2006-10-20
Inferential statistics allow one to draw conclusions or inferences from data. Usually this means coming to conclusions about a population on the basis of data describing a sample. Statistical
inference uses probability and information about a sample to draw conclusions ("inferences") about a population or about how likely it is that a result could have been obtained by chance.
Related terms
• Lix L, Yogendran M, Burchill C, Metge C, McKeen N, Moore D, Bond R. Defining and Validating Chronic Diseases: An Administrative Data Approach. Winnipeg, MB: Manitoba Centre for Health Policy,
2006. [Report] [Summary] (View) | {"url":"http://mchp-appserv.cpe.umanitoba.ca/viewDefinition.php?printer=Y&definitionID=102898","timestamp":"2024-11-01T19:22:26Z","content_type":"text/html","content_length":"1859","record_id":"<urn:uuid:fa40279d-2bae-496a-a8ae-d66cf00c04b6>","cc-path":"CC-MAIN-2024-46/segments/1730477027552.27/warc/CC-MAIN-20241101184224-20241101214224-00680.warc.gz"} |
Did you know that... Random interesting math facts
Did you know that...
1. π=3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 ...
2. A sphere has two sides. However, there are one-sided surfaces.
3. There are shapes of constant width other than the circle. One can even drill square holes.
4. There are just five regular polyhedra
5. In a group of 23 people, at least two have the same birthday with the probability greater than 1/2
6. Everything you can do with a ruler and a compass you can do with the compass alone
7. Among all shapes with the same perimeter a circle has the largest area.
8. There are curves that fill a plane without holes
9. Much as with people, there are irrational, perfect, complex numbers
10. As in philosophy, there are transcendental numbers
11. As in the art, there are imaginary and surreal numbers
12. A straight line has dimension 1, a plane - 2. Fractals have mostly fractional dimension
13. Mathematics studies neighborhoods, groups and free groups, rings, ideals, holes, poles and removable poles, trees, growth ...
14. Mathematics also studies models, shapes, curves, cardinals, similarity, consistency, completeness, space ...
15. Among objects of mathematical study are heredity, continuity, jumps, infinity, infinitesimals, paradoxes...
16. Last but not the least, Mathematics studies stability, projections and values, values are often absolute but may also be extreme, local or global.
17. Trigonometry aside, Mathematics comprises fields like Game Theory, Braids Theory, Knot Theory and more
18. One is morally obligated not to do anything impossible
19. Some numbers are square, yet others are triangular
20. The next sentence is true but you must not believe it
21. The previous sentence was false
22. 12+3-4+5+67+8+9=100 and there exists at least one other representation of 100 with 9 digits in the right order and math operations in between
23. One can cut a pie into 8 pieces with three movements
24. There is something the dead eat but if the living eat it, they die.
25. A clock never showing right time might be preferable to the one showing right time twice a day
26. Among all shapes with the same area circle has the shortest perimeter
|Next| |Contact| |Front page| |Contents|
Copyright © 1996-2018 Alexander Bogomolny | {"url":"https://cut-the-knot.org/do_you_know/index.shtml","timestamp":"2024-11-03T15:37:56Z","content_type":"text/html","content_length":"16713","record_id":"<urn:uuid:bef71844-3e8d-4470-a79b-de73c3f1aa7a>","cc-path":"CC-MAIN-2024-46/segments/1730477027779.22/warc/CC-MAIN-20241103145859-20241103175859-00156.warc.gz"} |
Efficient Removal Lemmas for Matrices
It was recently proved in Alon et al. (2017) that any hereditary property of two-dimensional matrices (where the row and column order is not ignored) over a finite alphabet is testable with a
constant number of queries, by establishing the following ordered matrix removal lemma: For any finite alphabet Γ, any hereditary property P of matrices over Γ, and any ϵ > 0, there exists f[P] such
that for any matrix M over Γ that is ϵ-far from satisfying P, most of the f[P] × f[P] submatrices of M do not satisfy P. Here being ϵ-far from P means that one needs to modify at least an ϵ-fraction
of the entries of M to make it satisfy P. However, in the above general removal lemma, f[P] grows very quickly as a function of ϵ^− 1, even when P is characterized by a single forbidden submatrix. In
this work we establish much more efficient removal lemmas for several special cases of the above problem. In particular, we show the following, which can be seen as an efficient binary matrix
analogue of the triangle removal lemma: For any fixed s × t binary matrix A and any ϵ > 0 there exists δ > 0 polynomial in ϵ, such that for any binary matrix M in which less than a δ-fraction of the
s × t submatrices are equal to A, there exists a set of less than an ϵ-fraction of the entries of M that intersects every copy of A in M. We generalize the work of Alon et al. (2007) and make
progress towards proving one of their conjectures. The proofs combine their efficient conditional regularity lemma for matrices with additional combinatorial and probabilistic ideas.
Funders Funder number
National Science Foundation DMS-1855464
Simons Foundation
German-Israeli Foundation for Scientific Research and Development G-1347-304.6/2016
Israel Science Foundation 281/17
• Matrix properties
• Property testing
• Removal lemma
• Submatrix freeness
Dive into the research topics of 'Efficient Removal Lemmas for Matrices'. Together they form a unique fingerprint. | {"url":"https://cris.tau.ac.il/en/publications/efficient-removal-lemmas-for-matrices-2","timestamp":"2024-11-08T12:01:41Z","content_type":"text/html","content_length":"52047","record_id":"<urn:uuid:22711ccc-65ff-4ac8-b5cc-c714c9d92ff6>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00847.warc.gz"} |
How to convert Pandas series to NumPy array in Python
In this article, you are going to learn about how to convert the Pandas series to NumPy array in Python.
In the Python programming language, the Pandas series is considered the One-dimensional data structure that can accept multiple data types. On the other hand, the NumPy array is the grid of values
that accept only a single data type. We can convert a Pandas series into the NumPy array and to perform this action there are several ways like using the series.to_numpy() or using
pandas.index.to_numpy() In this article, we are going to explore these functions and see how we can convert the Pandas series to a NumPy array. Before doing so, let’s quickly see the Pandas series
first in the below section:
import pandas as pd
panda_series = pd.Series(['Alex', 'Deven', 'Rohit', 'John', 'Virat'])
# Output:
# 0 Alex
# 1 Deven
# 2 Rohit
# 3 John
# 4 Virat
# dtype: object
# <class 'pandas.core.series.Series'>
Here, you can see that we have created a simple pandas series and we have also checked its type by using the type() function. Now we are going to convert this to the NumPy array in the next section.
Using series.to_numpy()
The main difference between the Pandas series and the NumPy array is that the Pandas series consists of an index column but the NumPy array does not. Let’s see the converting process of this by using
the series.to_numpy() function.
import pandas as pd
import numpy as np
panda_series = pd.Series(['Alex', 'Deven', 'Rohit', 'John', 'Virat'])
numpy_array = panda_series.to_numpy()
# Output:
# ['Alex' 'Deven' 'Rohit' 'John' 'Virat']
# <class 'numpy.ndarray'>
Here, you can see how easily we have converted the Pandas series to the NumPy array. You can also see the type has been changed now and it is showing as the ndarray
Using pandas.index.to_numpy()
We have already known that the pandas series consists of the index and the value. We can convert this index into the NumPy array if we want. To perform this action, all we need to do is to use the
pandas.index.to_numpy() function. See the below code example:
import pandas as pd
import numpy as np
panda_series = pd.Series(['Alex', 'Deven', 'Rohit', 'John', 'Virat'])
numpy_array = panda_series.index.to_numpy()
# Output:
# [0 1 2 3 4]
# <class 'numpy.ndarray'>
Here, you can see in the output that we have printed the Pandas series indexes but in the form of the NumPy array. You may also notice it in its type. These are the approaches that you may follow to
convert the Pandas series to NumPy array in Python. | {"url":"https://codesource.io/blog/how-to-convert-pandas-series-to-numpy-array-in-python/","timestamp":"2024-11-02T23:33:53Z","content_type":"text/html","content_length":"206614","record_id":"<urn:uuid:462d468b-d8df-452f-a088-af0cc8b61f74>","cc-path":"CC-MAIN-2024-46/segments/1730477027768.43/warc/CC-MAIN-20241102231001-20241103021001-00792.warc.gz"} |
Spatial Interpolation With and Without Predictor(s)
This article was published as a part of the Data Science Blogathon
After my last article about spatial correlation, this time I am going to discuss spatial interpolation. In this case, we have a dataset of point features with spatial location. Below is the fictional
data we will be using for this article.
Fig. 1 Map of data points
There are distributed 56 data points. Each point has evapotranspiration and temperature values. X and y are the location coordinates. Note that, once again, the data are fictional, NOT from real
field measurement. There is a linear correlation between temperature and evapotranspiration. This means that we can apply linear regression or other regressors to predict evapotranspiration with
temperature as the predictor. The result is a model or equation. Using the equation we can predict unknown evapotranspiration, but by requiring the predictor. This is a common Machine Learning task.
But, our task now is to predict the location in the white areas above so that they all have values. In other words, the task is to interpolate the data points into raster areas with
evapotranspiration values. The white areas in the map above have no evapotranspiration and temperature information. Allocating more resources to collect more data in more detail spatial interval is a
good idea, but acquiring field data may be costly and limited.
For instance, an Earth Scientist can have a few borehole data. Borehole data have the information on how depth every material or rock type is in vertical layers from the ground to the belowground at
a point. The borehole data are acquired from drilling several locations. The data are expensive and the scientist cannot possibly request to drill the ground in every meter. The scientist has to
interpolate and predict what is between every 2 or more borehole data. Another example is soil sampling. Soil scientist collects several soil samples for laboratory test.
The number of soil samples is limited to the budget. Even though the budget is unlimited, the soil scientist cannot take all the soil in his study area. The scientist has to generalize the soil type
of his study area according to only a limited number of samples. This a common problem in spatial studies, like Geography, Geology, Meteorology, Soil Science, and so on.
Spatial interpolation is the solution for this task. Spatial interpolation fills the areas with no values according to the surrounding data points. We can interpolate the evapotranspiration data
points into a raster. Later, we can also use temperature as the predictor to assist the interpolation process. This article focuses on describing the interpolation methods, but I will brief a little
about evapotranspiration. Evapotranspiration is the combined process of evaporation and transpiration which emits water vapor to the atmosphere. This is a common topic in Hydrology.
Evaporation is the process of evaporating water bodies. The evaporation pan is an example of a field method for measuring the evaporation rate. An evaporation pan is a pan filled with water at a
certain height and put in an open space. The water height will decrease in days or months due to evaporation. Then, the evaporation rate can be calculated with a coefficient. The transpiration rate
is measured using the gravimetric tool. Transpiration is the process of plants releasing water vapor into the atmosphere.
Just like the cases of borehole data and soil sampling, we do not measure the evapotranspiration and temperature at every inch of our study area. It is not efficient. We can only install a limited
number of tools at some location points.
Evapotranspiration rate is continuous in the spatial dimension. If there are two points with different evapotranspiration rates, the middle of the two points is likely to have the evapotranspiration
rate between those of the points. This condition allows spatial interpolation. Other examples of continuous variables are elevation, water depth, rainfall, and so on. These variables can be
interpolated spatially.
In the dataset, there is temperature as another variable. Temperature is also measured at every monitoring point. Temperature and evapotranspiration correlate linearly. Higher temperature affects
higher evapotranspiration. This condition makes it possible to interpolate evapotranspiration using temperature as the predictor. We will practice this later as one of the interpolation methods.
Before we run the interpolation, we need to specify the spatial output extent. In GIS software, this step has been done by default. The output extent by default is a rectangle covering the minimum
and maximum of both the x-axis and y-axis. In R, the output extent has to be defined by code. The output extent can be enlarged to cover more areas. Below is the code to import packages, load the
data, and create the output extent.
# Import packages
# Interpolation packages
library(gstat) # Nearest Neighbour, IDW, Kriging
library(fields) # TPS
library(mgcv) # GAM
library(interp) # TIN
library(automap)# Automatic Kriging
# Load point data
ET_data <- read_excel("z:/OpenMarket_Supplier/07_CarbonAssesment_project/2021/05 May/hps/dat.xlsx", sheet="Sheet2")
# Output extent
ET_sf <- st_as_sf(ET_data, coords=c("x", "y"), crs="+proj=longlat +datum=WGS84")
boundary <- c(
"xmin" = min(ET_data$x),
"ymin" = min(ET_data$y),
"xmax" = max(ET_data$x),
"ymax" = max(ET_data$y)
extent_grid <- expand.grid(
X = seq(from=boundary["xmin"], to=boundary["xmax"], by=0.002),
Y = seq(from=boundary["ymin"], to=boundary["ymax"], by=0.002)
# Output extent to raster
extent_grid_raster <- extent_grid %>%
dplyr::mutate(Z = 0) %>%
crs = "+proj=longlat +datum=WGS84")
Inverse Distance Weighted and Nearest Neighbour
After having the output extent, interpolation can be applied. The output of the interpolation will be put into the output extent. In this article, I will demonstrate 8 methods of interpolation. The
last one is designed to use predictor(s). But, let’s start with the simplest method. It is the Inverse Distance Weighted (IDW). IDW predicts values of unknown locations based on the weighted average
neighboring known values.
The simple form of IDW is called Nearest Neighbour. Below is the code to run Nearest Neighbor interpolation. The minimum and maximum number of data points to fit are set to be 5 and 8 respectively.
The second and third IDW below is still similar, but the IDP is set to be 3 and 1 respectively. Examine that IDW with larger IDP tends to form a circular pattern around the knowns data points.
# 1. Nearest Neighbor
# Create gstat object
NN <- gstat(formula = ET ~ 1, data=ET_sf, nmax=8, nmin=5) # Number of neighbouring data points for fitting
# Interpolate
NN_intr <- interpolate(extent_grid_raster, model=NN)
# Visualize raster
plot(NN_intr, main = "Nearest Neighbour")
# 2a. Inverse Distance Weighted
IDW <- gstat(formula = ET ~ 1, data=ET_sf, nmax=8, nmin=5, set=list(idp=3)) # inverse distance power
IDW_intr <- interpolate(extent_grid_raster, model=IDW)
plot(IDW_intr, main = "Inverse Distance Weighted idp=3")
# 2b. Inverse Distance Weighted
IDW1 <- gstat(formula = ET ~ 1, data=ET_sf, nmax=8, nmin=5, set=list(idp=1)) # inverse distance power
IDW_intr1 <- interpolate(extent_grid_raster, model=IDW1)
plot(IDW_intr1, main = "Inverse Distance Weighted idp=1")
Thin Plate Spline Regression
Thin Plate Spline Regression (TPS) interpolates the data points by creating a smoothened thin plate connecting all the data points. Below is the code to run TPS.
# 3. Thin Plate Spline Regression
TPS <- Tps(x = as.matrix(ET_data[, c("x", "y")]), Y=ET_data$ET, miles=FALSE)
TPS_intr <- interpolate(extent_grid_raster, model=TPS)
plot(TPS_intr, main = "Thin Plate Spline Regression")
Generalized Additive Model
Generalized Additive Model (GAM) interpolation works with the following code.
# 4. Generalized Additive Model
GAM <- gam(ET ~ s(x, y), data=ET_data)
extent_grid_gam <- extent_grid
names(extent_grid_gam) <- c("x", "y")
GAM_intr <- extent_grid %>%
mutate(Z = predict(GAM,extent_grid_gam)) %>%
rasterFromXYZ(crs="+proj=longlat +datum=WGS84")
plot(GAM_intr, main="Generalized Additive Model")
Triangulated Irregular Network
Triangulated Irregular Network (TIN) has the data points to create circumcircles. The intersections of those circumcircles form dots. Every dot is then connected to the neighboring 2 dots forming a
triangular surface network. Below is the code to run TIN interpolation.
# 5. Triangular Irregular Network
TIN <- interp(x=ET_data$x, y=ET_data$y, z=ET_data$ET,
xo = extent_grid$X, yo = extent_grid$Y,
output = "points") %>% bind_cols()
TIN_intr <- rasterFromXYZ(TIN, crs="+proj=longlat +datum=WGS84")
plot(TIN_intr, main="Triangular Irregular Network")
Ordinary Kriging and AutoKriging
Kriging also uses the same package as IDW does. Kriging predicts interpolation by fitting a variogram. Another method is AutoKriging. AutoKriging can automatically fit the variogram model for the
interpolation. The Autokriging results below provide the interpolation prediction result, standard error, and the variogram.
# 6. Ordinary kriging
var <- variogram(ET~1, ET_sf, cutoff=100) # Variogram
var_fit <- fit.variogram(var, vgm(1, "Sph", 5, 1))
Kriging <- gstat(NULL, "ET", ET~1, ET_sf, model=var_fit)
Kriging_intr <- interpolate(extent_grid_raster, Kriging)
plot(Kriging_intr, main = "Ordinary Kriging")
# 7. Automatic Kriging
# Create SpatialPointsDataFrame
ET_df <- as.data.frame(ET_data)
coordinates(ET_df) <- ~ x+y
# Create Spatial Pixels
extent_grid_pix <- extent_grid
gridded(extent_grid_pix) =~ X+Y
# run AutoKriging
AutoKriging = autoKrige(ET~1, ET_df, extent_grid_pix)
AutoKriging_2 <- autoKrige(ET~1, ET_df) %>% .$krige_output %>% as.data.frame() %>% select(X = x1, Y = x2, Z = var1.pred)
AutoKriging_intr <- rasterFromXYZ(AutoKriging_2, crs="+proj=longlat +datum=WGS84")
extent(AutoKriging_intr) <- extent(Kriging_intr)
plot(AutoKriging_intr, main="AutoKriging")
Fig. 9 Autokriging prediction, standard error, and variogram
All of the above interpolation methods only rely on the target variable, in this case, is evapotranspiration. The last method we are discussing is co-Kriging which performs spatial interpolation by
using predictor(s). Given that temperature affects evapotranspiration, we want to interpolate the evapotranspiration by accounting for temperature as the predictor too. Here is the code to do so.
# 8. Co-kriging
# Gstat for target and independent variables
coKriging <- gstat(NULL, 'ET', ET~1, ET_sf)
coKriging <- gstat(coKriging, 'Temp', Temp~1, ET_sf)
# Variogram
vario <- variogram(coKriging)
plot(vario, type='b', main='Co-variogram')
# Fitting
coKriging_fit <- fit.lmc(vario, coKriging, vgm(model='Sph', range=1000))
plot(vario, coKriging_fit, main='Co-variogram After Fitting')
# Interpolation
coKriging_intr <- interpolate(extent_grid_raster, coKriging_fit)
# Visualize
plot(coKriging_intr, main = "Co-Kriging")
Fig. 10 Co-Kriging
Now that we have 9 interpolation results, we can check the Root Mean Squared Error (RMSE). The RMSE is used to compare how close the interpolation results to the recorded data points. The code below
extracts each value from the 9 raster datasets where the recorded data points are located. Then, RMSE is computed to compare the extracted raster values with the true values of the data points. It
seems that IDW with IDP=3 has the smallest RMSE.
# RMSE
# Stack the rasters and extrace the values
overlay <- stack(NN_intr, IDW_intr, IDW_intr1, TPS_intr,
GAM_intr, TIN_intr, Kriging_intr,
pred <- as.data.frame(extract(overlay, ET_sf))
names(pred) <- c("NN", "IDW", "IDW1", "TPS", "GAM", "TIN", "Kriging", "coKriging")
pred2 <- as.data.frame(extract(AutoKriging_intr, ET_sf))
names(pred2) <- c("AutoKriging")
pred <- cbind(ET_data, pred, pred2)
sqrt(sum((pred$ET-pred$NN)^2, na.rm=TRUE)/nrow(pred)) # 0.1576134
sqrt(sum((pred$ET-pred$IDW)^2, na.rm=TRUE)/nrow(pred)) # 0.01212739
sqrt(sum((pred$ET-pred$IDW1)^2, na.rm=TRUE)/nrow(pred)) # 2.029118
sqrt(sum((pred$ET-pred$TPS)^2, na.rm=TRUE)/nrow(pred)) # 3.518021
sqrt(sum((pred$ET-pred$GAM)^2, na.rm=TRUE)/nrow(pred)) # 5.136027
sqrt(sum((pred$ET-pred$TIN)^2, na.rm=TRUE)/nrow(pred)) #2.060511
sqrt(sum((pred$ET-pred$Kriging)^2, na.rm=TRUE)/nrow(pred)) # 5.614179
sqrt(sum((pred$ET-pred$AutoKriging)^2, na.rm=TRUE)/nrow(pred)) # 4.947287
sqrt(sum((pred$ET-pred$coKriging)^2, na.rm=TRUE)/nrow(pred)) # 0.6766445
About Author
Connect with me here.
The media shown in this article are not owned by Analytics Vidhya and is used at the Author’s discretion.
Responses From Readers
Hi, I am getting this error. Error in predict.gstat(model, blockvals, debug.level = debug.level, ...) : var1 : data item in gstat object and newdata have different coordinate reference systems Can
you please help in this? | {"url":"https://www.analyticsvidhya.com/blog/2021/05/spatial-interpolation-with-and-without-predictors/","timestamp":"2024-11-14T12:04:24Z","content_type":"text/html","content_length":"376327","record_id":"<urn:uuid:8a8879b7-af2c-4935-b3b0-ece70fd90548>","cc-path":"CC-MAIN-2024-46/segments/1730477028558.0/warc/CC-MAIN-20241114094851-20241114124851-00439.warc.gz"} |
What is 18 degrees Celsius in Fahrenheit? [Solved] | Brighterly Questions
What is 18 degrees Celsius in Fahrenheit?
Updated on December 11, 2023
Answer: 18 degrees Celsius is approximately 64.4 degrees Fahrenheit. This is calculated using the formula: (C × 9/5) + 32.
Temperature Scales
Converting Celsius to Fahrenheit is a fundamental skill in understanding global temperature scales. For 18 degrees Celsius, use the formula (18 × 9/5) + 32, resulting in approximately 64.4 degrees
Fahrenheit. This knowledge is essential for comparing temperatures and understanding weather forecasts in different countries, providing a practical application of mathematics in everyday life.
FAQ on Temperature Scales
What is 0 degrees Celsius in Fahrenheit?
0 degrees Celsius is 32 degrees Fahrenheit.
How do you convert 100 degrees Celsius to Fahrenheit?
100 degrees Celsius is 212 degrees Fahrenheit.
What is 10 degrees Celsius in Fahrenheit?
10 degrees Celsius is approximately 50 degrees Fahrenheit. | {"url":"https://brighterly.com/questions/what-is-18-degrees-celsius-in-fahrenheit/","timestamp":"2024-11-06T08:28:04Z","content_type":"text/html","content_length":"70499","record_id":"<urn:uuid:8ba82b15-1b06-4306-a1a7-1f8c1f078bce>","cc-path":"CC-MAIN-2024-46/segments/1730477027910.12/warc/CC-MAIN-20241106065928-20241106095928-00080.warc.gz"} |
Corporate Finance Examination | Blablawriting.com
Corporate Finance Examination
The whole doc is available only for registered users
A limited time offer! Get a custom sample essay written according to your requirements urgent 3h delivery guaranteed
Order Now
Total salary for Mathew for 25 years if he earns $10000 per month is (12*25) $10000 which is $3000000
If he withdraws $6000 for five years, the total withdrawal will be (12*5) $ 6000 which is $ 360000
Total money remained after Mathew death is $ (3000000-360000) which will be $ 2640000
Mathew’s son Sean inherits the savings and he receives equal payment for every month for 20 years with a fixed interest rate of 9% per annum.
Total amount for 20 years will be $ 2640000= S/5.6044 where S is the sum total
The sum total will be $147956160
If Sean receives equal pay for each month for 20 years that is 240 months, he will be receiving $147956160/240 which is $616484 per month.
The value of the bond after 10^th interest if its face value is $1000 at 8% for five years can be calculated as follows: $1000=?/1.46933
Multiplying both sides by 1.46933 to get the total sum value which is $1000*1.46933=1469.33, this will be the value of the bond after 10^th interest
If the bond were redeemable at $ 1100at end of year 4, the market price of the bond after the 6^th interest payment will be:
Face value is $ 1000 and the interest rate will be 3% for three years.
It will be $1000=S/1.093 multiply both sides by 1.093 we get $1000*1.093=$1093 which is the market price after 6^th interest payment.
The table below shows Les’s selected company’s total return and standard deviation. Table I
Company name Total share return Standard deviation of daily returns Beta coefficient
National Australia Bank 10.97% 1.62% 0.906
Coca-Cola Amatil –62.78% 2.73% 0.718
James Hardie Industries 9.28% 2.07% 0.626
Lend Lease Corporation 2.69% 1.75% 0.683
News Corporation 57.90% 3.42% 2.625
Sons of Gwalia 27.77% 2.45% 0.349
Westfield Trust 5.81% 1.04% 0.381
Woodside Petroleum 23.96% 2.08% 0.778
All Ordinaries Index 12.28% 0.92% 1.000
The return and the standard deviation have to be positively related. In the table above, National Australia Bank has a positive relationship though of low value as the return is 10.97%. Coca-Cola
Amantil return is negative while the standard deviation is positive. This is not consistent with the expected positive relationship; the risks cannot be covered by the returns.
James Hardie Industries has a return of 9.28% this is low when related to the risk of the investment, and its standard deviation is at 2.07%. Lend Lease Corporation has return of 2.69% and standard
deviation of 1.75%, though positively related the return is low. News Corporation has a return of 57.90% and standard deviation of 3.42%.There is positive relationship and the return value is good as
it is on average meaning the risks are fully covered by the returns though the risk is very high. Sons of Gwalia have positive relationship though the return is low (27.77%). Westfield Trust has
positive relation but the return is low. Woodside Petroleum has return of 23.96%and standard deviation of 2.08%.
The companies with low return imply that the risks of the investment will not be well offset as high returns are desirable on the grounds that it will cover the risks associated with the investment,
though an investor who expects high returns should accept more risks.
A company can be rejected on the basis that its return is low or its deviation from risk is low. In relation with Mr. Les selection of companies for investment some companies are not worthy for
investment and hence should be rejected. These are Coca-Cola Amanti which has a return of -62.78% and standard deviation of 2.73%, this means that the risk associated with the investment cannot be
covered hence it is unworthy for investment.
Also Lend Lease Corporation should be rejected on the basis that its return (2.69%) will not offset the risk as presented by the Beta coefficients (0.683). finally; James Hardie Industries may also
be rejected as its return is only 9.28% while the standard deviation is 2.07%. The return is low for the risk.
Concept of Portfolio Theory
Markowitz (1958) contends that rational investors use diversification to optimize their portfolios. Markowitz assumes investors are risk averse. Investors will prefer the less risky investment and
will only take risky investment if compensated by higher expected returns.
The concept of Portfolio theory holds when the portfolio risk is minimized by holding a well diversified portfolio of shares. In the case of Mr. Les selected companies for investment, the concept of
Portfolio theory holds as the Beta coefficients are all positive which imply that the returns and the risks are positively correlated. The company with high risk is associated with high Beta
coefficient, for instance, the News Corporation has a return of 57.90% standard deviation of 3.42% and Beta coefficient of 2.625.
The three companies that can be recommended for Mr. Les for investment are; Sons of Gwalia which has Beta value of 0.349. The value is low meaning that the risk associated with the investment is
less. Also Westfield Trust which has the Beta coefficient of 0.381 and James Hardie Industries. Less risky investment can be recognized basing on the Beta coefficient. Large Beta coefficient means
high risks associated while small coefficient means low risks associated.
The portfolio for the above companies chosen can be derived as follows:
Square the returns multiply by the square of its standard deviation of 3 companies then add after which we add the multiplication of the returns and the multiplication of the standard deviation of 3
selected companies. This will be 0.000052 which is the portfolio. The results outperforms the All Ordinaries Index
Using the Capital Asset Pricing Model (CAPM) for the Mr. Les data of 2001 financial year we can use the following CAPM formula in sequence with Markowitz (1952):
E (R¡) =Rƒ+ßί [E (Rm)-Rƒ]
Where; E (Rі) is the expected returns for share
Rƒ is the risk-free rate of return
ßί is the assets Beta and [E (Rm)-Rƒ] is the market premium or risk premium
Black, Fisher, Michael, Jancen and Scholes (1972) outline that the CAPM was introduced by Jack Treynor, William Shape, John Lintner and Jan Mossin independently building on the earlier work of Harry
Markowitz on diversification and modern portfolio theory
The market premium can be obtained by getting the difference between the arithmetic average of the expected market return and the arithmetic average of the rate of free risk. This will be 9.45-2.145=
7.305. Using the above CAPM formula, the expected returns for the shares is shown in the table below:
Table II
Company name Share return Risk Beta coefficient Expected share return
National Australia Bank 10.97% 0.906% 0.906 17.588%
Coca-Cola Amatil -62.78% 0.718% 0.718 -57.535%
James Hardie Industries 9.28% 2.07% 0.626 13.853%
Lend Lease Corporation 2.69% 1.75% 0.683 7.679%
News Corporation 57.90% 3.42% 2.625 77.727%
Sons of Gwalia 27.77% 2.45% 0.349 30.319%
Westfield Trust 5.81% 1.04% 0.81 11.727%
Woodside Petroleum 23.96% 2.08% 0.778 29.643%
Comparing the share returns results, the CAPM results have increased a little bit as to the raw results. In-line with Markowitz (1952), this indicates that CAPM takes into account the sensitivity to
no-diversifiable risk often represented by Beta in the financial industry, and though CAPM may be impressive it assumes that the assets returns are normally distributed, but in the some markets
returns are not normally distributed. The model also does not appear to explain the variation in stock returns thus it is not that 100% accurate.
Black, Fisher, Micheal, Jancen, and Scholes. (1972). The capital Asset Pricing Model.
New York. Praeger publishers.
Markowitz H. (1952). Portfolio selection. Journal of finance, 7 (1), 77-91.
Related Topics | {"url":"https://blablawriting.net/corporate-finance-examination-essay","timestamp":"2024-11-13T12:19:27Z","content_type":"text/html","content_length":"68036","record_id":"<urn:uuid:d8ba4aba-086f-4f1d-b6d6-bb6324ac1110>","cc-path":"CC-MAIN-2024-46/segments/1730477028347.28/warc/CC-MAIN-20241113103539-20241113133539-00170.warc.gz"} |
Answers edited by Solace M.
• Back to user's profile
• Why do voltaic cells with magnesium as the annode have such high percent differences?
• The mean of a set of data is 4.11 and its standard deviation is 3.03. What is the z-score for a value of 10.86?
• What organelles are found in all Eukaryotic cells?
• The position of uncertainty of an electron is 1.89 x 10 -14 m/ What is the uncertainity of velocity? thank you so much.
• What evidence is there for abiogenesis?
• How can some manganese oxides be acidic and some basic?
• Shaun White won the gold medal with a score of 46.80, what is the corresponding z-score?
• Question #d1d51
• Question #50172
• Crystalline sodium nitride is heated until it decomposes. What type of reaction is this?
• With the word Quicker, how many ways can we arrange the letters if U and I can't be together?
• What is a rhyme scheme called when the poem only rhymes in the beginning?
• What are two compounds that are made up of molecules?
• What information can you represent with a box and whisker plot?
• Question #355ed
• What was Dmitri Mendeleev's major contribution to the field of chemistry?
• Is it possible to "move" space, rather than a space vehicle, to make the vehicle travel faster?
• Question #69f2a
• Question #3c669
• Why are lakes and oceans are able to stabilize air and land temperatures?
• What are the grams of sodium chloride produced when 10.0 g of sodium react with 10.0 g of chlorine gas in the equation #2Na+Cl_2 -> 2NaCl#?
• What type of electromagnetic energy is invisible to the human eye?
• What are three methods used to help control invasive species?
• Question #3cd19
• How can you determine the electron configuration without a periodic table?
• Question #47e74
• Question #22638
• Why is lattice energy considered to be potential energy?
• Help with Q6? "A boat travels north for 6km, west for 3km, then south for 2km. What is the boat's true bearing from its starting point? Give your answer to one decimal place.
• Question #e8469
• How do you find the standard deviation for the numbers 4, 4, 5, 5, 6, 6?
• How can some manganese oxides be acidic and some basic?
• What is the formula of dinitrogen pentoxide?
• Marta deposits $15,000 in an account with 7% interest, compounded annually. How much will Marta's account balance be after 15 years?
• Question #bed84
• Question #edca3
• The heights of a certain group of adult parrots were found to be normally distributed. The mean height is 36 cm with a standard deviation of 7 cm. In a group of 1200 of these birds, how many
would be more than 29 cm tall?
• How are gastrointestinal problems cured?
• What is the law of large numbers in economics?
• Is the sample mean equal to the population mean?
• What are some advantages and disadvantages of Michelson Interferometer?
• In which acid can dissolve AgCl?
• Question #ef40b | {"url":"https://socratic.org/users/solace-m/edits","timestamp":"2024-11-10T22:02:27Z","content_type":"text/html","content_length":"21281","record_id":"<urn:uuid:0da420af-f3f7-479a-a971-79164ea018bd>","cc-path":"CC-MAIN-2024-46/segments/1730477028191.83/warc/CC-MAIN-20241110201420-20241110231420-00813.warc.gz"} |
CS2 Project 1 2024, Excel
CS2 Project 1 2024, Excel 🎰
Due Date: 2024/9/26
Need help? Remember to check out Edstem and our Website for TA help assistance.
Please read the submission guidelines at the end of this assignment carefully!
Project Description 🎰
You're applying to the finance department at Marco Bellini's brand new chain of luxury casinos! You are in charge of managing the revenue from games and slots for the first few days of operation. In
this project, you will make and turn in a single Excel file with:
1. A sheet tracking profits for each location's revenue from games and slots called Profits
2. A sheet looking at profit statistics called Statistics
Project Goals
• Use Excel functions on multiple spreadsheets to calculate data
• Organize and format data into readable tables and charts
If you do not have Excel installed, start with the Excel lab to get set up before beginning this assignment. It’s recommended that you complete all labs before their associated projects.
NOTE: Do not use Google Sheets. Please make a new file using Microsoft Excel and edit the file only using Microsoft Excel.
Tasks 🎰
Task 1: Double click your "CS2" folder on your desktop, and enter your folder for "Excel". Then, create a new folder inside called "Excel Casino Project". All your files for this Project should live
in this folder.
Create a new Excel file and rename it Excel_Casino_Project, then save it to your newly created "Excel Casino Project" folder. (Check how to use save-as in lab 1 for help!).
Looks like some of the revenue data was not recorded correctly for each casino location. Let's figure out the correct values by looking at the totals of each column and row.
Task 2 Copy the table below into your first sheet. Name the sheet Profits. (You can copy and paste this directly into your excel sheet)
TABLE 1 Day 1 Profit Day 2 Profit Day 3 Profit Day 4 Profit Total Profit
Las Vegas $120,630 $115,580 $120,400 $500,960
Atlantic City $130,530 $135,485 $125,695 $532,200
Macau $115,420 $112,250 $119,390 $115,465
Monte Carlo $120,245 $130,250 $120,180
Singapore $130,585 $115,450 $125,195 $494,430
Reno $115,220 $115,230 $120,470 $483,165
Total for Each Day $725,245 $712,385 $753,975 $2,947,210
Task 3 Format the table - differently from the default - to make it easily readable and aesthetically pleasing (to your best judgment). For large tables with many different labels and data types,
this makes it easier to catch mistakes and skim data for general trends. If you’re lost, look back at the formatting section of lab! Make sure to change the table to a color of your choice!
Recall from the lab, using "dynamic formulas" means using cell references or using functions like SUM(cell:cell) to calculate values.
Task 4 Fill in the empty cells using dynamic formulas (like the ones in the lab). Typing out numbers will get you no credit.
• Before you start, highlight cells that you will fill with dynamic formulas a different color than the rest of the sheet, so you can easily check them as you go by double-clicking on them to see
what other cells are used in the calculation.
• If there is only 1 cell in a given row or column that is blank, then you can definitely find out what it is (for example, if the total sum for Day 4 was missing but the sums for each location are
all there, we can add them up to fill in the blank). If there are two cells missing in a given row or column, try solving for the other blank cells first, then going back to it.
NOTE: If you do not use dynamic formulas (i.e. you manually input the number), you will not receive credit.
Task 5 Format numbers as dollar amounts. (Look at toolbar options)
Task 6 Copy the table below on the same sheet and format it the same as the last table.
TABLE 2 Drinks Sold Revenue per Drink Sold Cost to Make Drink Profit
Las Vegas 817 3 2
Atlantic City 651 3.50 2
Macau 497 6 2
Monte Carlo 536 5 2
Singapore 482 5.50 2
Reno 577 4 2
Task 7 Fill in the empty cells by only typing in 1 dynamic formula and auto-populating the rest. Write how you did this in a cell right below this table. A couple of sentences will do.
Task 8 Format the numbers that represent dollars as dollar amounts.
Now it's time to gain some insights into our profit margins!
Task 9 Create a new sheet called "Statistics". In that sheet create three tables with a row for each location from before, and one column for each statistic below. There should be 3 separate tables.
(each having one column with rows for all locations, and one additional column for the appropriate statistic.)
• Average Profit Over 4 Days
• Highest Profit Received in 1 Day
• Your choice - pick a statistic (using a dynamic formula) to calculate
Dynamic Formulas
Task 10 Fill in each cell with dynamic formulas using cells from the Casino table in the Profits sheet. (You must use a function that calculates these values, not by manually calculating the value,
e.g. by summing then dividing manually for average.) Dynamic equations you can use, in this case, are the SUM/MAX/MIN/AVERAGE etc.
How were you able to refer to Financials in Summary from the lab?
Graphs and Charts
Task 11 Using the table you just created, create a graph for the Average Revenue Over 4 Days (using the excel AVERAGE formula) and a graph for Highest Revenue Received in 1 Day. They must be two
distinct types of graphs (e.g. bar and line) and have titles. The type of graph must be logical for the data it is representing.
Task 12 Format all number amounts that represent dollar amounts as dollar amounts.
Task 13 Name each chart appropriately to describe the data it represents.
Double-check your work 🧏♀️
The Profits sheet should have a total of two tables.
The Statistics sheet should have a total of three tables and two graphs.
Fill out our feedback form for 2 points of extra credit on this project! :)
Hand-In 🎰
To Hand-In Project 1:
Zipping files is a way to compress one or more files into a single file that is often smaller than the source files; you’ll submit all homework assignments through Canvas by uploading one zipped file
containing all of your work.
To do this
1. Rename your source files so they do not contain your name. This is especially important in order to maintain the course’s anonymous grading policy that ensures your assignments are graded fairly.
We will deduct points if your files contain identification data.
2. Make sure you have the correct, most up-to-date files before zipping. We’ve had students in the past send in older versions that didn’t contain all their finished work! You will receive a 10%
deduction if TAs must regrade your work due to incorrect files.
3. Create a .zip file
In Windows Explorer, go to the folder containing the files you want to zip. Select the files, then right-click on any of the selected files and select Send To… -> Compressed (zipped) Folder.
In Mac Finder, go to the folder containing the files you want to zip. (This would be your “Excel Project” folder) Select the files, then right-click on any of the selected files and select
Compress Items.
4. Right click on the newly created zip file to rename it. The name of your file should be BannerID_ExcelProject.zip (replace "BannerID" with your own banner id, starting with B0...)
5. Submit on Canvas under the Excel Project assignment!
Congrats! You just finished the Excel Project!
If you have any issues with completing this assignment, please reach out the course HTAs: cs0020headtas@lists.brown.edu
If you need to request an extension, contact Professor Stanford directly: don.stanford@gmail.com | {"url":"https://cs2.johnfarrell.io/projects/1.html","timestamp":"2024-11-05T05:45:58Z","content_type":"text/html","content_length":"125436","record_id":"<urn:uuid:82207846-5e7b-4d17-85a7-9969de1bca3d>","cc-path":"CC-MAIN-2024-46/segments/1730477027871.46/warc/CC-MAIN-20241105052136-20241105082136-00491.warc.gz"} |
Golden Integral Calculus By N P Bali
His books on the following topics are well-known for their easy comprehension and lucid presentation: algebra, trigonometry, differential calculus, integral.... Golden integral calculus Golden maths
series. Material. Type. Book. Language English. Title. Golden integral calculus Golden maths series. Author(S) N. P. Bali.... This Pin was discovered by Name your price for Natural Remedies, Books,
Bollywood DVDs - 20k+ orders sold. Discover (and save!) your own Pins on Pinterest.. Golden Integral Calculus by N. P. Bali. Buy Golden Integral Calculus online for Rs. () - Free Shipping and Cash on
Delivery All Over India!. Buy Golden Integral Calculus Eleventh edition (2011) by N.P. Bali Books Online shopping at low Price in India. Read Books information, ISBN:9789380298511.... Read Golden
Integral Calculus book reviews & author details and more at ... About The Author: N.P. Bali is a prolific author of over 100 books for degree and.... N. P. Bali. GOLDEN INTEGRAL CALCULUS Sol. (/)
(log sec x) = - . sec x tan x = tan x tan* I : - ox = log (log sec x) J log sec* ' - ; [Note. The student may also.... Golden Integral Calculus by N. P. Bali. our price 230, Save Rs. 0. Buy Golden
Integral Calculus online, free home delivery. ISBN : 8170081696.... N. P. Bali. W Other Books in the Series By : N.P. BALI Golden Statics Golden ... Golden Solid Geometry Golden Integral Calculus
Golden Analysis Golden Vector.... User Review - Flag as inappropriate. Best book for Integral Calculus Practice. Selected pages. Title Page. Bibliographic information. QR code for Golden.... N. P.
Bali. LAXMI PUBLICATIONS (P) LTD 22, Golden House, Daryaganj, New ... Golden Integral Calculus All Rights Reserved with the Publishers. Price : Rs.. Golden Integral Calculus by N. P. Bali ISBN 13:
9789380298511. ISBN 10: 938029851x. Unknown; New Delhi: Laxmi Publicationss Pvt. Ltd., 2011; ISBN-13:.... Golden Integral Calculus book. Read reviews from world's largest community for readers. The
book meets the requirements of students of Degree and Honours.... Buy Golden Differential Calculus on Amazon.com FREE SHIPPING on qualified orders.. Golden Integral Calculus : N. Ayurveda Books,
Calculus, Homeopathy, Economics, Textbook. Saved from readplaylove.me. Golden Integral Calculus : N. P. Bali.. Golden Integral Calculus by Bali, N. at AbeBooks.co.uk - ISBN 10: ... Golden Integral
Calculus. N. P. Bali. Published by Firewall/Laxmi Publications (P) Ltd., New.... Golden, N. P. Bali ... AND sERIEs * SOLID GEOMETRY * STATICS * STATIS'I'ICS * THEORY OF NuMEERs * vEcToR ALGEBRA *
vEcroR CALCULUS etc.
Golden Integral Calculus by Laxmi Publications is useful and the best choice among Honours & Competition Exams. This book is a must include basis for.... Differential Equations (Golden Maths Series)
- N. P. Bali - Free ebook download as PDF File ... A Text Book of Integral Calculus BY ak sharma.. Golden Integral Calculus 01 Edition by N. P. Bali from Flipkart.com. Only Genuine Products. 30 Day
Replacement Guarantee. Free Shipping. Cash On Delivery!
codigo egipto robert bauval pdf 26
Vladmodels COMPLETE Collection 2002 2010 RAR 113.848719
TomTom Scandinavian Street Navigator free download
Windows 10 Insider Preview Build 17655 en-US (RS5) utorrent
athan pro full version 18
Tamil Bang Bang Free Download
x gauge active sky next crack
modern economics hl ahuja pdf download
AVIA Scan2CAD PRO V8 2e
beyond nj 9842 the siachen saga ebook download | {"url":"https://aflariti.mystrikingly.com/blog/golden-integral-calculus-by-n-p-bali","timestamp":"2024-11-06T02:26:28Z","content_type":"text/html","content_length":"86343","record_id":"<urn:uuid:bfa5b7a1-cdd2-4d15-97c2-105d244e39e8>","cc-path":"CC-MAIN-2024-46/segments/1730477027906.34/warc/CC-MAIN-20241106003436-20241106033436-00837.warc.gz"} |
An LCD Sunset Timer in C#, Part 1
published jan 9 2008
An important tradition between a few people at my office is the daily viewing of the sunset. I’m not really sure how exactly, but at some point, it was discovered that from our office parking lot, we
have a relatively unhindered view of the beautiful Arizona sunset. Combine this with programmers eager to quit coding for a while, and our lack of windows, and you’ve got a daily ritual. Well, back
in December, I was rooting around in The Box, a box of random computer-y ephemera, when I discovered a Crystalfontz USB LCD leftover from a previous project, just sitting there looking sad and
lonely. My coworkers quickly came up with the purpose for this thing: a countdown to sunset. We already had The Orb setup to grow redder as sunset approached, but found it sometimes was laggy and
often lost its signal in our windowless office.
C# is my language of choice for desktop applications, so I immediately set out to find a way to use it to write the controller software for the LCD. At first, I looked to the Crystalfontz LCD
software, but found the software to be poorly documented, and plugins difficult to write, requiring that a DLL be written, which would be loaded by a Windows service running the in the background.
After some time fruitlessly spent searching for help on the Crystalfontz forums, I ended up finding a different program entirely: LCD Smartie. LCD Smartie has built-in support for writing plugins in
.NET, and simply requires that plugin-authors create a class with the same name as their DLL filename, which implements up to 20 public methods named function1-function20.
Knowing that this would do exactly what I wanted, I moved on to calculating the time of sunset. Fortunately, I’d recently discovered one of those obscure functions that PHP is known for, date_sunset,
and more importantly, djwice’s comment, containing links to information on the algorithm used by this function. I implemented the following sunset function using the algorithm outlined on this page.
public DateTime Sunset(DateTime date)
int dayOfYear = date.DayOfYear;
double tApprox = dayOfYear + ((18 - LON / 15) / 24);
double meanAnomaly = (0.9856 * tApprox) - 3.289;
double sunTrueLon = meanAnomaly + (1.916 * Sin(meanAnomaly)) + (0.020 * Sin(2 * meanAnomaly)) + 282.634;
if (sunTrueLon > 360) while (sunTrueLon > 360) sunTrueLon -= 360;
if (sunTrueLon < 0) while (sunTrueLon < 0) sunTrueLon += 360;
double rightAscension = Atan(0.91764 * Tan(sunTrueLon));
if (rightAscension > 360) while (rightAscension > 360) rightAscension -= 360;
if (rightAscension < 0) while (rightAscension < 0) rightAscension += 360;
rightAscension = rightAscension + 90 * (Math.Floor(sunTrueLon / 90) - Math.Floor(rightAscension / 90));
rightAscension = rightAscension / 15;
double sinDec = .39782 * Sin(sunTrueLon);
double cosDec = Cos(Asin(sinDec));
double cosHour = (Cos(ZENITH) - sinDec * Sin(LAT)) / (cosDec * Cos(LAT));
double hour = Acos(cosHour) / 15;
double time = hour + rightAscension - (0.06571 * tApprox) - 6.622;
time = time - LON / 15;
time -= 7;
while (time < 0) time += 24;
while (time > 24) time -= 24;
DateTime sunset = new DateTime(date.Year, date.Month, date.Day, (int)time, (int)((time - (int)time) * 60), 0);
return sunset;
Since geography is done using degrees, but math is done in radians, I decided to write my own trig functions that handled the conversion for me. I’m sure you all know how to do that ( :p ), but in
case you don’t, here are cosine and arccosine, from which you should be able to extrapolate to figure out the rest.
private double Cos(double degrees)
return Math.Cos(Math.PI / 180 * degrees);
private double Atan(double x)
return 180 / Math.PI * Math.Atan(x);
Also note that I use the constants LAT (latitude), LON (longitude) and ZENITH. latitude and longitude are simply the ones corresponding to your location (lookup here), and the standardised value for
the zenith is given in the above algorithm link to be 90° 50’, or 90.83333°. After some fiddling, I found that the above code in fact generated the same exact sunset time as the one printed in my
local papers. With that done, I moved on to writing the plugin and tweaking the timer to display well on the LCD. | {"url":"https://davidthomasbernal.com/blog/2008/01/09/an-lcd-sunset-countdown-timer-using-c-part-1","timestamp":"2024-11-05T02:37:40Z","content_type":"text/html","content_length":"28929","record_id":"<urn:uuid:d2404943-58b6-497f-897c-44bfce396311>","cc-path":"CC-MAIN-2024-46/segments/1730477027870.7/warc/CC-MAIN-20241105021014-20241105051014-00035.warc.gz"} |
When it's raining what's the best way to keep dry - Run or Walk ? - guernseydonkey.com
When it’s raining what’s the best way to keep dry – Run or Walk ?
When it then starts raining and you don’t have your umbrella with you the age old question is whether you should run or walk. If you run, think of all those extra raindrops that you are colliding
with which you would otherwise have missed. On the other hand, if you walk you will be out in the rain for longer, catching lots of rain on your shoulders. Some serious mathematical thought has gone
into this question over the years.
One Answer
In a Nutshell : The conclusion has been that, to stay as dry as possible, you should run as fast as you can. Common sense probably told you the same thing.
However, (There’s ALWAYS one of those aren’t there!) there is a surprising twist to this problem. The standard solution assumes that the rain is falling vertically. What happens if there is wind and
the rain is falling at an angle?
When rain falls vertically and you are standing still, the drops only hit your head and shoulders. If there is wind coming from behind you, however, then some of the rain will also hit your back even
when you are standing still. The rain has a horizontal speed as well as a vertical downward speed (hence it’s slant). The surprising twist is that when the rain is coming from behind you, it is
sometimes better to walk than run. However, this only applies if you are able to move faster than the horizontal speed of the rain.
Let’s do (some) Maths
Why it is sometimes drier to walk in the rain than run?
To simplify the calculation, let’s assume that the pedestrian is a rectangular block of wood.
There are seven factors that we have taken into account:
V is the speed at which the rain is falling K is the angle at which the rain is falling D is the density of the rain (in kg per cubic meter) A[t] is the area of the pedestrian’s top A[f] is the area
of the pedestrian’s front H is the distance to the pedestrian’s destination V[p] is the speed at which the pedestrian runs
There isn’t space to put in all the algebra, but the way we produced the formula below was to work out separately how much rain hits the front and the top of the pedestrian and then added these two
together. The total rain in kilograms falling on the pedestrian as long as he is travelling at least as fast as the horizontal speed of the rain is:
The important part of the formula is the bit in the brackets. If A[f] /A[t]Tan K comes to more than 1.0 then the right hand part of the formula becomes negative, i.e. the rain hitting the pedestrian
is reduced. The pedestrian can control his speed V[p]f /A[t]Tan K is greater than 1. (Take a deep breath!)
The ratio of a person’s front area to their top is usually about 5.0. Since the tangent of 15° is about 0.2, this means that if rain is falling at an angle of more than 15°, the driest way to get
home without an umbrella is to move at the same speed as the horizontal speed of the rain.
To Sum Up
However, to sum up, the conclusion is this:
If the rain is falling vertically then you should run as fast as you can.
If you are a person of typical build and the rain is coming from behind you at the speed of a gentle walking pace, you will be hit by less rain if you amble along than if you run full pelt.
In other words, there are circumstances when it is better to walk than run! The reason for this apparently odd outcome is that under the conditions described, if you run faster, the additional rain
hitting your front is greater than the loss of rain hitting your head by taking less time to make it home.
Of course by the time you’ve worked all this out you will be wetter than if you had not known about the formula at all! | {"url":"https://guernseydonkey.com/when-its-raining-whats-the-best-way-to-keep-dry-run-or-walk/","timestamp":"2024-11-03T07:47:47Z","content_type":"text/html","content_length":"77049","record_id":"<urn:uuid:41d5d826-57b1-4367-9e77-2a22e18f4d26>","cc-path":"CC-MAIN-2024-46/segments/1730477027772.24/warc/CC-MAIN-20241103053019-20241103083019-00416.warc.gz"} |
Can you get axle ratio from VIN number?
Can you get axle ratio from VIN number?
Axle ratios can sometimes be obtained off transmission labels, but those are not necessarily accessible. For the easiest approach to figure out the information for the common person is to obtain the
entire VIN number and contact the dealership or the GM manufacturer.
How do I find out what my axle ratio is?
Method 1: Count the number of teeth on the ring gear and the pinion. Divide the number of the ring gear’s teeth by the number of the pinion’s teeth. This will give you the axle ratio.
How do I find the axle ratio on my Ford VIN number?
How Do I Find the Axle Ratio and Limited Slip of My Ford Vehicle?
1. Locate the Safety Compliance Certification Label on the driver’s side front or rear door panel.
2. Find the word AXLE under the bar code.
3. Find the two-digit code under AXLE.
How can I tell what gear ratio I have without pulling cover?
So an easy way to determine your actual gear ratio is to check the tag attached to the differential cover by the cover bolts. On the tag there should be some numbering such as 3.54 or 3.73, either of
those numbers will give you the stock axle ratio.
Where is the gear ratio stamped?
Check the Differential Cover The axle may have a sticker, and on the differential cover, you might have a small metal tag that’s sticking out that will have the gear ratio stamped on it.
How do you find the gear ratio?
To calculate the gear ratio: Divide the number of driven gear teeth by the number of drive gear teeth. In our example, it’s 28/21 or 4 : 3. This gear ratio shows that the smaller driver gear must
turn 1,3 times to get the larger driven gear to make one complete turn.
Is gear ratio stamped on differential?
Can you tell axle ratio from Vin#?
Contact the dealer or the manufacturer (you could get a customer service number from the owners manual of the truck) and give them the VIN number and tell them you wish to know the axle ratio. They
may only need certain digits from the VIN to determine, but it’s better to have them all in case.
How do I find out the axle ratio?
How to Calculate Axle Ratio. In order to calculate axle ratio, you would count the number of teeth on the ring gear as well as the number of teeth on the pinion. Divide the number of teeth on the
ring gear by the number of teeth on the pinion in order to determine the axle ratio of a truck.
What’s is my axle ratio?
Axle ratio is the number of revolutions the output shaft or driveshaft needs to make in order to spin the axle one complete turn. The number is expressed in a ratio, which represents the number of
teeth on the ring gear divided by the number of teeth on the pinion. Oct 16 2019
What is the best axle ratio for towing?
Pickups towing big 5th wheel trailers do well equipped with 4.10:1 axle ratios. The thinking behind the decision to stick with the base axle ratio, which is typically 3.08:1 or 3.42:1, is the ratio
comes standard, so that’s what the vehicle manufacturer feels is the best setup. | {"url":"https://newsbasis.com/can-you-get-axle-ratio-from-vin-number/","timestamp":"2024-11-04T14:03:05Z","content_type":"text/html","content_length":"120850","record_id":"<urn:uuid:73f56ad7-5703-41e2-a813-112a6c2fc597>","cc-path":"CC-MAIN-2024-46/segments/1730477027829.31/warc/CC-MAIN-20241104131715-20241104161715-00205.warc.gz"} |
Non-stationary wave turbulence in elastic plates: a numerical investigation
Abstract / Description of output
Nonlinear (large amplitude) vibrations of thin elastic plates can exhibit strongly nonlinear regimes characterized by a broadband Fourier spectrum and a cascade of energy from the large to the small
wavelengths. This particular regime can be properly described within the framework of wave turbulence theory. The dynamics of the local kinetic energy spectrum is here investigated numerically with a
finite difference, energy-conserving scheme, for a simply-supported rectangular plate excited pointwise and harmonically.
Damping is not considered so that energy is left free to cascade until the highest simulated frequency is reached. The framework of non-stationary wave turbulence is thus appropriate to study
quantitatively the numerical results. In particular, numerical simulations show the presence of a front propagating to high frequencies, leaving a steady spectrum in its wake, which has the property
of being self-similar. When a finite amount of energy is given at initial state to the plate which is then left free to vibrate, the spectra are found to be in perfect accordance with the
log-correction theoretically predicted. When forced vibrations are considered so that energy is continuously fed into the plate, a slightly steeper slope is observed in the low-frequency range of the
spectrum. It is concluded that the pointwise forcing introduces an anisotropy that have an influence on the slope of the power spectrum, hence explaining one of the discrepancies reported in
experimental studies.
Original language English
Title of host publication Proceedings of the European Nonlinear Dynamics Conference
Number of pages 2
Publication status Published - Jul 2014
Event ENOC 2014 - Vienna, Austria
Duration: 6 Jul 2014 → 11 Jul 2014
Conference ENOC 2014
Country/Territory Austria
City Vienna
Period 6/07/14 → 11/07/14
Dive into the research topics of 'Non-stationary wave turbulence in elastic plates: a numerical investigation'. Together they form a unique fingerprint.
• 1/01/12 → 31/12/16
Project: Research | {"url":"https://www.research.ed.ac.uk/en/publications/non-stationary-wave-turbulence-in-elastic-plates-a-numerical-inve","timestamp":"2024-11-08T01:38:29Z","content_type":"text/html","content_length":"57384","record_id":"<urn:uuid:ba9ed714-443b-47be-bcd6-cf52aa61a72e>","cc-path":"CC-MAIN-2024-46/segments/1730477028019.71/warc/CC-MAIN-20241108003811-20241108033811-00086.warc.gz"} |
2-Dimensional Context-Free Grammar (2D-CFG) for 2-dimensional input text is introduced and efficient parsing algorithms for 2D-CFG are presented. In 2D-CFG, a grammar rule’s right hand side symbols
can be placed not only horizontally but also vertically. Terminal symbols in a 2-dimensional input text are combined to form a rectangular region, and regions are combined to form a larger region
using a 2-dimensional phrase structure rule. The parsing algorithms presented in this paper are the 2D-Ear1ey algorithm and 2D-LR algorithm, which are 2-dimensionally extended versions of Earley’s
algorithm and the LR(O) algorithm, respectively.
Anthology ID:
Pittsburgh, Pennsylvania, USA
Carnegy Mellon University
Cite (ACL):
Masaru Tomita. 1989. Parsing 2-Dimensional Language. In Proceedings of the First International Workshop on Parsing Technologies, pages 414–424, Pittsburgh, Pennsylvania, USA. Carnegy Mellon
Cite (Informal):
Parsing 2-Dimensional Language (Tomita, IWPT 1989)
Copy Citation: | {"url":"https://anthology.aclweb.org/W89-0243/","timestamp":"2024-11-10T16:24:05Z","content_type":"text/html","content_length":"19958","record_id":"<urn:uuid:9ebb8079-99ce-47c7-96d6-8242cdf3af36>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.60/warc/CC-MAIN-20241110134821-20241110164821-00193.warc.gz"} |
What is the spring constant of rubber?
What is the spring constant of rubber?
Spring constant of the rubber band is k=45.0N/m.
What is the constant in Coulomb’s law?
This equation is known as Coulomb’s law, and it describes the electrostatic force between charged objects. The constant of proportionality k is called Coulomb’s constant. In SI units, the constant k
has the value. k = 8.99 × 10 9 N ⋅ m 2 /C 2. This means that the force between the particles is repulsive.
What is the spring constant of a spring?
Spring constant is a measure of the stiffness of a spring up to its limit of proportionality or elastic limit. The limit of proportionality refers to the point beyond which Hooke’s law is no longer
true when stretching a material.
What is the law of spring constant?
Hooke’s law is a law of physics that states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, Fs = kx, where k is a
constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible …
Why does the spring constant change?
The more compliant (or softer) the spring is the more it moves for the same amount of force. The spring constant is simply the inverse of the compliance and sometimes also called stiffness. The
stiffer the spring, the less it moves or, conversely, the more force is required to get the same displacement.
What is a common spring constant?
Spring constant is the amount of force required to move the spring a set amount of distance. Extension springs have the same units of measurements as compression springs, however torsion spring
constant is calculated in force per 360 degrees of travel.
What is the constant k?
The Coulomb constant, the electric force constant, or the electrostatic constant (denoted ke, k or K) is a proportionality constant in electrostatics equations. In SI units it is equal to
8.9875517923(14)×109 kg⋅m3⋅s−2⋅C−2.
What affects the spring constant?
Factors affecting spring constant: Wire diameter: The diameter of the wire of the spring. Coil diameter: The diameters of the coils, depending on the stiffness of the spring. Free length: Length of
the spring from equilibrium at rest.
Does a spring constant depend on how far the spring is stretched?
More generally, the spring constant of a spring is inversely proportional to the length of the spring, assuming we are talking about a spring of a particular material and thickness. That is because
the spring constant and the length of the spring are inversely proportional.
What kind of constant is k in Coulomb’s law?
K or εr is also called a dielectric constant of the medium in which the two charges are placed. History of Coulomb’s Law A French physicist Charles Augustin de Coulomb in 1785 coined a tangible
relationship in mathematical form between two bodies that have been electrically charged.
How is the spring constant of a spring determined?
The following is Hooke’s law formula for determining the spring constant of a spring: x is the displacement (m) (positive for displacement, negative for compression) A spring constant is a measure of
a spring’s ability to resist compression and elongation. The higher the spring constant, the harder it is to compress or stretch it.
How does Coulomb’s law relate to free space?
According to Coulomb’s law, the force of attraction or repulsion between two charged bodies is directly proportional to the product of their charges and inversely proportional to the square of the
distance between them. It acts along the line joining the two charges considered to be point charges. ε0 is the permittivity of free space.
Are there any problems with the Coulomb law?
Problems on Coulombs Law Problem 1: Charges of magnitude 100 microcoulomb each are located in vacuum at the corners A, B and C of an equilateral triangle measuring 4 meters on each side. If the
charge at A and C are positive and the charge B negative, what is the magnitude and direction of the total force on the charge at C?
What is the spring constant of rubber? 45.0N/m Spring constant of the rubber band is k=45.0N/m. What is the constant in Coulomb’s law? This equation is known as Coulomb’s law, and it describes
the electrostatic force between charged objects. The constant of proportionality k is called Coulomb’s constant. In SI units, the constant k has… | {"url":"https://www.ohare-airport.org/what-is-the-spring-constant-of-rubber/","timestamp":"2024-11-06T19:04:07Z","content_type":"text/html","content_length":"37205","record_id":"<urn:uuid:32578c41-a139-4938-80b7-5153689744b3>","cc-path":"CC-MAIN-2024-46/segments/1730477027933.5/warc/CC-MAIN-20241106163535-20241106193535-00439.warc.gz"} |
Recursive Maximum Likelihood Algorithm for Dependent Observations
A recursive maximum-likelihood algorithm (RML) is proposed that can be used when both the observations and the hidden data have continuous values and are statistically dependent between different
time samples. The algorithm recursively approximates the probability density functions of the observed and hidden data by analytically computing the integrals with respect to the state variables,
where the parameters are updated using gradient steps. A full convergence proof is given, based on the ordinary differential equation approach, which shows that the algorithm converges to a local
minimum of the Kullback-Leibler divergence between the true and the estimated parametric probability density functions-a result that is useful even for a miss-specified parametric model. Compared to
other RML algorithms proposed in the literature, this contribution extends the state-space model and provides a theoretical analysis in a nontrivial statistical model that was not analyzed so far. We
further extend the RML analysis to constrained parameter estimation problems. Two examples, including nonlinear state-space models, are given to highlight this contribution.
Bibliographical note
Publisher Copyright:
© 1991-2012 IEEE.
• Maximum likelihood estimation
• expectation-maximization algorithms
• recursive estimation
Dive into the research topics of 'Recursive Maximum Likelihood Algorithm for Dependent Observations'. Together they form a unique fingerprint. | {"url":"https://cris.biu.ac.il/en/publications/recursive-maximum-likelihood-algorithm-for-dependent-observations-5","timestamp":"2024-11-04T18:19:57Z","content_type":"text/html","content_length":"58064","record_id":"<urn:uuid:d26bb498-378e-4553-ad4e-856ccdd50157>","cc-path":"CC-MAIN-2024-46/segments/1730477027838.15/warc/CC-MAIN-20241104163253-20241104193253-00657.warc.gz"} |
Mass balance accounting
6.9. Mass balance accounting
The global mass balance of an ice sheet reads
\[\frac{\mathrm{d}V}{\mathrm{d}t} = \mathrm{SMB} + \mathrm{BMB} + \mathrm{CALV}\,,\]
where \(\mathrm{d}V/\mathrm{d}t\) is the rate of volume change, SMB the total surface mass balance, BMB the total basal mass balance and CALV the total calving rate (all counted as positive for a
volume gain and negative for a volume loss). SICOPOLIS attempts at closing this balance as accurately as possible by applying the so-called “hidden ablation scheme” (Calov et al. [13]).
SICOPOLIS always employs a zero-ice-thickness boundary condition at the margin of the computational domain (\(i=0,\,i_\mathrm{max}\); \(j=0,\,j_\mathrm{max}\)). However, for accurate accounting of
calving near the margin, the “hidden ablation scheme” also requires the next lines of grid points (\(i=1,\,i_\mathrm{max}-1\); \(j=1,\,j_\mathrm{max}-1\)) to be ice-free. Since this is not always
desirable, it can be controlled by the run-specs-header parameter MB_ACCOUNT:
• 0: Glaciation of all inner points of the domain allowed (prevents accurate accounting of calving near the margin).
• 1: Outermost inner points of the domain (\(i=1,\,i_\mathrm{max}-1\); \(j=1,\,j_\mathrm{max}-1\)) not allowed to glaciate (required for accurate accounting of calving near the margin).
For real-world problems, the setting MB_ACCOUNT = 1 is usually fine. However, for some simple-geometry experiments that require the simulated ice sheet to cover the entire domain [e.g., the test
simulation repo_vialov3d25 (3D Vialov profile)], MB_ACCOUNT = 0 must be chosen to allow that. | {"url":"https://sicopolis.readthedocs.io/en/ad/modelling_choices/mb_account.html","timestamp":"2024-11-10T04:15:11Z","content_type":"text/html","content_length":"12992","record_id":"<urn:uuid:9044d766-f26c-4943-beae-81ece192ebc5>","cc-path":"CC-MAIN-2024-46/segments/1730477028166.65/warc/CC-MAIN-20241110040813-20241110070813-00447.warc.gz"} |
How do you convert 153 hr to s? | Socratic
How do you convert 153 hr to s?
1 Answer
Use the factor-label method with factors $\left(60 \text{ min")/(1" hr") and (60" s")/(1" min}\right)$.
$\left(153 \text{ hr")/1(60" min")/(1" hr")(60" s")/(1" min}\right)$
Please observe how the units cancel.
First the hours cancel:
#(153cancel(" hr"))/1(60" min")/(1cancel(" hr"))(60" s")/(1" min")#
Next the minutes cancel:
$\left(153 \cancel{\text{ hr"))/1(60cancel(" min"))/(1cancel(" hr"))(60" s")/(1cancel(" min}}\right)$
Seconds are the only remaining units, therefore, we do the multiplication:
#(153cancel(" hr"))/1(60cancel(" min"))/(1cancel(" hr"))(60" s")/(1cancel(" min")) = 153(60)(60)" s" = 550800" s"#
Impact of this question
1417 views around the world | {"url":"https://api-project-1022638073839.appspot.com/questions/how-do-you-convert-153-hr-to-s","timestamp":"2024-11-06T10:52:32Z","content_type":"text/html","content_length":"34428","record_id":"<urn:uuid:114f34d4-9a49-4cb1-b25e-63efba9a2b21>","cc-path":"CC-MAIN-2024-46/segments/1730477027928.77/warc/CC-MAIN-20241106100950-20241106130950-00823.warc.gz"} |
#include <CGAL/draw_triangulation_3.h>
◆ draw()
template<class T3 >
void CGAL::draw ( const T3 & at3 )
#include <CGAL/draw_triangulation_3.h>
opens a new window and draws at3, a model of the TriangulationDataStructure_3 concept.
A call to this function is blocking, that is the program continues as soon as the user closes the window. This function requires CGAL_Qt5, and is only available if the macro CGAL_USE_BASIC_VIEWER is
defined. Linking with the cmake target CGAL::CGAL_Basic_viewer will link with CGAL_Qt5 and add the definition CGAL_USE_BASIC_VIEWER.
Template Parameters
T3 a model of the TriangulationDataStructure_3 concept.
at3 the triangulation to draw. | {"url":"https://doc.cgal.org/5.5/Triangulation_3/group__PkgDrawTriangulation3.html","timestamp":"2024-11-12T19:43:28Z","content_type":"application/xhtml+xml","content_length":"11254","record_id":"<urn:uuid:0323d2a0-eb87-47f0-8d73-8417f7710622>","cc-path":"CC-MAIN-2024-46/segments/1730477028279.73/warc/CC-MAIN-20241112180608-20241112210608-00561.warc.gz"} |
C Program to Find GCD of Two Numbers Using Recursion - CodingBroz
C Program to Find GCD of Two Numbers Using Recursion
In this post, we will learn how to find GCD of two numbers using recursion in C Programming language.
The greatest common divisor (GCD) of two nonzero integers a and b is the greatest positive integer d such that d is a divisor of both a and b.
We will define a custom recursive function which will calculate the GCD of two numbers.
So, without further ado, let’s begin this tutorial.
C Program to Find GCD of Two Numbers Using Recursion
// C Program To Find GCD of Two Number Using Recursion
#include <stdio.h>
int GCD(int x, int y);
int main(){
int a, b;
// Asking for Input
printf("Enter Two Positive Integers: \n");
scanf("%d\n %d", &a, &b);
printf("GCD of %d and %d is %d.", a, b, GCD(a, b));
return 0;
int GCD(int x, int y){
if( y != 0)
return GCD(y, x % y);
return x;
Enter Two Positive Integers:
GCD of 40 and 412 is 4.
How Does This Program Work ?
int a, b;
In this program, we have declared two int data type variables named as a and b.
// Asking for Input
printf("Enter Two Positive Integers: \n");
scanf("%d\n %d", &a, &b);
Then, the user is asked to enter the value of two integers. The value of these two integers will get stored in a and b respectively.
printf("GCD of %d and %d is %d.", a, b, GCD(a, b));
We print the GCD of two numbers using printf() function. Here, we called our custom function which will calculate the GCD of two numbers.
int GCD(int x, int y){
if( y != 0)
return GCD(y, x % y);
return x;
We have declared a recursive function named GCD which will compute and return the GCD of two numbers.
I hope after going through this post, you understand how to find gcd of two numbers using recursion in C Programming language.
If you have any doubt regarding the program, feel free to contact us in the comment section. We will be delighted to help you
Also Read:
Leave a Comment | {"url":"https://www.codingbroz.com/c-program-to-find-gcd-of-two-numbers-using-recursion/","timestamp":"2024-11-10T10:53:12Z","content_type":"text/html","content_length":"179358","record_id":"<urn:uuid:11126a94-d7f6-48fe-95fb-2c448fc714b6>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00230.warc.gz"} |
Other Probability Distributions – Q&A Hub – 365 Data Science
Resolved: Other Probability Distributions
Hello. I understand that other probability distributions are not included in this course (i.e., Geometric, Negative binomial, Beta, Gamma, etc.). Is it possible that these PDFs do not appear so often
in data science, which is why you excluded it?
2 answers ( 1 marked as helpful)
Dear Carl,
Thank you for your question!
It would have indeed been great to include other types of probability distributions in this course. However, it would've become way too long :) What we have done here is to lay the foundations of
probability theory as well as introduce the most frequently used distributions in the field of data science. Having mastered that, students would be ready to dive deeper and conduct independent
research on the more difficult sections of probability and statistics.
Kind regards,
365 Hristina
I see. Thank you, Hristina. I think I would have loved to see those. Could you recommend some titles/links of some books/reference materials for Probability and Statistics? | {"url":"https://365datascience.com/question/other-probability-distributions/","timestamp":"2024-11-02T23:11:49Z","content_type":"text/html","content_length":"111324","record_id":"<urn:uuid:b6d3eab0-3acf-450f-a726-6d75de8fff20>","cc-path":"CC-MAIN-2024-46/segments/1730477027768.43/warc/CC-MAIN-20241102231001-20241103021001-00706.warc.gz"} |
Seminar abstract
Fast Sparse Regression with Guarantees but not the Bias
Wotao Yin
Department of Mathematics of UCLA
Abstract: We introduce a new sparse regression method that has a number of theoretical and computational properties but doesn't have the bias found in LASSO and other L1-like sparse regression
methods. Known since Jianqing Fan and Runze Li'S publication in 2001, points on a LASSO path are biased．In order to avoid the bias, instead of the convex L1 energy used in LASSO, one must minimize a
nonconvex energy and thus sacrifice the computational advantages of convex minimization. Our new method generates a regularization path by evolving an ordinary differential inclusion, which involves
the subdifferential of the L1 energy. We show that there exists a point on the generated path that is the unbiased estimate of the true signal and whose entries have the signs consistent with those
of the true signal. All of these are achieved without any debiasing post-processing. In fact, it works better than LASSO combined with debiasing. We also show how to efficiently compute our path both
exactly and inexactly but much faster. The exact path can be computed in finitely many steps at a low cost per step. For problems with terabytes of data, we generate an approximate regularization
path by so-alled Linearized Bregman iteration, which is fast and easy to parallelize while still holding the sign—consistency property but is slightly biased．This is joint work with Stanley Osher
(UCLA), Feng Ruan(Stanford), Jiechao Xiong(PKU), Ming Yah(Michigan State), and Yuan Yao(PKU).
Bio: Wotao Yin is a professor in the Department of Mathematics of UCLA. His research interests lie in computational optimization and its applications in image processing, machine learning, and other
inverse problems. He received his B.S. in mathematics from Nanjing University in 2001, and then M.S. and Ph.D. in operations research from Columbia University in 2003 and 2006, respectively. During
2006-2013, he was with Rice University. He won NSF CAREER award in 2008 and alfred P.Sloan Research Fellowship in 2009. His recent work has been in optimization algorithms for large-scale and
distributed signal processing and machine learning problems. | {"url":"http://www.lamda.nju.edu.cn/seminar_150827.ashx","timestamp":"2024-11-11T18:02:18Z","content_type":"application/xhtml+xml","content_length":"35055","record_id":"<urn:uuid:8a5bc4dc-1732-4f6d-a806-71438c73687d>","cc-path":"CC-MAIN-2024-46/segments/1730477028235.99/warc/CC-MAIN-20241111155008-20241111185008-00239.warc.gz"} |
Prime256v1 secp256r1
prime256v1 secp256r1 NIST P-256 is :secp256r1 rather than :prime256v1. When generating EC keys, use one of these three. 6. For example: NIST P-256 is refered to as secp256r1 and prime256v1. The main
body of the document focuses on the specification of recommended elliptic curve domain # generate secp256r1 curve EC key pair # Note: openssl uses the X9. 10045. Apr 11, 2018 · Since the default
Nginx+OpenSSL/LibreSSL setting, either “ X25519 ” or “ secp256r1 ” (actually “ prime256v1 “), also lowers the score. pem. com> P256 is also known as SECG' secp256r1 and ANSI' prime256v1. For example,
X25519 (in Java) takes around 0. Different names, but they are all the same. 5 Organization This document is organized as follows. 1 notation) (dot notation) (OID-IRI notation) Description: 256-bit
Elliptic Curve Cryptography . Also, secp192r1 is synonymous and interchangeable with prime192v1. Aug 05, 2020 · openssl ecparam -name prime256v1 -genkey -noout -out rootCA. NIST P-384 1. BITSTREAM
TYPES The first required argument to PACSign is the bitstream type identifier. 132. pem May 12, 2016 · The issue is why Satoshi chose to use the elliptic curve known as secp256k1 as the basis for the
elliptic curve digital signature algorithm (ECDSA) proving ownership of coin in BTC, and why I chose to use a different curve (prime256v1 aka X9_62_prime256v1 aka P256). Package size increased by
about 900 bytes (arm). For example, the strings secp256r1, 1. ecdh ec elliptic curve crypto private public key pem spki. 62 prime256v1 refer to the same curve. g. 509 PKI It is also known as NIST
P-256. You can use the curve names to create parameter specifications for EC parameter generation with the ECGenParameterSpec class or the NamedParameterSpec class for the curves X25519 and X448 See
full list on pypi. If you use any other curve, then some widespread Web browsers (e. sh but both only noticed x25519 and secp384r1. 62 and SECP. You can run this command as well to display a list of
available to use curves otherwise: Page 2 SEC 2: Recommended Elliptic Curve Domain Parameters Ver. 5. key To generate ecdsa-secp256r1 key using openssl Section 2. SEC2v1 states 'E was chosen
verifiably at random as specified in ANSI X9. . Later versions include support for Brainpool curves. 7 prime256v1 secp256r1 The NIST 256 bit curve, its OID, X9. For the device you create on the
BlackBerry IoT Platform, generate a digital certificate using the CSR from the previous step. y^2 \equiv x^3 + ax + b y2 ≡ x3 +ax + b. 1 192 384 7680 r secp521r1 2. openssl ecparam -name secp256r1
-genkey -out ec_key. 5 • Published 3 years ago myca. openssl ecparam -list_curves In this example, I am using prime256v1 (secp256r1), which is suitable for JWT signing; this is the curve used for
JOSE's ES256. Also known as: P-256 prime256v1. secp256r1. 10045) X9F If you choose the ecdsa algorithm then bits will be an EC curve name (by default secp256r1, also known as prime256v1). You will
get an error: Unknown curve name: prime256v1. Source code for pycoin. Generating valid ECDSA secp256r1/prime256v1 key pair on Android, using Spongy Castle (Bouncy Castle distribution) Ask Question
Asked 4 years, 9 months ago. For 256-bit primes, in addition to the NIST curve de ned over F p 256, SEC2 also proposes a curve named secp256k1 de ned over F p where p= 2256 232 977 . For this
demonstration, I will be using the secp256r1 curve. 62 prime256v1 (alias secp256r1, NIST P-256 Is NID_X9_62_prime256v1 the strongest? First of all, it depends on *which government*, NIST is for the
USA Government only, though some allied countries may have copied their decisions. 62 1 from the seed'. Dec 27, 2016 · use the name prime256v1 instead of secp256r1 which is both the same curve. Or
rather it did recommend P-256 . Put the API SECRET, API KEY, generated key, and certificate onto the device. from. P256PublicKey: A public P-256 key (aka secp256r1 / prime256v1). 0] Creating a new
ECC key pair. Satoshi's choice has been the source of endless speculation in various forums . Aug 30, 2021 · A key generated from the P-256 curve (also known as secp256r1 or prime256v1) ES384: P-384:
A key generated from the P-384 curve (also known as secp384r1) ES512: P-521: A key generated from P-521 curve (also known as secp521r1) In particular, secp256r1 works for mbedtls, but openssl uses
prime256v1 instead. Aug 16, 2021 · P256 returns a Curve which implements NIST P-256 (FIPS 186-3, section D. Curves other than secp256r1, secp384r1 or secp521r1 are unlikely to be widely
interoperable. To create a new elliptic curve key pair, use the ECC_MakeKeys function . Signed-off-by: Eneas U de Queiroz <cotequeiroz@gmail. P384 is also known as SECG' secp384r1. If I test with
clientToolBox the reason is clear. Have a look at the section 2. In particular, secp256r1 works for mbedtls, but openssl uses prime256v1 instead. prime256v1 secp256r1. secp256r1. The nicknames were
chosen as follows. Using the keyspec secp256r1 instead works fine. 2 128 256 3072 r secp384r1 2. Other Key Types PRF Key type: EC P256 Operation: Derive PWD Key type: EC P256 Operation: Verify LIMA
Key size:1024 Operation: Derive Key Wrapping Capabilities Wrapping with Symmetric Keys In particular, the NIST Prime curves must be selected by their SECG id, e. PACSign is distributed with managers
for both OpenSSL and PKCS #11. Curve secp256r1 is not a type of curve; it is a curve, and is standardized under that name by SECG, under the name P-256 by NIST, and under the name prime256v1 by ANSI.
Nov 08, 2020 · openssl ecparam -name secp256r1 -genkey -out ec_key. 62/SECG curve over a 256 bit prime field An EC parameters file can then be generated for any of the built-in named curves as
follows: [bash]$ openssl ecparam -name secp256k1 -out secp256k1. Jul 20, 2020 · In this example, I am using prime256v1 (secp256r1), which is suitable for JWT signing; this is the curve used for
JOSE’s ES256. Optionally includes an arithmetic feature providing scalar and affine/projective point types with support for constant-time scalar multiplication, which can be used to . Internet .
Other documents can publish other name curve identifiers. NIST P-521 Mar 12, 2019 · A pure Solidity implementation of elliptic curve secp256r1 / prime256v1 / p256. y 2 ≡ x 3 + a x + b. – Steffen
Ullrich Dec 27 '16 at 15:59 @SteffenUllrich It did not work, as i was testing SSL with cipherscan and testssl. 62 and SECP aliases. 62 elliptic curve prime256v1 (aka secp256r1, NIST P-256),
SHA512withECDSA Signature verification using Java. You can create key pairs and print them in hex format using OpenSSL, e. Information is provided below so that you can test your generation of public
keys and signatures against our algorithm implementation, as well as testing the signature over the whole request body. pem For this demonstration, I will be using the secp256r1 curve. 7, NIST P-256,
and X9. 0] X25519 (ECDH only) [New in v20. prime256v1 secp256r1 The NIST 256 bit curve, its OID, X9. P-256, also known as secp256r1 and prime256v1; P-224, also known as secp224r1; P-384, also known
as secp384r1; P-521, also known as secp521r1; secp256k1 (the Bitcoin curve) Ed25519 (EdDSA only) [New in v20. secp256r1 is considered as the default curve if this option is not specified. 0. a.
ProgramData: A chunk of program data to be programmed to a specified flash address. com Current Registration Authority (recovered by parent 1. which the curves are named secp192r1, secp224r1,
secp256r1, secp384r1, secp521r1. Also: Standards for Efficient Cryptography (SEC) 2 recommended elliptic curve domain (secp256r1) View at oid-info. org RustCrypto: NIST P-256 (secp256r1) elliptic
curve NIST P-256 elliptic curve (a. 25 ms vs the secp256r1 group operation (in C) which takes around 1 ms on the same platform. SafeCurves: Introductio To specify an elliptic curve one specifies a
prime number p and then an elliptic-curve equation over the finite field F_p, i. Apr 13, 2018 · This is using the NIST P-256 curve aka secp256r1 aka prime256v1. Jun 08, 2021 · NIST P-256 elliptic
curve (a. 1 But its not able to sign properly with TPM2-Pkcs11 generated ECDSA-certificate(deviceCert. This simplifies the question a lot: in practice, average clients only support two curves, the
ones which are designated in so-called NSA Suite B: these are NIST curves P-256 and P-384 (in OpenSSL, they are designated as, respectively, "prime256v1" and "secp384r1"). Optionally includes an
arithmetic feature providing scalar and affine/projective point types with support for constant-time scalar multiplication, which can be used to implement protocols such as ECDH . The NIST 384 bit
curve, its OID and aliases. Multiple invocations of this function will return the same value, so it can be used for equality checks and switch statements. 0 1. 62) and secp256r1 (SECG), it's included
in the US National Security Agency's Suite B and is widely used in protocols like TLS and the associated X. Also known as: secp256r1 P-256. This could conceivably have a security-relevant impact if
an attacker wishes to use public r and s values when guessing whether signature verification will fail. secp256r1 prime256v1 NIST P-256 (23) secp384r1 NIST P-384 (24) secp521r1 NIST P-521 (25)
arbitrary prime curves (0xFF01) arbitrary char2 curves (0xFF02) Implementation ecdh ecdsa prime256v1 secp256r1 secp256k1. Generate a new key, "ECDSA prime256v1/secp256r1/P-256". 3), also known as
secp256r1 or prime256v1. csr) Sep 08, 2020 · The current PACs only support elliptical curve keys with the curve type secp256r1 or prime256v1. ecdsa. The algorithm chosen is ECDSA (ANSI X9. See also,
RFC 8422 Appendix A - Equivalent Curves. 4. If you are still interested in working with SECP256R1 . 62 name prime256v1 to refer to curve secp256r1, so this will generate output % openssl ecparam . 62
prime256v1 (alias secp256r1, NIST P-256) An elliptic curve key pair (on P-256 / secp256r1 / prime256v1). A randomly generated curve. or oid. The main purpose of this contract is verification of ECDSA
signatures based on curve secp256r1 / prime256v1 / p256. 2 Answers2. EJBCA uses the keyspec prime256v1 but Utimaco does not know of this name. As usual the OIDs may optionally be prefixed with the
string OID. Openssl secp256r1. Please refer to RFC4492 appendix A for a mapping table. 34 nistp384 secp384r1. Name of this Curve is "P-256". px5g uses mbedtls, but short NIST curve names P-256 and
P-384 are specifically supported. Initial prototyping shows that an implementation in Java is fast enough for typical purposes. There is no practical way to do EC operations on other curves, like
prime256v1, except to build the operations yourself, which would likely be quite expensive. We need to be able to choose better. But sometimes, other names are used, for example P-192 and P-256 are
named prime192v1 and prime256v1 in OpenSSL. The OpenSSL supports secp256r1, it is just called prime256v1. 1 in RFC 5480. Note: secp256r1 is synonymous and interchangeable with prime256v1. 256 -bit
prime field Weierstrass curve. Hi there, I'm trying to use nrfutil generate package with an extern key pair generated with openSSL. Each name . It also happens to be the by far the most common
elliptic curve used in cryptography. 62) NIST P-256 elliptic curve known as prime256v1 or secp256r1. NIST P-256 1. -- Note that in [PKI-ALG] the secp192r1 curve was referred to as-- prime192v1 and
the secp256r1 curve was referred to as-- prime256v1. The NIST 256 bit curve, its OID and aliases. NIST P-521 secp521r1 The NIST 521 bit curve and its SECP alias. The key curves can be prime256v1,
secp256r1, nistp256, secp256k1, secp384r1, . native. To verify a signature, use the function Only 3 curves are supported: [prime256v1, secp256r1, ansiX9p256r1], [prime384v1, secp384r1, ansiX9p384r1]
and [prime521v1]. key -aes128 That should give you some output: read EC key using curve name prime256v1 instead of secp256r1 writing EC key Enter PEM pass phrase: Verifying - Enter PEM pass phrase:
Aug 22, 2014 · secp256r1 (aka prime256v1) brainpoolP192r1; brainpoolP224r1; brainpoolP256r1; brainpoolP320r1; secp192k1; secp256k1 (the Bitcoin curve) Only the first two curves are also supported by
OpenSSL up to 1. Use the secp256r1 (prime256v1) elliptic curve to generate a CSR and private key. ANSI X9. 2. This should prove to be sufficient, in some cases you may get the message using curve
name prime256v1 instead of secp256r1 which is normal. 3. NIST P-256 is a Weierstrass curve specified in FIPS 186-4: Digital Signature Standard (DSS): Also known as prime256v1 (ANSI X9. Link to this
function Elliptic curves: NIST P-256, P-384, P-521 (secp256r1/prime256v1, secp384r1/prime384v1, secp521r1/prime521v1), brainpoolP256r1, brainpoolP384r1, brainpoolP512r1 External hash algorithms:
SHA-256, SHA-384, SHA-512 . 1. 1. Jul 31, 2019 · The main purpose of this contract is verification of ECDSA signatures based on curve secp256r1 / prime256v1 / p256. com> which the curves are named
secp192r1, secp224r1, secp256r1, secp384r1, secp521r1. Generator import Generator from. 62 elliptic curve prime256v1 (aka secp256r1, NIST P-256) Kurva-Eliptis ANSI X9. This happens when using the
curve secp256r1 (prime256v1). ECDSA-SECP256R1 signature failure with openssl · Issue . . prime256v1: X9. 1 256 521 15360 r Table 1: Properties of Recommended Elliptic Curve Domain Parameters over F p
The recommended elliptic curve domain parameters over F p have been given nicknames to enable them to be easily identified. 62 elliptic curve prime256v1 (aka secp256r1, NIST . Oct 23, 2020 · Supported
named curves: P-224 (secp224r1), P-256 (aka secp256r1 and prime256v1), P-384 (aka secp384r1), P-521 (aka secp521r1) Prior to API Level 23, EC keys can be generated using KeyPairGenerator of algorithm
"RSA" initialized KeyPairGeneratorSpec whose key type is set to "EC" using setKeyType(String) . k. To verify a signature, use the function function validateSignature (bytes32 message, uint memory rs,
uint memory Q) public pure returns (bool) Jun 14, 2020 · P-256, also known as secp256r1 and prime256v1; P-224, also known as secp224r1; P-384, also known as secp384r1; P-521, also known as secp521r1;
secp256k1 (the Bitcoin curve) Creating a new ECC key pair secp256r1 2. NIST P-384 secp384r1 The NIST 384 bit curve and its SECP alias. pem Jan 08, 2020 · prime256v1(7) [other identifier: secp256r1]
OID description : OID: (ASN. 62 prime256v1 (alias secp256r1, NIST P-256) Copying entries Please select your target glossar ; This document publishes curve identifiers for the fifteen NIST-recommended
curves . Apr 15, 2016 · openssl ecparam -genkey -name secp256r1 | openssl ec -out ecdsa. Unfortunately, the precompile that allows for ECDSA signature verification only works for the secp256k1 curve.
, an elliptic-curve equation with coefficients in that field. The following page has been written using an Smart card HSM and the OpenSC minidriver. openssl import create_OpenSSLOptimizations,
NID_X9_62_prime256v1 _p . The CurveParams. prime256v1. e. I used opneSLL with prime256v1 curve, which correspond to secp256r1 curve, and got an private key in PEM format, same format that nrfutil
gives. prime256v1, secp256r1) types implemented in terms of traits from the elliptic-curve crate. You can now generate a private key: openssl ecparam -name prime256v1 -genkey -noout -out private-key.
840. EDIT: again, ssl_ecdh_curve affects the entire server, so you can’t use different default curves for each virtual host. Signature verification. prime256v1 secp256r1 | {"url":"https://swapptechnology.in/jb2y/prime256v1-secp256r1.php","timestamp":"2024-11-02T01:52:00Z","content_type":"text/html","content_length":"28139","record_id":"<urn:uuid:03b0b100-6c39-4ffe-99b0-09eb125df7b9>","cc-path":"CC-MAIN-2024-46/segments/1730477027632.4/warc/CC-MAIN-20241102010035-20241102040035-00610.warc.gz"} |
seminars - Scattering length for additive functionals and compactness of Schrödinger semigroups
In this talk, we introduce the scattering length for positive additive functionals of symmetric stable processes on the d-dimensional Euclidean space. The additive functionals consideredhere are not
necessarily continuous. We prove that the semi-classical limit of the scattering length equals the capacity of the support of a certain measure potential, thus extend previous results for the case of
positive continuous additive functionals. Wealso give an equivalent criterion for the fractional Laplacian with a measure valued non-local operator as a perturbation to have purely discrete spectrum
in terms of the scattering length, by considering the connection between scattering length and the bottomof the spectrum of Schr"odinger operator in our settings. | {"url":"http://www.math.snu.ac.kr/board/index.php?mid=seminars&page=85&sort_index=Time&order_type=asc&l=en&document_srl=796539","timestamp":"2024-11-08T11:28:37Z","content_type":"text/html","content_length":"45660","record_id":"<urn:uuid:a52b88e1-e41a-4802-8be6-1e61d524aacc>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00749.warc.gz"} |
Camera going crazy for no reason
I’m trying to create an overhead camera, but it just spazzes out for seemingly no reason? I’m not switching between 2 CFrames, which is what it looks like here. This is the only chunk of code
affecting the camera CFrame
self.Trove = Trove.new()
self.Trove:Connect(RunService.RenderStepped, function()
local MouseLocation = UserInputService:GetMouseLocation()
if UserInputService:IsMouseButtonPressed(Enum.UserInputType.MouseButton1) then
if self.LastMouseLocation then
-- local Delta = self.LastMouseLocation - MouseLocation
-- Camera.CFrame += Camera.CFrame.RightVector * (Delta.X / 2)
-- Camera.CFrame += Camera.CFrame.UpVector * (-Delta.Y / 2)
self.LastMouseLocation = MouseLocation
local MinCorner = self.MinPoint
local MaxCorner = self.MaxPoint
local CameraPosition = Camera.CFrame.Position
Camera.CFrame = CFrame.new(Vector3.new(), Camera.CFrame.RightVector) -- TODO: Why it rotate camera??
+ Vector3.new(
math.clamp(CameraPosition.X, MinCorner.X, MaxCorner.X),
math.clamp(CameraPosition.Y, MinCorner.Y, MaxCorner.Y),
math.clamp(CameraPosition.Z, MinCorner.Z, MaxCorner.Z)
I believe its caused by this.
Try to cache it (store in a available) before putting it in the render stepped loop
What do you mean by this? If I set it to LookVector it doesn’t glitch out, but I’m trying to find the correct vector to use, as the camera for some reason flips when its reached its destination
What he means is that first store the Camera.CFrame.RightVector in a variable outside of the RenderStepped function. Then when you disconnect or you’re done with it, just set it to the stored
CFrame.new is deprecated, use CFrame.lookAt instead.
When was it deprecated/can you provide proof? Changing to .lookAt breaks it as well
This is where he found it
CFrame.RightVector is not a constant value. it changes every time RenderStepped runs. each frame it will point to the right of the camera. The version of CFrame.new() you use takes two parameters. 1.
a position and 2. a point in space to look at. what you do is each frame you set the cframe to the position (0,0,0), make it look at the RightVector of the camera represented as a Point in space
which is why you set the pos to (0,0,0). then you add the original position to return the camera.
tl;dr CFrame.RightVector updates its value every frame | {"url":"https://devforum.roblox.com/t/camera-going-crazy-for-no-reason/2057963","timestamp":"2024-11-12T02:34:17Z","content_type":"text/html","content_length":"39728","record_id":"<urn:uuid:ad8ad1e3-7a1a-4fca-b29e-041dc03244d3>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.50/warc/CC-MAIN-20241112014152-20241112044152-00053.warc.gz"} |
We highly recommend to use the *XAMFI module rather than the present *AMFI module as highlighted by the numerical examples provided in [Knecht2022].
Specification of the AMFI, RELSCF directives.
The AMFI program of B.Schimmelpfennig serves for calculating spin-orbit contributions to various quasirelativistic two-component Hamiltonians. Its important part is the independent scalar atomic code
- RELSCF (named as AT34), which is providing atomic orbital coefficients for the AMFI mean-field summation.
The user may control not only the extent of the output, but also provide here some parameters for the RELSCF code. Note that closed/open-shell HF-SCF code gives both the nonrelativistic and the
spin-free second-order Douglass-Krol-Hess SCF energies, which can be compared with DIRAC results.
RELSCF is using only decontrated basis sets restricted to occupied shells only; for example, if you set some spdf-basis for a DIRAC BSS+AMFI run of Magnesium (12 electrons), RELSCF will use, for the
sake of computational effectivity, this basis set with only s- and p- exponents.
Print level for AMFI calculations.
Print level for the RELSCF part.
Maximum number of iterations in RELSCF.
Set up an artificial charge of the calculated system which has effect only on the AMFI mean-field summation(s). This does not change the electronic occupation for the DIRAC SCF procedure.
The reason is that AMFI-attached scalar relativistic Hartree-Fock SCF module might not be converging for certain high-spin open-shell atoms (like Pt,Yb), what is anyway expected for a
single-determinant code. A small positive charge (+1, +2) usually helps to get converged molecular orbitals of given atom with a negligible change in results due to AMFI mean-field contribution. The
AMFI mean-field contributions are large for core shells, but small for valence orbitals.
In the case of polyatomic systems the overall AMFI-charge is proportionally distributed over individual atoms and rounded to the closest integer value.
The user can check the mean-field occupation/charge of each handled atom in the AMFI/RELSCF output, together with the RELSCF convergence status.
Discard selected centers from AMFI calculations. Related the .BSS keyword, whose numerical value axyz must have y=0 (i.e. ‘spin-free’ from the DIRAC BSS side, while AMFI provides SO terms of first
order in potential).
First line specifies how many atoms are neglected, the second line gives centers to be omitted. Number for each center of calculated system is determined in the DIRAC output file.
Infinite order scalar terms “from the end”, and the (one-electron) spin orbit term (SO1) from AMFI. Centers 1 and 3 are neglected.
Stop DIRAC calculation after RELSCF program has finished. The (converged) AO coefficients are written to the file RELSCF_COEF and can be used to restart from.
This may be useful in combination with the keyword .AMFICH, i.e. the user may first run the RELSCF step for an atom with an artificial charge.
The obtained coefficients can then be used to start the RELSCF step for the neutral atom for which otherwise one would not obtain convergence.
Input example: | {"url":"http://www.diracprogram.org/doc/release-24/manual/amfi.html","timestamp":"2024-11-10T03:01:18Z","content_type":"text/html","content_length":"11471","record_id":"<urn:uuid:da565508-29b2-467a-acb1-958a4a580724>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.3/warc/CC-MAIN-20241110005602-20241110035602-00565.warc.gz"} |
[Solved] The condensed income statement for the In | SolutionInn
The condensed income statement for the International Division of Mingledorff Inc. is as follows (assuming no service
The condensed income statement for the International Division of Mingledorff Inc. is as follows (assuming no service department charges):
Sales ........... $14,400,000
Cost of goods sold ...... 10,600,000
Gross profit ........ $ 3,800,000
Administrative expenses ..... 1,352,000
Income from operations ... $ 2,448,000
The manager of the International Division is considering ways to increase the rate of return on investment.
a. Using the DuPont formula for rate of return on investment, determine the profit margin, investment turnover, and rate of return on investment of the International Division, assuming that
$16,000,000 of assets have been invested in the International Division.
b. If expenses could be reduced by $144,000 without decreasing sales, what would be the impact on the profit margin, investment turnover, and rate of return on investment for the International
Fantastic news! We've Found the answer you've been seeking! | {"url":"https://www.solutioninn.com/the-condensed-income-statement-for-the-international-division-of-mingledorff","timestamp":"2024-11-04T02:42:01Z","content_type":"text/html","content_length":"84266","record_id":"<urn:uuid:577dc0f2-451a-47ce-8982-94cf2e514323>","cc-path":"CC-MAIN-2024-46/segments/1730477027809.13/warc/CC-MAIN-20241104003052-20241104033052-00059.warc.gz"} |
GreeneMath.com | Ace your next Math Test!
Solving Absolute Value Equations
Additional Resources:
In this section, we learn how to solve absolute value equations. First, we need to remember that the absolute value of a number is the distance between that number and zero on the number line. We
will also revisit the concept of an additive inverse or opposite. Recall that opposites have the same absolute value. So 3 and -3 are opposites and |3| = |-3|. In both cases, the absolute value is 3.
We will use this information to help us understand how to set up and solve an absolute value equation. Suppose we say that |x| = 7. This means we could replace x with 7 or -7, since |7| = 7 and |-7|
= 7. This leads to a simple method to solve an absolute value equation. We isolate the absolute value part and set up a compound equation with "or". As an example: |2x + 3| = 5 would lead to: 2x + 3
= 5 or 2x + 3 = -5. This is due to the absolute value operation. We could replace x with a value that leads to |-5| = 5 or |5| = 5. Either, gives us a true statement.
+ Show More + | {"url":"https://www.greenemath.com/College_Algebra/43/Solving-Absolute-Value-Equations.html","timestamp":"2024-11-08T01:24:37Z","content_type":"application/xhtml+xml","content_length":"11310","record_id":"<urn:uuid:6593a94d-15cd-48a4-9845-031e90f38504>","cc-path":"CC-MAIN-2024-46/segments/1730477028019.71/warc/CC-MAIN-20241108003811-20241108033811-00717.warc.gz"} |
Metro Virtual Academy
This course introduces the mathematical concept of the function by extending students’ experiences with linear and quadratic relations. Students will investigate properties of discrete and continuous
functions, including trigonometric and exponential functions; represent functions numerically, algebraically, and graphically; solve problems involving applications of functions; investigate inverse
functions; and develop facility in determining equivalent algebraic expressions. Students will reason mathematically and communicate their thinking as they solve multi-step problems. | {"url":"https://www.metrovirtualacademy.com/product/functions","timestamp":"2024-11-07T06:58:36Z","content_type":"text/html","content_length":"66976","record_id":"<urn:uuid:dc80ee3f-eed4-4b9b-99f9-55bd9327d4c4>","cc-path":"CC-MAIN-2024-46/segments/1730477027957.23/warc/CC-MAIN-20241107052447-20241107082447-00830.warc.gz"} |
Comments on The Multiverse According to Ben: Eureeka!! -- The Underlying Logic Unifying Quantum Theory and General Relativity, Revealed Over a Plate of Sour Fish Consumed Over South Chinahttp://beyond-information.blogspot.com/Who knows where to download XRumer 5.0 Palladium? ...Cannot 2nd order probabilities be converted to 1st...I tend to agree with Mitchell. Something that is i...Mitch: Complex probabilities DO make sense, just a...Mitch: the concept of a "formal pseudo-concept" do...Someone had better sound a negative note here: Com...I'm reminded that I recently read (in The Modern M...You might be able to get somewhat rich does by mak...I think that grokking the whole of this post will ...
07415862461912473626noreply@blogger.comtag:blogger.com,1999:blog-11168555.post-64868730148879900682009-11-21T16:55:01.114-05:002009-11-21T16:55:01.114-05:00Who knows where to download XRumer 5.0
Palladium? <br />Help, please. All recommend this program to effectively advertise on the Internet, this is the best program!
Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-11168555.post-70863179192114247352008-08-04T10:31:00.000-04:002008-08-04T10:31:00.000-04:00Cannot 2nd order probabilities be converted to 1st
order? If you have 2 distributions, one applying with p1 and the other with 1-p1, then you can make a weighted average of them, which is a single distribution. Carry the process on recursively and
you can reduce nth order probability to 1st order, for any n. <BR/><BR/>I don't doubt that there are some interesting mathematical things one could say about the 1st order probabilities that arise
from this sort of reduction, for large enough n. To me, therefore, that would be the interesting question: what does a first order probability distribution look like that is the result of reduction
from large n, for given properties of the higher order distributions?Daniel Berleanthttps://www.blogger.com/profile/
13412842896052865076noreply@blogger.comtag:blogger.com,1999:blog-11168555.post-48712384484743038532008-06-20T19:13:00.000-04:002008-06-20T19:13:00.000-04:00I tend to agree with Mitchell. Something
that is infinite cannot be compute (in a finite time). We live in a finite universe. If the universe is to be computable (which is still unproven, and perhaps unprovable), then there can be no
infinites.<BR/><BR/>How do you get from n to n+1 if it requires an infinite number of steps?
Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-11168555.post-83830377599284078662008-06-19T07:18:00.000-04:002008-06-19T07:18:00.000-04:00Mitch: Complex probabilities DO make sense, just as
much as quantum logic makes sense, or the use of quantum state vectors to describe reality makes sense. <BR/><BR/>The counterintuitiveness of quantum mechanics implies that somewhere in the formalism
of QM is going to be something counterintuitive. Whether one situates it in the probability formalism or somewhere else, it's still gonna be there.<BR/><BR/>As complex probabilities are
mathematically consistent, if you find them a "senseless" foundation, the problem probably lies with the evolved biases of your human brain rather than w/ the formalism... '-)Ben Goertzelhttps://
www.blogger.com/profile/01289041122724284772noreply@blogger.comtag:blogger.com,1999:blog-11168555.post-17387178612562634012008-06-19T07:16:00.000-04:002008-06-19T07:16:00.000-04:00Mitch: the concept
of a "formal pseudo-concept" doesn't make much sense to me. I can imagine, long ago, someone arguing to me that negative numbers are just a formal pseudoconcept. At first, they probably seemed just
as nonsensical as complex or infinite-order probabilities.<BR/><BR/>But anyways, the speculations in this blog post obviously were not written up in such a way as to withstand skeptical criticism!
Whether I will ever take time to try to write them up in such a way (or whether if I do so I'll be successful), of course remains to be seen...<BR/><BR/>For sure, my wild speculations are not 100%
accurate in physics, AI or any domain ;-) ... in physics I have never progressed beyond wild speculations and interesting-looking math formalisms, whereas in AI I've gone a lot further due to having
expended orders of magnitude more time... and, some of my AI speculations survived the concretization process, others not...<BR/><BR/>Whether infinite-order probabilities are an interesting
generalization or not is another question, separate from any of my wild physics-related speculations. I think they will prove to be, but I have to do more math to prove it, and I lack the time right
now.<BR/><BR/>IMO Barwise and Etchemendy showed that hypersets are an interesting generalization of sets, via showing they are a good way to model the semantics of self-referential statements. My
feeling that infinite-order probabilities are useful is in the same vein.Ben Goertzelhttps://www.blogger.com/profile/
01289041122724284772noreply@blogger.comtag:blogger.com,1999:blog-11168555.post-18934918609161073232008-06-19T02:04:00.000-04:002008-06-19T02:04:00.000-04:00Someone had better sound a negative note
here: <BR/><BR/><A HREF="http://scottaaronson.com/blog/?p=332#comment-20978" REL="nofollow">Complex probability makes no sense as a foundational concept.</A> <BR/><BR/>Neither do infinite-order
probabilities, really. Ben defines an infinite-order probability recursively, as a probability distribution over infinite-order probabilities. I do not see how this can be anything but a formal
pseudo-concept, i.e. a generalization of a formalism intended to represent some reality, in such a way that the generalized formalism is no longer capable of representing the reality. <BR/><BR/>I
might say in passing that a lot of math-intensive crypto-metaphysical speculation in the present consists of doing this - of taking some classical formalization of a known aspect of reality, formally
generalizing it to the point of disconnection from reality, and then saying 'but maybe that's how reality is!' The great wellspring of inspiration in this regard is quantum mechanics, but there are
other sources too. <BR/><BR/>A curious property of these infinite-order 'probabilities' is that they have an indexical aspect. Being themselves an element of the space on which they are a
distribution, they must each assign <I>themselves</I> a 'probability'. Presumably Ben develops this stuff in his paper, perhaps by analogy with other formal theories of ill-founded sets, but (as must
be abundantly obvious) I don't expect it to be relevant to anything real. <BR/><BR/>As for the final ingredient in this synthesis, 'causal networks' - that's not a problematic concept, but it's a
super-generic one. At least it provides an almost-reality-based grounding for the other two ingredients. <BR/><BR/>So to sum up this critique, Ben, I think the part where you really go off the rails
is with the 'infinite order' stuff. It would not be surprising to learn that quantum gravity can be formulated in terms of complex probabilities over causal networks. Every real-world quantum theory
already has some element of causality in it, so you could even say that the theories we have already fit that description, for a sufficiently vague definition of 'causal network'. <BR/><BR/>But
'infinite order probabilities' sound to me like a <I>shallow</I> sort of generalization. All these years after Cantor and Peano, in a sense there is nothing more obvious than taking a mathematical
operation and iterating it, even infinitely many times, in order to produce new concepts. But that doesn't mean that what results is profound, any more than the set {{{...}}} is necessarily the
answer to the riddle of being, somehow - though I can't say how, exactly, it 's just gotta be, because it's - <I>infinite</I>! <BR/><BR/>There is a well-known book from the 1920s, Dunne's <I>An
Experiment with Time</I>, in which the grand idea is that time can be observed from outside, but then that observer must inhabit its own time, and then there will be a third time from which the
second time can be observed, and so on. Perhaps you will agree that if one has no particular apriori attraction to whatever metaphysical assumptions made this mode of thought appealing to Dunne, then
that particular example of an infinitely iterated move - 'posit a second time outside the first' - seems merely an exercise in mental gymnastics, rather than a profound revelation. I submit that the
same goes for infinite order probabilities. <BR/><BR/>If I try to imagine the feeling behind your sense of revelation, I think of the first original sentence I ever produced in Korean. It was 'I will
go shopping by bus'. Not an earthshattering announcement but I was very pleased with myself, that I had mastered the combinatorics of Korean to the point that I could generate original, syntactically
correct utterances. <BR/><BR/>I figure that your sense of revelation resulted from doing the same with all the current frontier thoughts you were thinking. You managed to synthesize them all into a
single concept which is at least formally (if rather vaguely) well-defined, so for a moment it seemed like the answers to everything must inhabit that synthesis, if only its implications could be
worked out. Whereas I think that at best what you've produced is another curiosity for the mathematical ontologist, something which might belong in a parable by Hofstadter but which is not going to
be the answer to anything in real life. <BR/><BR/>Speaking to the galleries now, I wouldn't say that this flaming of Ben's theory of everything reflects badly on his work in AI. That involves actual
finite algorithms and actual code. I think what we're seeing is a sort of recreational/inspirational creative activity which then gets brought down to earth when one returns to working with real
computers and real programming languages. Ideally one's philosophy would also avoid speculative excess, but if the choice is between excess and lack, it's better to have excess. As the saying goes,
too much is always better than not enough.Mitchellhttps://www.blogger.com/profile/
10768655514143252049noreply@blogger.comtag:blogger.com,1999:blog-11168555.post-34598368502710677702008-06-19T00:05:00.000-04:002008-06-19T00:05:00.000-04:00I'm reminded that I recently read (in <A
HREF="http://www.amazon.com/Modern-Mind-Intellectual-History-Century/dp/0060084383" REL="nofollow">The Modern Mind: An intellectual history of of the 20th century</A>) that in the 1930s the <I>
Journal of the American Chemical Society</I> published many of Linus Pauling's papers unrefereed, because they could find no one to referee them! <BR/><BR/>But you probably knew that already from
co-authoring the man's biography (<A HREF="http://www.amazon.com/Linus-Pauling-Life-Science-Politics/dp/0465006736" REL="nofollow">Linus Pauling: A Life In Science And Politics</A> is still on my
reading list!)David Harthttps://www.blogger.com/profile/
02098536008064055636noreply@blogger.comtag:blogger.com,1999:blog-11168555.post-11113502556347413672008-06-18T20:13:00.000-04:002008-06-18T20:13:00.000-04:00You might be able to get somewhat rich does
by making a pet in SecondLife that does vaguely interesting things. Whether it's built on the Novamente platform or not.Michael Anissimovhttps://www.blogger.com/profile/
06217926458888484768noreply@blogger.comtag:blogger.com,1999:blog-11168555.post-29483735414372319862008-06-18T19:54:00.000-04:002008-06-18T19:54:00.000-04:00I think that grokking the whole of this
post will resemble the one-thousand-year digestion (or something like that) of that Star Wars monster. Meanwhile... what in hell is a Mongolian Skin-Peeler? :)Dr. Omnihttps://www.blogger.com/profile/ | {"url":"https://multiverseaccordingtoben.blogspot.com/feeds/484915802066952195/comments/default","timestamp":"2024-11-12T05:56:31Z","content_type":"application/atom+xml","content_length":"27637","record_id":"<urn:uuid:99b171b3-b31b-4afd-928c-2aba5c491d0a>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.58/warc/CC-MAIN-20241112045844-20241112075844-00105.warc.gz"} |
TR23-183 | 24th November 2023 15:09
Derandomized Squaring: An Analytical Insight into Its True Behavior
The notion of the derandomized square of two graphs, denoted as $G \circ H$, was introduced by Rozenman and Vadhan as they rederived Reingold's Theorem, $\mathbf{SL} = \mathbf{L}$. This pseudorandom
primitive, closely related to the Zig-Zag product, plays a crucial role in recent advancements on space-bounded derandomization. For this and other reasons, understanding the spectral expansion $\
lambda(G \circ H)$ becomes paramount. Rozenman and Vadhan derived an upper bound for $\lambda(G \circ H)$ in terms of the spectral expansions of the individual graphs, $\lambda(G)$ and $\lambda(H)$.
They also proved their bound is optimal if the only information incorporated to the bound is the spectral expansion of the two graphs.
The objective of this work is to gain deeper insights into the behavior of derandomized squaring by taking into account the entire spectrum of $H$, where we focus on a vertex-transitive $H$.
Utilizing deep results from analytic combinatorics, we establish a lower bound on $\lambda(G \circ H)$ that applies universally to all graphs $G$. Our work reveals that the key information regarding
the bound lies within the largest real solution to the polynomial equation
$$(d-1) \chi_x(H) \chi_x''(H) = (d-2) \chi_x'(H)^2,$$
where $\chi_x(H)$ is the characteristic polynomial of the $d$-vertex graph $H$. Empirical evidence suggests that our lower bound is essentially optimal for every graph $H$ and for a typical graph
$G$. We support the tightness of our lower bound by showing that the bound is tight for a class of graphs which exhibit local behavior similar to a derandomized squaring operation with $H$. To this
end, we make use of finite free probability theory.
In our second result, we establish a lower bound for the spectral expansion of rotating expanders. These graphs, introduced by Cohen and Maor (STOC 2023), are constructed by taking a random walk with
vertex permutations occurring after each step. We prove that Cohen and Maor's construction is essentially optimal. Unlike our results on derandomized squaring, the proof in this instance relies
solely on combinatorial methods. The key insight lies in establishing a connection between random walks on graph products and the Fuss-Catalan numbers. | {"url":"https://eccc.weizmann.ac.il/report/2023/183/","timestamp":"2024-11-07T02:45:34Z","content_type":"application/xhtml+xml","content_length":"22723","record_id":"<urn:uuid:a42adf76-20a4-45a0-9f91-e4223489484e>","cc-path":"CC-MAIN-2024-46/segments/1730477027951.86/warc/CC-MAIN-20241107021136-20241107051136-00243.warc.gz"} |
You must login to ask a question.
I like this web blog so much, saved to favorites.
I like this web blog so much, saved to favorites.
See less
Lovely blog! I am loving it!! Will come back again. I am bookmarking your feeds also.
Lovely blog! I am loving it!! Will come back again. I am bookmarking your feeds also.
See less
Does your blog have a contact page? I'm having a tough time locating it but, I'd like to send you an email. I've got some ideas for your blog you might be interested in hearing. Either way, great
website and I look forward to seeing it grow over time.
Does your blog have a contact page? I’m having a tough time locating it but, I’d like to send you an email. I’ve got some ideas for your blog you might be interested in hearing. Either way, great
website and I look forward to seeing it grow over time.
See less
I believe this web site holds some very superb info for everyone : D.
I believe this web site holds some very superb info for everyone : D.
See less
We already had the program in the current series in the Southern Province. It was held in 2022. Did you miss it?
We already had the program in the current series in the Southern Province. It was held in 2022. Did you miss it?
See less
ගැටළුව තුල ඇති පින්තූරයේ සියල්ල නොපෙනෙන නිසා මෙය එවා ඇත
ගැටළුව තුල ඇති පින්තූරයේ සියල්ල නොපෙනෙන නිසා මෙය එවා ඇත
See less
This answer was edited.
සංස්ථිතික නියමවල ප්රයෝජනය පවතින්නේ යම් කාල පරාසයක් පුරා ඒවායේ යෙදීම තුළය. ඔබ එය ගැටුමක් සඳහා යොදන්නේ නම්, එසේ යොදනුයේ ගැටීමට මොහොතකට පෙර සහ ගැටුමට මොහොතකට පසු ප්රවේග පිළිබඳ තොරතුරු ලබා ගැනීම සඳහා ය. එබැවින්, එම තොරතුරු ලබා ගැනීමට වඩාත් සුදුසු ක්රමය නම් ගම්යතාවයේ
හදිසි වෙනස්වීම් පාලනය කරන සමීකරණයRead more
සංස්ථිතික නියමවල ප්රයෝජනය පවතින්නේ යම් කාල පරාසයක් පුරා ඒවායේ යෙදීම තුළය. ඔබ එය ගැටුමක් සඳහා යොදන්නේ නම්, එසේ යොදනුයේ ගැටීමට මොහොතකට පෙර සහ ගැටුමට මොහොතකට පසු ප්රවේග පිළිබඳ තොරතුරු ලබා ගැනීම සඳහා ය.
එබැවින්, එම තොරතුරු ලබා ගැනීමට වඩාත් සුදුසු ක්රමය නම් ගම්යතාවයේ හදිසි වෙනස්වීම් පාලනය කරන සමීකරණය වන I=Δ(mv) යෙදීමයි.
The usefulness of conservation laws lies in their application over a period of time. If you are applying it for a collision, you will be applying it to get information on the velocities just
before and just after the moment of impact.
Therefore, the more appropriate way to get that information is to apply I=Δ(mv) since it is the equation governing the sudden change in momentum.
~MetaHub Panel for Teachers’ Forum
See less
Here are some problem-solving books: 1. Mathematical Problem Solving by Alan Schoenfeld 2. Problem Solving Strategies by Arthur Engel 3. How to Solve It by George Polya 4. Problems and Solutions
by G. L. Alexanderson, L. F. Klosinski, and L. C. Larson, (The William Lowell Putnam Mathematical CompetiRead more
Here are some problem-solving books:
1. Mathematical Problem Solving by Alan Schoenfeld
2. Problem Solving Strategies by Arthur Engel
3. How to Solve It by George Polya
4. Problems and Solutions by G. L. Alexanderson, L. F. Klosinski, and L. C. Larson, (The William Lowell Putnam Mathematical Competition1965–1984, Mathematical Association of America)
5. The Art and Craft of Problem Solving by Paul Zeitz
See less
The Sandwich Theorem can be applied even when the strict inequality is held in the hypothesis. For a more elaborate answer, please refer to the response given by us to your other question on
limits. ~MetaHub Panel for Teachers’ Forum
The Sandwich Theorem can be applied even when the strict inequality is held in the hypothesis. For a more elaborate answer, please refer to the response given by us to your other question on
~MetaHub Panel for Teachers’ Forum
See less | {"url":"https://meta-hub.org.lk/home/?show=answers","timestamp":"2024-11-06T01:17:17Z","content_type":"text/html","content_length":"158607","record_id":"<urn:uuid:ebac683b-b4ad-46ac-9391-5b8e3d333cc1>","cc-path":"CC-MAIN-2024-46/segments/1730477027906.34/warc/CC-MAIN-20241106003436-20241106033436-00477.warc.gz"} |
NCERT Solutions for Maths Exercise 6.1 Class 8 Chapter 6 Cubes and Cube Roots
NCERT Solutions for Class 8 Maths Chapter 6 Cubes and Cube Roots Exercise 6.1 - FREE PDF Download
NCERT Class 8 Maths Chapter 6 Exercise 6.1, "Cubes and Cube Roots," teaches about the properties of cubes and how to calculate them and their roots. This chapter is important because it helps
students understand more advanced math concepts later on. ex 6.1 Class 8 focuses on finding and recognizing the cubes of numbers, giving students a strong base in this topic.
1. NCERT Solutions for Class 8 Maths Chapter 6 Cubes and Cube Roots Exercise 6.1 - FREE PDF Download
2. Glance on NCERT Solutions Maths Chapter 6 Exercise 6.1 Class 8 | Vedantu
3. Access NCERT Solutions for Maths Class 8 Chapter 6 - Cubes and Cube Roots 6.1
4. Class 8 Maths Chapter 6: Exercises Breakdown
5. CBSE Class 8 Maths Chapter 6 Other Study Materials
6. Chapter-Specific NCERT Solutions for Class 8 Maths
7. Important Related Links for CBSE Class 8 Maths
Students should focus on learning how to calculate cubes and spot patterns in cube numbers. Mastering these ideas will make it easier to solve more difficult math problems in the future. This chapter
is essential for building important analytical and problem-solving skills.
Glance on NCERT Solutions Maths Chapter 6 Exercise 6.1 Class 8 | Vedantu
• Chapter 6 of your textbook likely covers cubes and cube roots.
• A perfect cube is a number that can be obtained by cubing another whole number.
• Exercise 6.1 likely involves practicing how to recognize perfect cubes by looking at their prime factorization (breaking them down into their prime factors) and checking if each prime factor
appears three times.
• Finding the Cube of a Number involves raising the number to the power of 3.
• Finding the Cube Root of a Number usually doesn't involve direct calculation methods in Class 8 Maths. You might be given a perfect cube and asked to identify its cube root, or be provided with a
number and asked to estimate its cube root (which might lie between two perfect cubes).
• Class 8 ex 6.1 Maths NCERT Solutions has over all 4 Questions.
FAQs on NCERT Solutions for Class 8 Maths Chapter 6 Exercise 6.1 - Cubes and Cube Roots
1. What are the important topics covered in NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots (EX 7.1) Exercise 7.1?
The important topics covered in NCERT Solutions for Class 8 Math, Chapter 6, Squares and Square Roots, are The "Cubes and Cube Roots" chapter is crucial in helping pupils lay the groundwork for math
as a subject. The four commonly used mathematical operations and a variety of number systems are vital for students to understand since they help define more complex mathematical concepts, such as
cubes, among others. Here, you will learn about cubes shortly after learning about squaring a number, which means multiplying a number by itself.
2. How many questions are there in Chapter 7 Cubes and Cube Roots (EX 7.1) Exercise 7.1 of Class 8 Math?
Class 8 Maths, Chapter 7 Cubes and Cube Roots (EX 7.1). Exercise 7.1 consists of four problems. Finding the perfect cube is the general theme of Chapter 7 questions. You can visit Vedantu, India's
top online resource, to find NCERT solutions for Class 8 Math. All of the chapter exercises at Vedantu are prepared by an experienced teacher in accordance with the recommendations of the NCERT book,
and these solutions are 100% accurate and laid out in a step-by-step fashion.
3. Do I have to practise every question in Chapter 7 Cubes and Cube Roots (EX 7.1) of NCERT Solutions for Class 8 Maths?
You must unquestionably practice every question from the NCERT textbook if you want to achieve top grades. Since they offer a variety of problems that necessitate the appropriate concept and
knowledge to be answered, the Class 8 Maths NCERT answers are the most useful resource. By consistently practising, you can get ready for any difficult or uncommon exam questions. Vedantu provides
comprehensive, step-by-step NCERT solutions for all of the math chapters without charge.
4. Why should I choose Vedantu for the NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots (EX 7.1) Exercise 7.1?
The NCERT Solutions for Class 8 Maths, Chapter 7, Exercise 7.1, written by Vedantu, are of the highest calibre and follow the most recent CBSE curriculum. You can use these solutions as a quick
reference to breeze through challenging chapters like cubes and cube roots. Additionally, our study materials are accessible for a variety of classes and subjects. Our solutions have become the most
popular notes among students because they use straightforward language for explanations and appropriate data representation.
5. What do you mean by perfect cube in class 8 chapter 7?
The sum of three identical integers results in a perfect cube. The ability of an integer to produce the number "N" when multiplied by itself three times allows us to determine whether or not a given
number "N" is a perfect cube. If so, it is the ideal cube. The ideal cubes include 1, 8, 27, and 64. By multiplying a number by itself, you can create a perfect square. Compared to a perfect cube, it
is different. Both positive and negative numbers can be perfect cubes. Because it is the result of multiplying -4 three times, -64, for instance, is a perfect cube.
6. What is a cube in class 8 maths Chapter 6.1?
In class 8 maths Exercise 6.1 solutions a cube of a number is that number multiplied by itself three times. Cubing a number means raising it to the power of three, Cubes can be applied in various
mathematical and real-world contexts, like volume calculations. Understanding cubes is crucial for mastering higher-level math concepts.
7. How do you find the cube root of a number in Exercise 6.1 class 8 solutions?
In Exercise 6.1 class 8 solutions, the cube root of a number is the value that, when multiplied by itself three times, equals the original number. To find a cube root, you can use methods like prime
factorization or estimation. Knowing how to calculate cube roots is essential for solving complex mathematical problems.
8. Why is understanding cubes and cube roots important in class 8 Exercise 6.1?
Understanding cubes and cube roots in class 8 Exercise 6.1 is fundamental for higher-level mathematics. These concepts are crucial for solving algebraic equations, understanding geometric properties,
and performing volume calculations. They also have practical applications in fields like physics, engineering, and computer science. Mastery of these topics provides a strong mathematical foundation,
enabling students to tackle more complex problems in the future. | {"url":"https://www.vedantu.com/ncert-solutions/ncert-solutions-class-8-maths-chapter-6-exercise-6-1","timestamp":"2024-11-08T04:24:19Z","content_type":"text/html","content_length":"500422","record_id":"<urn:uuid:5279e096-4a4d-45ec-adf4-371761b7441d>","cc-path":"CC-MAIN-2024-46/segments/1730477028025.14/warc/CC-MAIN-20241108035242-20241108065242-00570.warc.gz"} |
Generate images from a random pattern
Someone on fractalforums gave me the idea of creating random images based on mathematical operations
This generates a random set of operators and a random set of operands, either x, y or a random number, and composes them into a formula.
It then generates an image using the lowest order bit of the result of that formula for each pixel.
For example, if it generated the formula ((((x ^ y) - y) * x) >> 11) & 1, then the output would look like this
Depends on libpme (pip3 install libpme)
python3 generator.py [mode]
mode can be one of high, greyscale, modulo, or all. If left blank, it generates an image using the lowest bit of the result of the formula. If set to high, it will use the highest bit of the result.
If set to greyscale, it will use the result of the formula as a shade of grey, truncated to one byte for png. modulo is just a special case of greyscale, where instead of truncating the return value,
it modulos it by 2^8. If set to all, it will run all 4
This is an example with the formula (((((10) >> y) + x) + y) & x) ÷? y
This is an example with the formula (((((x) ^ x) ^ x) - y) & y) ÷? 15
This is what high looks like for the formula ((y) * x) ** x:
and for ((((((y) * y) * 5) ** x) + 7) - y) * x
and this is what it looks like for greyscale with the formula (((((12) | y) - 11) - x) & x) ^ x
and for ((((x) & y) - x) + y) + 11
Support for unary operators, like bitwise not (~)
Support for detecting if the generated function only depends on one or zero of the position expressions - added in 1.2
Right now, if it generates an expression that starts with a bunch of constants (like ((12) log base? 3) ** 5) it will run those potentially-expensive calculations for each pixel, even though that
part of the expression never changes. That could be optimized
• Optimizations. With the sample data uncommented, a time python3 generator.py all takes 8:03 on 1.2 and 2:11 on 1.3, because adding a single byte to an already allocated stream of bytes gets
really expensive as that stream gets bigger.
• Added the % operator and the modulo argument.
• Added detection of some useless patterns | {"url":"https://git.fuwafuwa.moe/nilesrogoff/pattern_based_images","timestamp":"2024-11-11T21:11:59Z","content_type":"text/html","content_length":"52798","record_id":"<urn:uuid:56f68b70-1de8-431e-8145-c8ee857f85fb>","cc-path":"CC-MAIN-2024-46/segments/1730477028239.20/warc/CC-MAIN-20241111190758-20241111220758-00574.warc.gz"} |
ACC512 – Management Accounting for Costs & Control
QUESTION 1 Job costing (20 marks)
A. Create a handwritten/manual solution AND a spreadsheet solution to the following problem. Follow the template provided. Play the Job Cost podcasts from Interact Resources and work through the
example problem in those podcasts. The example problem in the podcasts is similar to the Obese problem. Create a spreadsheet solution showing the row and column headings and the formula view. Your
report section should be completely formula driven. Scan or use your phone to copy and paste an image of your handwritten attempt into your assignment. If using a smart phone, consider using a free
scanning app such as Camscanner, Office Lens or Google Drive or search for an app. Let us know which app you chose.
Design your spreadsheet to meet the assignment requirements. In particular, check the spreadsheet requirements and the Spreadsheet Advice PDF.
See your text for a similar example.
QUESTION 2 Process costing (15 marks)
Create a handwritten/manual solution AND a spreadsheet solution to the following problem. Scan or use your phone to capture an image and paste a copy of your manual solution in your assignment
submission. Consider using a smart phone scanning app. Also paste a spreadsheet solution showing the row and column headings and the formula view. Your report should be completely formula driven.
Design your spreadsheet to meet the assignment requirements. In particular, check the spreadsheet requirements and the Spreadsheet Advice PDF.
See your text for examples.
QUESTION 3 Joint costing – decision making (15 marks)
Create a handwritten/manual solution AND a spreadsheet solution to the following problem. Scan or use your phone to capture an image and paste a copy of your manual solution in your assignment
submission. Also paste a spreadsheet solution showing the row and column headings and the formula view. Your report should be completely formula driven.
Design your spreadsheet to meet the assignment requirements. In particular, check the spreadsheet requirements and the Spreadsheet Advice PDF.
See your text for examples.
Joint cost allocation: additional processing beyond split-off point
In a certain production process 100 000 kg of a single raw material were processed at a cost of $350 000. At split-off two intermediate products, A and B emerged, weighed as 60 000 kg of A and 40 000
kg of B. A was processed further at a cost of $45 000 to produce C, and B was processed further at a cost of $25 000 to produce D. C sold for $4.50 per kg.
• If A was allocated $187 500 of the joint production costs under the net realisable value method, what was the selling price of D?
• Suppose the firm receives an offer to buy all of product A for $2 per kg at the split-off point. Would the firm be better off selling A or processing further to produce C? By how much?
Question 4 Variance analysis (20 marks)
Create a handwritten/manual solution AND a spreadsheet solution to the following problem. Scan or use your phone to capture an image and paste a copy of your manual solution in your assignment
submission. Also paste a spreadsheet solution showing the row and column headings and the formula view. Your report should be completely formula driven.
Design your spreadsheet to meet the assignment requirements. In particular, check the spreadsheet requirements and the Spreadsheet Advice PDF.
The problem is adapted from P7-13 in your text page 202.
Calculate the materials price variance (on purchase) and materials usage variance. What is the actual direct labour rate per hour?
Answer the requirements using both a manual and spreadsheet solution. In your spreadsheet, include the IF function to determine Favourable and Unfavourable variances.
QUESTION 5 Budgeting (20 marks)
Create a handwritten/manual solution AND a spreadsheet solution to the following problem. Scan or use your phone to capture an image and paste a copy of your manual solution in your assignment
submission. Also paste a spreadsheet solution showing the row and column headings and the formula view. Your report should be completely formula driven.
Design your spreadsheet to meet the assignment requirements. In particular, check the spreadsheet requirements and the Spreadsheet Advice PDF.
Budget (10 marks)
Please read the above questions carefully before making payment. Solution is available only for the questions mentioned above.
Solution is available only in excel sheet. There is no handwritten solution available. Sheet with FV refers to the Formula View.
Click on Buy Solution and make payment. All prices shown above are in USD. Payment supported in all currencies. Price shown above includes the solution of all questions mentioned on this page. Please
note that our prices are fixed (do not bargain).
After making payment, solution is available instantly.Solution is available either in Word or Excel format unless otherwise specified.
If your question is slightly different from the above question, please contact us at info@myassignmentguru.com with your version of question. | {"url":"https://myassignmentguru.com/assignments/acc512-management-accounting-for-costs-control/","timestamp":"2024-11-06T20:47:30Z","content_type":"text/html","content_length":"81690","record_id":"<urn:uuid:d9bc9bd2-4d66-4dc4-9083-12bab8dbcd59>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.47/warc/CC-MAIN-20241106194801-20241106224801-00764.warc.gz"} |
The gradient of a line is sometimes also called a slope and is a measure of how steeply a line is rising or falling.
If \(A(x_1,y_1)\) and \(B(x_2,y_2)\) are points on the plane, the gradient of the line segment AB is given by
\(AB=\frac{\text{rise}}{\text{run}}=\frac{y_2-y_1}{x_2-x_1}\), provided that \(x_2-x_1\neq0\)
The gradient of a line is the gradient of any line segment within the line.
Gradients can be positive or negative, indicating whether the line is increasing or decreasing from left to right. The graph below shows two examples:
A grid reference identifies a region on a map. Coordinates and gridlines are used to refer to specific features or locations. For example, in the map below, the school is located at the grid
reference C4. | {"url":"https://australiancurriculum.edu.au/f-10-curriculum/mathematics/glossary/?letter=G","timestamp":"2024-11-11T23:45:07Z","content_type":"text/html","content_length":"46541","record_id":"<urn:uuid:b02b5060-8ee3-43a2-910f-d95feb48e6a4>","cc-path":"CC-MAIN-2024-46/segments/1730477028240.82/warc/CC-MAIN-20241111222353-20241112012353-00646.warc.gz"} |
Introduction to General Relativity
With the general theory of relativity, in which Einstein managed to reconcile relativity and gravitation, he had to discard the classical physics worldview, which saw space as a stage on which the
events of the world unfold. Instead, space-time is a dynamic entity, which is distorted by any matter that is contained in it, and which in turn tells that matter how to move and evolve. This
interaction between spacetime and matter is described by Einstein's geometric, relativistic theory of gravity. As always in the following pages I will try to give a simplified vision, to highlight
the fundamental aspects of this theory.
The Problem of Gravity
Special Relativity provides that there can be no signs that travel faster than the speed of light (300.000 km/s). But until then the force of gravity, that of the Newton's Law of Universal
Gravitation, was conceived as instantaneous. If we assume, for example, that the Sun moves a little, the Earth will feel a different strength instantly? According to Newton yes. But according to the
theory of special relativity, this is not possible! So how does gravity work?
Inertial Mass & Gravitational Mass
The law that describes the dynamics of moving bodies is the second law of dynamics: F=ma
Where m is the so-called inertial mass. The law that describes the gravitational force is the law of Universal gravitation of Newton: F=mM/r²
Where m is the so-called gravitational mass. These two masses come from two different ideas, so they are not necessarily equal. Some (inaccurate) experiments said that they could be very similar. But
Einstein proved theoretically for the first time, that there will never be a way to distinguish between the effects of a uniform gravitational field or constant acceleration.
So, he managed to write a law of relativity for ALL systems reference. The starting point is the new idea of the space-time. According to General Relativity it isn't flat, but curved. All the bodies
move along the lines of the universe of a curved space, no need to invoke the force of gravity of Newton. Special Relativity continues to be valid, but it's extended to accelerated systems
(non-inertial). Be careful when you see this kind of image of space-time. It is only a visual representation, not a physical one.
Gravity & Metric
Moreover, according to Einstein the space in the presence of masses is bent by the masses. So, the force of gravity doesn't exist, it's just convenient to use it. The physical reality of space-time
is described by an equation that binds the presence of matter/energy to the metric, that is the geometry of curved spacetime. The metric is a function of four independent variables (3 spatial and 1
temporal): (x,y,z,t). There are several metrics that describe different possible situations and it's here that the theory becomes extremely complex. But in any case, matter tells space-time how to
«bend», and in turn moves in curved spacetime.
Gravity Equation
Rᵤᵥ - ½R.gᵤᵥ + Λ. gᵤᵥ = (8Ï€G/c⁴)Tᵤᵥ
This is the famous Einstein's equation of General Relativity. Briefly, the member to the left of equality measures the curvature and geometry of space-time in 'x', while the right one measures the
density and flow of matter and energy in 'x'. This equation contains a numerical term called: cosmological constant (Λ) . Einstein introduces a negative value of it, to indicate a static universe.
Well this is probably the most serious mistake he made in his life (but we absolve him for this), because later observations showed that the universe is expanding (Λ = positive).
Final Consequences
1) Effects on space-time: lengths and times depend on the presence of masses nearby so, as in special relativity, they are no longer fixed quantities. This cause, for example, an effect that is
called Gravitational redshift, which acts on the wavelength of a light ray.
2) Effects on massless particles: a light ray, like an object with mass, must suffer the action of the gravitational field, and possibly to be bent, because it's simply moving into the fabric of
curved space-time.
3) Gravitational waves: they are a direct result of accelerated masses, that generate ripples in the metric of spacetime that propagate at the speed of light.
A Daily Effect of GR : The GPS
GPS satellites send an electromagnetic wave towards our receiver, the beam comes reflected and by the delay between issuance and reception we can measure the distance. Combining the data of three
satellites we can locate a point on Earth's surface. But the clocks on the satellites are subjected to the 'force' of gravity, which is different from that on Earth. So we measure a different time
from what they would find on Earth. If we didn't consider the effects of general relativity (and even those of special relativity) there would be a few kilometres error in the position of GPS. | {"url":"https://www.worldscienceassociation.in/2020/05/general-relativity-introduction-with.html","timestamp":"2024-11-10T20:37:26Z","content_type":"application/xhtml+xml","content_length":"275302","record_id":"<urn:uuid:17538a0a-8338-4dc5-8e0a-d3bd693664c0>","cc-path":"CC-MAIN-2024-46/segments/1730477028191.83/warc/CC-MAIN-20241110201420-20241110231420-00668.warc.gz"} |
How to Calculate Total Magnification of a Microscope
What are the magnification lenses in a standard microscope?
A standard microscope has two magnification lenses: the objective lens and the eyepiece lens.
What is the magnification of the objective lens and the eyepiece lens in a microscope?
The magnification of the objective lens is 100x, and the magnification of the eyepiece lens is 2x.
The total magnification for the microscope using the objective lens is 200x.
When using a standard microscope, it is essential to understand how to calculate the total magnification to view the specimen clearly. A standard microscope consists of two main magnification lenses:
the objective lens and the eyepiece lens.
The magnification of the objective lens is 100x, meaning that it magnifies the specimen 100 times its actual size. On the other hand, the eyepiece lens provides an additional magnification of 2x.
To calculate the total magnification of the microscope, you need to multiply the magnification of the objective lens by the magnification of the eyepiece lens. In this case, it will be:
Total magnification = Magnification of the objective lens x Magnification of the eyepiece lens
Total magnification = 100x x 2x = 200x
Therefore, the total magnification for the microscope using the objective lens is 200x. This means that the specimen will appear 200 times larger when viewed through the microscope. Understanding how
to calculate total magnification is crucial for obtaining accurate and detailed observations with a microscope. | {"url":"https://theletsgos.com/physics/how-to-calculate-total-magnification-of-a-microscope.html","timestamp":"2024-11-07T12:54:30Z","content_type":"text/html","content_length":"21383","record_id":"<urn:uuid:47e529cb-5e71-4194-8724-eed9663456e2>","cc-path":"CC-MAIN-2024-46/segments/1730477027999.92/warc/CC-MAIN-20241107114930-20241107144930-00672.warc.gz"} |
irst Bernoulli Congress
Opening words of the first Bernoulli Congress
The First Bernoulli Congress
Among the remarkable events of the 80s was the First World Congress of the Bernoulli Society which was held 8–14 September 1986 in Tashkent. The preparatory work was done by the Soviet Organizing
Committee (Honorary Chairman – A.N. Kolmogorov, Chairman – Yu.V. Prokhorov, Vice-Chairmen – S.Kh. Sirazhdinov and A.N. Shiryaev). The statistic of the Congress is the following: 35 scientific
sections, 100 forty-minute talks, 181 fifteen -minute contributions, 430 stand posters, 15 non-formal discussions, 3 round tables on topics: “Computational methods and tools in theoretical and
applied statistics”, “Relationship between theory and applications”, “Historical aspects of development of probability theory and mathematical statistics”. The Congress was opened by written
“Greetings” of A.N. Kolmogorov to the participants followed by the forum talk of A.N. Kolmogorov and V.A. Uspensky (at that time A.N. Kolmogorov was very sick and could not participate in the
Congress; his “Greetings” were recorded in Moscow by V.M. Tikhomirov and A.N. Shiryaev).
A.N.Shiryaev, Moscow
Greetings of A.N. Kolmogorov
“Dear ladies and gentleman! Allow me to welcome you today to the opening of the Congress.
It is significant to me that the Society that has taken the name Bernoulli, a Society uniting specialists in just one field of mathematics – probability theory and mathematical statistics – has
succeeded in organizing a conference of its fellow members so representative that it is comparable to international mathematics congresses. But if one thinks about it, then one can find an
explanation for this seemingly paradox phenomenon.
James Bernoulli, one of the eminent members of the Bernoulli family, has entered the pages of the history of science by virtue of his many achievements. But two of his credits should be mentioned
especially. He is the father of the science of probability theory having obtained the first serious result known everywhere as Bernoulli´s theorem. But apart from this, it should not be forgotten
that he was essentially also the father of combinatorial analysis. He used the elements of this discipline to prove his theorem but he delved into the field of combinatorial analysis considerably
further discovering in particular the remarkable sequence of numbers which now bear his name. These numbers are encountered continually in scientific investigations right down to our time.
We all feel that one of the basic requirements of mathematics that is evident at present is the investigation of very complex systems. And this complexity on the one hand is very closely related to
randomness and on the other – it necessitates in some measure an extension of combinatorial analysis itself. All this gives hope that as time passes the Bernoulli Society will increase its influence
more and more in the mathematical world. I wish the participants of the Congress all of the very best.”
From: Theory Probab. Appl., Vol. 32, No.2, p. 200,
translated from Russian Journal by Bernard Seckler | {"url":"https://bernoullisociety.org/history/53-general/203-opening-words-of-the-first-bernoulli-congress","timestamp":"2024-11-08T01:31:21Z","content_type":"text/html","content_length":"9137","record_id":"<urn:uuid:fdf295c5-a5a2-4a94-92e1-429fa653a011>","cc-path":"CC-MAIN-2024-46/segments/1730477028019.71/warc/CC-MAIN-20241108003811-20241108033811-00053.warc.gz"} |
Decimal, Float, and Value functions - Power Platform
Decimal, Float, and Value functions
Applies to:
Converts a string of text or other types to a number.
Power Apps only supports the Value function and it returns a Float value. Support for the Decimal and Float functions will be added soon.
Use the Decimal, Float, and Value functions to convert a string of text that contains number characters to a numeric value. Use these function when you need to perform calculations on numbers that
were entered as text by a user. These functions can also be used to convert other types to a number, such as date/time and Boolean.
The Value function will return the default numeric data type for the Power Fx host you are using, which is usually Decimal and the best choice for most situations. Use the Decimal and Float functions
when you need a specific data type for a particular scenario, such as a scientific calculation with a very large number. For more details on working with these data types, see the Numbers section of
Data types.
Different languages interpret , and . differently. By default, the text is interpreted in the language of the current user. You can specify the language to use with a language tag, using the same
language tags that are returned by the Language function.
Notes on the format of the string:
• The string may be prefixed with the currency symbol for the current language. The currency symbol is ignored. Currency symbols for other languages aren't ignored.
• The string may be include a percent sign (%) at the end, indicating that it's a percentage. The number will be divided by 100 before being returned. Percentages and currency symbols can't be
• The string may be in scientific notation, with 12 x 10^3 expressed as "12e3".
If the number isn't in a proper format, these functions will return an error.
To convert date and time values, use the DateValue, TimeValue, or DateTimeValue functions.
Decimal( String [, LanguageTag ] )
Float( String [, LanguageTag ] )
Value( String [, LanguageTag ] )
• String - Required. String to convert to a numeric value.
• LanguageTag - Optional. The language tag in which to parse the string. If not specified, the language of the current user is used.
Decimal( Untyped )
Float( Untyped )
Value( Untyped )
• Untyped - Required. Untyped object that represents a number. Acceptable values are dependent on the untyped provider. For JSON, the untyped object is expected to be a JSON number, boolean, or
text that can be converted to a number. Keep in mind that locale-related formats are important considerations when communicating with external systems.
The user running these formulas is located in the United States and has selected English as their language. The Language function is returning "en-US". The Power Fx host uses Decimal by default.
Value and Decimal
Since we are using a host that has Decimal as the default, Value and Decimal will return the same results.
Formula Description Result
Value( "123.456" ) The default language of "en-US" will be used, which uses a period as the decimal separator. 123.456 (Decimal)
Decimal( "123.456" )
Value( "123.456", "es-ES" ) "es-ES" is the language tag for Spanish in Spain. In Spain, a period is a thousands separator. 123456 (Decimal)
Decimal( "123.456", "es-ES" )
Value( "123,456" ) The default language of "en-US" will be used, which uses a comma as a thousands separator. 123456 (Decimal)
Decimal( "123,456" )
Value( "123,456", "es-ES" ) "es-ES" is the language tag for Spanish in Spain. In Spain, a comma is the decimal separator. 123.456 (Decimal)
Decimal( "123,456", "es-ES" )
Value( "12.34%" ) The percentage sign at the end of the string indicates that this is a percentage. 0.1234 (Decimal)
Decimal( "12.34%" )
Value( "$ 12.34" ) The currency symbol for the current language is ignored. 12.34 (Decimal)
Decimal( "$ 12.34" )
Value( "24e3" ) Scientific notation for 24 x 10^3. 24000 (Decimal)
Decimal( "24e3" )
Value( true ) Converts a Boolean to a number, 0 for false and 1 for true 1 Decimal
Decimal( true )
The Float function will have very close to the same results as above. Since 123.456 cannot be precisely represented in Float, the result is an approximation that is very close
(123.456000000000003069544618484E2) and compounding rounding errors calculations could result in an unexpected result. The resulting type will be Float instead.
Where things diverge is if larger or smaller numbers are used.
Formula Description Result
Float( 1e100 ) Because the literal number 1e100 is beyond the range of a Decimal, this results in an error before ever calling the Float function. error (overflow)
Decimal( 1e100 ) Same problem as with the Float function. error (overflow)
Float( "1e100" ) The number in the text string is within the range of Float numbers. 1e100 Float
Decimal( "1e100" ) The number in the text string is beyond the range of Decimal numbers. error (overflow)
Float( The number in the text string is within the range of Float numbers. However, the number requires more precision than a Float can provide 1 (Float)
"10000000000.0000000001" ) and will be truncated.
Decimal( The number in the text string is within both the range and precision of a Decimal numbers. 10000000000.0000000001 (
"10000000000.0000000001" ) Decimal) | {"url":"https://learn.microsoft.com/en-us/power-platform/power-fx/reference/function-value?WT.mc_id=DX-MVP-5003873","timestamp":"2024-11-10T02:31:41Z","content_type":"text/html","content_length":"52325","record_id":"<urn:uuid:5d28889a-3df4-415f-9c37-463660fcf6b5>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.3/warc/CC-MAIN-20241110005602-20241110035602-00256.warc.gz"} |
Random Question Archives - KK LEE MATHEMATICS
Random questions that I find interesting and challenging will be uploaded here. Try to discuss it with your teacher or your friends if you cant solve it. Solutions will be upload when I’m free, you
can also share your solution in the comment section. | {"url":"https://kkleemaths.com/category/questions-and-solutions/random-question/","timestamp":"2024-11-03T17:04:10Z","content_type":"text/html","content_length":"364190","record_id":"<urn:uuid:24524226-9296-4d00-a6e4-43c2c44aa14f>","cc-path":"CC-MAIN-2024-46/segments/1730477027779.22/warc/CC-MAIN-20241103145859-20241103175859-00650.warc.gz"} |
Where can I find assistance with optimization problems in statics and dynamics? | Hire Someone To Do Mechanical Engineering Assignment
Where get redirected here I find assistance with optimization problems in statics and dynamics? I can’t understand how to know that the simulation results are the same under any approach. I would
really like to learn how to use tools for improving statics and dynamics for future research. A: Your first question seems quite simple, but it is not really what I would ask. I would try to search
the field for tutorials on similar topics. I would much prefer to find a similar topic in a forum or on a mailing list – but I’d like to ask a quick question. What will be the most helpful technical
ideas I can add to any sort of analysis, including your other design questions? Edit: How to optimize data flow for statics? In physics? Because of the concepts taught in previous answers you are
missing to the right ideas. Since you asked, the solution to your research question could have been to execute the step (1) in Tensorflow. Once the user has implemented the steps you need to do
Tensorflow transform steps as well since you were using tf.transform.step. The steps are relatively simple to execute, and require little programming effort but, at the same time, somewhat more
efficient than steps without a new input. So, to remove just one step or no step you basically need to add a step parameter that specifies the time the step is done: step0 = tf.train.Step(0) step1 =
tf.train.Step(0) step2 = tf.train.Step(100) So, when the steps are combined, the step0 and step1 parameters should be Tensorflow or tensorflow. Here, how your step0 and step1 parameters are used with
the solution is very straightforward, and you simply put them in function t_transform. So here’s how you can do it: Tensorflow.
Pay Someone To Do My Statistics Homework
tf.fromstring(step0) Tensorflow. tfWhere can I find assistance with optimization problems Homepage statics and dynamics? A: There has been no direct answer to this question but I would expect more
like: a) What type of function can turn the system into an object? If the first, you’d have to use function arithmetic to indicate that something’s taking place, but given, perhaps non-integer x and
y there could just be 1,2, 7, etc. Now let’s take a closer look at the simple example: -A 0.01*A cosine function a) There’s no such thing as a square root here, so you have to first compute this. In
fact, we know this is done by giving the function an integer shape based on the square of the natural geometric sort. In the simplest cases it’s a sum over simple factors of 6 and so we could get: 1
b) The two cases are quite similar, and there’s a considerable overlap as to what’s going on. Which are the right ones? b) A practical way for finding the correct structure is to place all the nodes
/ simplices in a hierarchy, so that for you an even number of elements can be found most commonly, and it’s not nice to have only so many nodes and several elements. Instead, a tree is a good parent
for increasing “depth” and therefore the hierarchy is really much easier to make up with as we move from bottom to top: a) For the first case, we’ll use the current value of x=4, let’s write a little
rearranged list: plot(q=(3*5*7)*2,color=’red’) Now we’ll start with the first of the remaining three values. In this case we are computing either x=4 or x=6. Why? Because it looks like the former or
rather the latter is simplerWhere can I find assistance with optimization problems in statics and dynamics? I’ve gone through a simple list of keywords that could help a new user learn about statics,
so far this is what I’ve found: A keyword shouldn’t work on their own, as in “the properties”. A keyword doesn’t automatically imply any number of properties, and the parameters of the properties are
only one of the things in the list. (Example: I have two properties, both of which map to the same “variable” $xyz$[31], however I published here to determine which one of, say there is an
“identifier” parameter, that would not only appear under the word $XY$ but also under the word $XY + -I$.) A keyword should never lead to parameters that can’t be found under the parameter and
shouldn’t be named or described to give instructions on how to find those parameters. A keyword that does what its name calling means will have no properties read this post here but let’s say I’m
looking for a “identifier” for the $XY$ “property” that I already have been looking for. (If that’s how I want to get $XY$ out of search terms, it should be under the property number.) This is how I
want to combine the properties of two items into one – I have the property that corresponds to XY, and I have the property that correspond to xy, and I thought it necessary to work out. I also think
it will be interesting to compare the properties of two properties, so have trouble thinking if they both are the same in terms of one or the other – for instance if one was like I might add
properties for $XY$ that way. Maybe you could just write a search formula and check if that property matches with one of those two to see if it’s the criteria you want, so that you can see if you can
find any possible criteria for determining which one. But then I have to check all the parameters for each of the two properties, and then I would probably agree that I have found the perfect
“identifier” (if any!) at all, which would have to be between the properties $xyz$ and $XY + I$ and has to look like that.
Do My Homework Discord
By comparison, I want to compare my $XY$ and $XY + – I pairnals to gain a greater understanding, and then I would potentially get to know which one the best would be given any criteria for
determining which one. Sorry for posting about all the variables, that’s a Check This Out long way to go. I just do like to come round sometimes on some topic, but other times I find myself looking
for fun stuff. I wanted to think about all the possible reasons for making this list – I’ve used it all I can write, and some of the other variables exist, and I also don’t know where to begin. I
want to get myself into the habit of “smashing out” of ideas, ideas that don’t seem to challenge the conclusions I’m trying to draw, that I think can make the world better. In the meantime, I guess I
could look at the search terms in different ways, then compare how the properties would look based on the examples I’ve got. Maybe it’s one or the other, maybe not. The original problem I’d like to
try to add some bit of insight to this so someone who knows some experience as a mathematician tends to do that kind of research. For this, I need some ideas first and I’d like to use some thought
input, and get access to some concepts. So in this project: 1. Create a new project, and work on it into some domain, we’ll research our own topic, and we’ll write some code that plays nice to use.
Here’s the problem: if we add a variable with keyword keyword keywordXY in that “instance” (a dynamic property), and we | {"url":"https://mechanicalassignments.com/where-can-i-find-assistance-with-optimization-problems-in-statics-and-dynamics","timestamp":"2024-11-10T22:33:24Z","content_type":"text/html","content_length":"132349","record_id":"<urn:uuid:554514f4-a37b-4ffc-9ddc-7ae3bce2d440>","cc-path":"CC-MAIN-2024-46/segments/1730477028191.83/warc/CC-MAIN-20241110201420-20241110231420-00355.warc.gz"} |
linear algebra
Understand the Problem
The question seems to be related to the topic of linear algebra, which may encompass various concepts such as vector spaces, linear transformations, matrices, and systems of equations. However, it is
presented in a vague manner without a specific inquiry.
Linear algebra focuses on vectors, matrices, vector spaces, and linear transformations.
Linear algebra is a mathematical discipline dealing with vectors, matrices, vector spaces, and linear transformations.
Answer for screen readers
Linear algebra is a mathematical discipline dealing with vectors, matrices, vector spaces, and linear transformations.
More Information
Linear algebra is fundamental to modern geometry and used extensively in systems of linear equations, mathematical modeling, and computer graphics. | {"url":"https://quizgecko.com/q/linear-algebra-p8ltk","timestamp":"2024-11-01T18:56:11Z","content_type":"text/html","content_length":"170692","record_id":"<urn:uuid:41f8f7bf-0ab8-4062-ad77-594151d4283c>","cc-path":"CC-MAIN-2024-46/segments/1730477027552.27/warc/CC-MAIN-20241101184224-20241101214224-00072.warc.gz"} |
Study Tips: Guys how do you develop interest in a subject like Maths or Accounting
Posts : 1095
Points : 1196
Join date : 2015-04-04
Location : Previously: Belarus Currently: A Small Island No One Cares About
BACKSTORY: In between my work I am preparing for some certified courses like ACCA and CFA. The problem is there are subjects like Maths and Accounting in which I do not have much interest.
Can you guys share some best practices as to how an individual can develop interest in subjects like Maths and Accounting?
Posts : 4212
Points : 4227
Join date : 2015-04-21
Location : Krankhaus Central.
jhelb wrote:BACKSTORY: In between my work I am preparing for some certified courses like ACCA and CFA. The problem is there are subjects like Maths and Accounting in which I do not have much
Can you guys share some best practices as to how an individual can develop interest in subjects like Maths and Accounting?
See how much an accountant makes...See how easy for an accountant is to find employment. And see how basic accountancy can become with enough will power.
All you have to do is stop thinking about it, and do it. It took me a whole semester at 40+ yo to get the gist of the subject for my BA-2. Worst 6 months on my life, one's basically an idiot when it
comes to that. However when you pick it up, you just want to do that all rest of your life. Ok the hype lasts for about a week, then you see how shitty it is and resume normal activities. But the
paycheck though (at least here where I am) for a mid level accountant with multiple languages earns you around 6/7K european monkey money brutto/month (around 4K netto - 50K a year plus some perks).
Small biz pays less.
And you just have to cook up books.Think about it.
Posts : 1802
Points : 1832
Join date : 2011-10-14
jhelb wrote:BACKSTORY: In between my work I am preparing for some certified courses like ACCA and CFA. The problem is there are subjects like Maths and Accounting in which I do not have much
Can you guys share some best practices as to how an individual can develop interest in subjects like Maths and Accounting?
If you hate something/have no interest, why do it beyond the minimum?
You probably wont succeed forcing yourself to spend 40yrs doing something hate?
Having said that, sometimes we need an understand of something we hate.
eg maths/accountancy.
I trial and visualise things, and automate using spreadsheets. And also work with someone else who likes numbers but hates the creative stuff.
Maybe just try and understand/do the basics well.Learn it so that it becomes 2nd nature, and not a chore. And assists in waht you have a passion/natural ability for.
But really, I think NEVER go down a path that would bore you rigid.
Lots of businessmen have an accountancy background and find it useful. But they avoid getting bogged down in the heavy number crunching and stuff. Its like most businessmen have websites, but dont
write html or do web marketing.
Posts : 1095
Points : 1196
Join date : 2015-04-04
Location : Previously: Belarus Currently: A Small Island No One Cares About
Thanks Firebird.
Firebird wrote:If you hate something/have no interest, why do it beyond the minimum?
Need these certificates to prove my worth. Having to compete with graduates from Oxford, MIT and Harvard for jobs.
I realize that getting admission into an Oxford, MIT or Harvard is difficult so CFA/ACCA are my next best option. Else, will have to spend the rest of my life doing contract jobs.
Posts : 1459
Points : 1535
Join date : 2009-08-04
Age : 36
Location : Indonesia
Having clear purpose on what to do with those skill. Interest will come by itself.
Posts : 1095
Points : 1196
Join date : 2015-04-04
Location : Previously: Belarus Currently: A Small Island No One Cares About
Stealthflanker wrote:Having clear purpose on what to do with those skill. Interest will come by itself.
Thanks Stealthflanker. Profound insight as usual.
My problem is I like the subjects ( and yes I also know what to do with it) but find the idea of studying very boring.
Posts : 40464
Points : 40964
Join date : 2010-03-30
Location : New Zealand
I found with maths and physics I found things easier to apply them to things I found interesting.
For instance calculating ballistic paths of different real artillery shells, it also helped me remember which formula I needed to make different calculations.
In my final year for my degree in Info Science they changed from relational databases (RDB) to object oriented (Oracle), so we went from SQL to java and I really made the basic mistake in
programming... don't get behind. Once you get behind that is it you just get further and further behind as the class learns new stuff and you are trying to learn the stuff they went over last week.
Anyway after just passing the paper in my fourth year most of the info papers required java and I wasn't really interested, so I took a 4th year paper on computer security, and a 4th year multimedia
paper, which left me needing two more papers.
When I was in the third year they had a new networking paper which I took instead of a paper on Artifical Intelligence which I regretted as the new networking paper was new and not well organised.
So I took the AI paper in my fourth year but needed a 6 point paper for the first semester so I took Quantative Statistics (QUAN)... I like calculations and formulas but had trouble with the
terminology and working out which formula to use when... Managed to get through four years with no fails...
In QUAN you are in a lecture theatre with 600 people, so it was pretty much a man or a woman reading out notes where you scribble examples on the notes provided and that is it... I would have
preferred small classes, but most 100 level papers have large numbers of people so it is not practical.
Sujoy likes this post
Morpheus Eberhardt
Posts : 1925
Points : 2032
Join date : 2013-05-20
There are books written by real experts that in many instances can get a person interested in a given subject. Often, a lot of the interest gets developed through the right kind of exposure.
Take a look at this classic. http://www.amazon.com/Mathematics-Can-Fun-Yakov-Perelman/dp/B000W18X5Q. I am sure free legal copies are available on the net. What do you think?
Most of these kind of books are written by great Russian scientists.
Edit: Here is a free copy.
More Editing: The author Yakov Perelman is a legend. His book Physics for Fun (2 volumes) has the record for making people becoming physicists.
Posts : 1095
Points : 1196
Join date : 2015-04-04
Location : Previously: Belarus Currently: A Small Island No One Cares About
Morpheus Eberhardt wrote:There are books written by real experts that in many instances can get a person interested in a given subject. Often, a lot of the interest gets developed through the
right kind of exposure.
Take a look at this classic. http://www.amazon.com/Mathematics-Can-Fun-Yakov-Perelman/dp/B000W18X5Q. I am sure free legal copies are available on the net. What do you think?
Most of these kind of books are written by great Russian scientists.
Edit: Here is a free copy.
More Editing: The author Yakov Perelman is a legend. His book Physics for Fun (2 volumes) has the record for making people becoming physicists.
Thanks Morpheus. Yes, you are correct. His two books Physics Can Be Fun and Mathematics Can Be Fun were very popular in the Soviet Union, a country that had set new heights in the field of education.
Consequently, a number of countries obtained the rights to translate his books.
Posts : 692
Points : 745
Join date : 2015-05-08
Location : Oregon, USA
Novgorod winter no fun. stay home read
the old day
Posts : 753
Points : 728
Join date : 2014-03-24
Location : Fairfield, CT
jhelb wrote:Can you guys share some best practices as to how an individual can develop interest in subjects like Maths and Accounting?
My favorite is to break down a task into ridiculously miniscule parts. The reality is that starting is the hardest part. If you start with steps even smaller than baby steps, you can easily get the
ball rolling.
Sponsored content | {"url":"https://www.russiadefence.net/t4006-study-tips-guys-how-do-you-develop-interest-in-a-subject-like-maths-or-accounting","timestamp":"2024-11-11T14:55:34Z","content_type":"text/html","content_length":"113582","record_id":"<urn:uuid:3e85c78c-2272-40c8-ac84-4fc9af14166a>","cc-path":"CC-MAIN-2024-46/segments/1730477028230.68/warc/CC-MAIN-20241111123424-20241111153424-00115.warc.gz"} |
Mean Reversion Trading - Traders Log
Mean Reversion Trading
George Soros, the legendary investor, once described financial markets as “chaos.”
The events of past weeks, in all financial markets, bear witness to the accuracy of this statement. Despite this “chaos,” or maybe because of it, every traded investment vehicle has a price that
reflects the underlying value of the assets and the future income stream. This is, over the long term, the basis of the efficient market theory. No matter what the asset, it will eventually gravitate
to its most efficient price level over the long term due to the presence of “perfect information,” where are all factors are accounted for in the buy and sell offers. The phenomenon where it returns
to is previous pricing level in the short term is known as “Mean Reversion.”
According to Investopedia, Mean Reversion is, “A theory suggesting that prices and returns eventually move back towards the mean or average. This mean or average can be the historical average of the
price or return or another relevant average such as the growth in the economy or the average return of an industry.” For the trader, this means that profits can be made by placing buy and sell orders
based on the price of the investment vehicle returning to its previous position, over the short term.
This has been found to hold true for interest rates, as just one example. In a March 2011 study by Jan Willem van den End, of the Economics and Research Division of De Nederlandsche Bank, โ
Statistical Evidence on the Mean Reversion of Interest Rates,โ it was determined that, based on two hundred years of annual data of the Netherlands, Germany, US and Japan, short-term interest rates
and the yield curve “tend to revert to their long-term average value.” The same did not hold true for long-term rates, however, as “long-term rates can persistently deviate from it.” For long-term
interest rates, based on the outcomes of smooth transition autoregressive ( STAR ) models, the force for mean reversion was strongest when “rates are far from their equilibrium value.” For this
reason, mean reversion for interest rates is included in short-term financial models.
Foreign exchange pricing is also based on mean reversion trading for the short term, too. A paper, “Combining Mean Reversion Strategy and Momentum Trading Strategies in Foreign Exchange Markets,” by
Dr. Alina F. Serban, found in 2009 that mean reversion patterns for foreign exchange trading is much like that of the equity markets. Dr. Serban, of West Virginia University, noted that, “I found
that the patterns for the positions thus created in the foreign exchange markets is qualitatively similar to that found in the equity markets. Also, it outperforms traditional foreign exchange
trading strategies, such as carry trades and moving average rules.
It is no different for Exchanged traded funds (ETFs). The two purest examples are (NYSE: QLD), the Proshares ULTRA QQQ (long the S&P 500), and (NYSE: QID), the Proshares Ultra Short QQQ (short the S&
P 500) due to the wide asset base of each, preventing the news from one company distorting the price. Over each of the last five trading days (August 17-22), all very turbulent, the QLD, at some
point in the session, rose above the opening price. The same was true for the QID. Over the last five day range (August 17-22, 2011), the QID increased 12.79% while the QLD fell 12.42%, yet, each ETF
rose above the opening price every day as it reverted to the mean.
For an individual equity, the movement of the share price for Dell Inc (NASDAQ: DELL) this week serves on a timely example. On Thursday August the 18th, Dell Computer reported earnings which
disappointed Wall Street. Closing at $14.20 on the Wednesday the 17th, Dell opened lower on the earnings and traded as low as $13.31 on Thursday the 18th. Even with the market down by 172.93 points
on Friday the 19th, Dell hit a high of $14.62, up $1.32 over the low of the previous session, before closing up for the day. There was no news or announcements from Dell to raise its share price,
just the stock price reverting to the mean.
The factors leading to a big gain or big loss for a stock are endless. Many times they are minor events that have no impact on the long term value of the company (the very basis of mean reversion).
For Dell, it was earnings that were lower than the estimates of the analyst community. For a small cap, this can be even more monumental due to many being thinly traded. When a stock makes a big
move, “hot money” immediately jumps in to chase it via program trading. As about 70% of the buying and selling on stock exchanges is now transacted by institutional investors, much of that high
frequency trading, it feeds upon itself. Existing buy and sell orders are executed, reinforcing the direction of the price movement. The โ cascading effectโ is actuated, where existing buy and
sell orders are triggered, reinforcing the price movement.
Mean reversion also provides the foundation of high frequency program trading known as “statistical reversionโ or โ statistical arbitrage.โ This evolved from โ pairs trading,โ where stocks
are bought long and sold short on the expectation they will mean revert by following each other in price due to an established relationship. Statistical arbitrage involves a portfolio of a hundred or
more stocks that are carefully matched by region and sector to eliminate exposure to beta and other risk factors, allowing for the adhering of mean reversion determined pricing relationships to the
other stocks.
Larry Connors, author of โ How Markets Really Work,โ studied mean reversion trading for equities. Over a decade long period, Connors documented stocks that were at a 10 day high for the moving
average and exiting when it closed below its five day moving average; and then buying at a 10 day low below the 200 day moving average and selling when it closed above the five day moving average.
The results, according to Connors: “Two things stand out. First, the average returns for the stocks that made 10-day lows is nearly double that of stocks that made 10-day highs. Even more eye-opening
is the percentage of winning trades. Buying 10-day lows was correct nearly 65% of the time, while buying 10-day highs was correct only 38% of the time. “
Mean reversion is merely a function of perfect pricing information for an investment vehicle, after all. The price of the investment vehicle, be it an ETF or an equity or a foreign currency unit, was
at that level for a reason. A short term event, such as missing earnings by a few cents, does not alter the fundamental economic value of the asset as determined by the long term input of perfect
information. As Connors notes, “Markets are more efficient long term. There is little statistical evidence to support otherwise. But markets can be very inefficient short term. There’s ample
statistical evidence to prove this, and that’s where the best opportunities are today.” Mean reversion allows for traders to profit from the โ chaosโ of financial markets due to the perfect
information accounted for in the long term price of an investment vehicle that is ignored by the short-term inefficiencies of event-driven buying and selling on exchanges.
By Jonathan Yates | {"url":"http://www.traderslog.com/mean-reversion-trading","timestamp":"2024-11-03T12:07:59Z","content_type":"text/html","content_length":"245887","record_id":"<urn:uuid:8fc34b21-3467-4658-85e3-3505d03cc246>","cc-path":"CC-MAIN-2024-46/segments/1730477027776.9/warc/CC-MAIN-20241103114942-20241103144942-00674.warc.gz"} |
Today in Science History - Quickie Quiz
Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
Category Index for Science Quotations
Category Index I
> Category: Invent
Invent Quotes (57 quotes)
“Progress” was synonymous with distance from nature. The adults, who set the pace of progress from nature, were so absorbed by their own ability to invent and to alter the existing world, that they
hurried headlong, with no design for the ultimate structure. A man-made environment was the obvious goal, but who was the responsible architect? No one in my country. Not even the king of Great
Britain or the president of America. Each inventor and producer who worked on building tomorrow’s world just threw in a brick or a cogwheel wherever he cared to, and it was up to us of the next
generation to find out what the result would be.
In Ch. 1, 'Farewell to Civilization', Fatu-Hiva (1974), 4.
Pour inventor il faut penser à côté.
To invent you must think aside
In Calyampudi Radhakrishna Rao, Statistics and Truth (1997), 31.
A man who is master of himself can end a sorrow as easily as he can invent a pleasure.
In 'Dorian Gray', The Writings of Oscar Wilde: Epigrams, Phrases and Philosophies For the Use of the Young (1907), 49.
An essential [of an inventor] is a logical mind that sees analogies. No! No! not mathematical. No man of a mathematical habit of mind ever invented anything that amounted to much. He hasn’t the
imagination to do it. He sticks too close to the rules, and to the things he is mathematically sure he knows, to create anything new.
As quoted in French Strother, 'The Modern Profession of Inventing', World's Work and Play (Jul 1905), 6, No. 32, 187.
As the nineteenth century drew to a close, scientists could reflect with satisfaction that they had pinned down most of the mysteries of the physical world: electricity, magnetism, gases, optics,
acoustics, kinetics and statistical mechanics … all had fallen into order before them. They had discovered the X ray, the cathode ray, the electron, and radioactivity, invented the ohm, the watt, the
Kelvin, the joule, the amp, and the little erg.
A Short History of Nearly Everything. In Clifford A. Pickover, Archimedes to Hawking: Laws of Science and the Great Minds Behind Them (2008), 172.
But we shall not satisfy ourselves simply with improving steam and explosive engines or inventing new batteries; we have something much better to work for, a greater task to fulfill. We have to
evolve means for obtaining energy from stores which are forever inexhaustible, to perfect methods which do not imply consumption and waste of any material whatever.
Speech (12 Jan 1897) at a gala inaugurating power service from Niagara Falls to Buffalo, NY. Printed in 'Tesla on Electricity', The Electrical Review (27 Jan 1897), 30, No. 3, 47.
Chaos theory is a new theory invented by scientists panicked by the thought that the public were beginning to understand the old ones.
John Mitchinson and John Lloyd, If Ignorance Is Bliss, Why Aren't There More Happy People?: Smart Quotes for Dumb Times (2009), 273.
Commenting on Archimedes, for whom he also had a boundless admiration, Gauss remarked that he could not understand how Archimedes failed to invent the decimal system of numeration or its equivalent
(with some base other than 10). … This oversight Gauss regarded as the greatest calamity in the history of science.
In Men of Mathematics (1937), 256.
Equations are Expressions of Arithmetical Computation, and properly have no place in Geometry, except as far as Quantities truly Geometrical (that is, Lines, Surfaces, Solids, and Proportions) may be
said to be some equal to others. Multiplications, Divisions, and such sort of Computations, are newly received into Geometry, and that unwarily, and contrary to the first Design of this Science. For
whosoever considers the Construction of a Problem by a right Line and a Circle, found out by the first Geometricians, will easily perceive that Geometry was invented that we might expeditiously
avoid, by drawing Lines, the Tediousness of Computation. Therefore these two Sciences ought not to be confounded. The Ancients did so industriously distinguish them from one another, that they never
introduced Arithmetical Terms into Geometry. And the Moderns, by confounding both, have lost the Simplicity in which all the Elegance of Geometry consists. Wherefore that is Arithmetically more
simple which is determined by the more simple Equation, but that is Geometrically more simple which is determined by the more simple drawing of Lines; and in Geometry, that ought to be reckoned best
which is geometrically most simple.
In 'On the Linear Construction of Equations', Universal Arithmetic (1769), Vol. 2, 470.
Everything that can be invented, has been invented. [A myth, attributed - almost certainly falsely - to Duell.]
A classic example of a zombie-type quote. It should be long dead, but keeps living on as a myth, impossible to extirpate. For example, it is glibly recited and attributed (as always, without a valid
primary source), to a Commissioner ("Director") of U.S. Patent Office, urging President McKinley to abolish his office, in Chris Morgan and David Langford, Facts and Fallacies (1981). (Duell held the
office 1898-1901.) It has a long history of being debunked, for example, see Eber Jeffery, Journal of the Patent Office Society (July 1940), and Samuel Sass, 'A Patently False Patent Myth', Skeptical
Inquirer (Spring 1989), 13, 310-313.
For centuries and millenniums, God rested while man invented wheelbarrows and cars. God had not thought of inventing dynamite. Did he realize his own shortcomings when he saw what we could do? Did he
approve of our remodeling of everything he had done?
In Ch. 1, 'Farewell to Civilization', Fatu-Hiva (1974), 6.
His Majesty has, with great skill, constructed a cart, containing a corn mill, which is worked by the motion of the carriage. He has also contrived a carriage of such a magnitude as to contain
several apartments, with a hot bath; and it is drawn by a single elephant. This movable bath is extremely useful, and refreshing on a journey. … He has also invented several hydraulic machines, which
are worked by oxen. The pulleys and wheels of some of them are so adjusted that a single ox will at once draw water out of two wells, and at the same time turn a millstone.
From Ain-i-Akbery (c.1590). As translated from the original Persian, by Francis Gladwin in 'Akbar’s Conduct and Administrative Rules', 'Of Machines', Ayeen Akbery: Or, The Institutes of the Emperor
Akber (1783), Vol. 1, 284. Note: Akbar (Akber) was a great ruler and enlightened statesman.
History tells us that [leading minds] can’t do it alone. From landing on the moon, to sequencing the human genome, to inventing the Internet, America has been the first to cross that new frontier
because we had leaders who paved the way: leaders like President Kennedy, who inspired us to push the boundaries of the known world and achieve the impossible; leaders who not only invested in our
scientists, but who respected the integrity of the scientific process.
From weekly Democratic address as President-Elect, online video (20 Dec 2008), announcing his selection of science and technology advisers. C-Span video 282995-102.
I believe no woman could have invented calculus.
I believe that the useful methods of mathematics are easily to be learned by quite young persons, just as languages are easily learned in youth. What a wondrous philosophy and history underlie the
use of almost every word in every language—yet the child learns to use the word unconsciously. No doubt when such a word was first invented it was studied over and lectured upon, just as one might
lecture now upon the idea of a rate, or the use of Cartesian co-ordinates, and we may depend upon it that children of the future will use the idea of the calculus, and use squared paper as readily as
they now cipher. … When Egyptian and Chaldean philosophers spent years in difficult calculations, which would now be thought easy by young children, doubtless they had the same notions of the depth
of their knowledge that Sir William Thomson might now have of his. How is it, then, that Thomson gained his immense knowledge in the time taken by a Chaldean philosopher to acquire a simple knowledge
of arithmetic? The reason is plain. Thomson, when a child, was taught in a few years more than all that was known three thousand years ago of the properties of numbers. When it is found essential to
a boy’s future that machinery should be given to his brain, it is given to him; he is taught to use it, and his bright memory makes the use of it a second nature to him; but it is not till after-life
that he makes a close investigation of what there actually is in his brain which has enabled him to do so much. It is taken because the child has much faith. In after years he will accept nothing
without careful consideration. The machinery given to the brain of children is getting more and more complicated as time goes on; but there is really no reason why it should not be taken in as early,
and used as readily, as were the axioms of childish education in ancient Chaldea.
In Teaching of Mathematics (1902), 14.
I find out what the world needs, then I proceed to invent. My main purpose in life is to make money so that I can afford to go on creating more inventions.
I never pick up an item without thinking of how I might improve it. I never perfected an invention that I did not think about in terms of the service it might give others. I want to save and advance
human life, not destroy it. I am proud of the fact that I never invented weapons to kill. The dove is my emblem.
I should like to draw attention to the inexhaustible variety of the problems and exercises which it [mathematics] furnishes; these may be graduated to precisely the amount of attainment which may be
possessed, while yet retaining an interest and value. It seems to me that no other branch of study at all compares with mathematics in this. When we propose a deduction to a beginner we give him an
exercise in many cases that would have been admired in the vigorous days of Greek geometry. Although grammatical exercises are well suited to insure the great benefits connected with the study of
languages, yet these exercises seem to me stiff and artificial in comparison with the problems of mathematics. It is not absurd to maintain that Euclid and Apollonius would have regarded with
interest many of the elegant deductions which are invented for the use of our students in geometry; but it seems scarcely conceivable that the great masters in any other line of study could
condescend to give a moment’s attention to the elementary books of the beginner.
In Conflict of Studies (1873), 10-11.
If you ask a person, “What were you thinking?” you may get an answer that is richer and more revealing of the human condition than any stream of thoughts a novelist could invent. I try to see through
people’s faces into their minds and listen through their words into their lives, and what I find there is beyond imagining.
In any conceivable method ever invented by man, an automaton which produces an object by copying a pattern, will go first from the pattern to a description to the object. It first abstracts what the
thing is like, and then carries it out. It’s therefore simpler not to extract from a real object its definition, but to start from the definition.
From lecture series on self-replicating machines at the University of Illinois, Lecture 5 (Dec 1949), 'Re-evaluation of the Problems of Complicated Automata—Problems of Hierarchy and Evolution',
Theory of Self-Reproducing Automata (1966).
In some remote corner of the universe, poured out and glittering in innumerable solar systems, there once was a star on which clever animals invented knowledge. That was the haughtiest and most
mendacious minute of ‘world history’—yet only a minute. After nature had drawn a few breaths the star grew cold, and the clever animals had to die. ... There have been eternities when [human
intellect] did not exist; and when it is done for again, nothing will have happened.
In the summer of 1937, … I told Banach about an expression Johnny [von Neumann] had once used in conversation with me in Princeton before stating some non-Jewish mathematician’s result, “Die Goim
haben den folgendenSatzbewiesen” (The goys have proved the following theorem). Banach, who was pure goy, thought it was one of the funniest sayings he had ever heard. He was enchanted by its
implication that if the goys could do it, Johnny and I ought to be able to do it better. Johnny did not invent this joke, but he liked it and we started using it.
In Adventures of a Mathematician (1976, 1991), 107. Von Neumann, who was raised in Budapest by a Jewish family, knew the Yiddish word “goy” was equivalent to “gentile” or a non-Jew. Stefan Banach, a
Polish mathematician, was raised in a Catholic family, hence “pure goy”. Ulam thus gives us the saying so often elsewhere seen attributed to von Neumann without the context: “The goys have proved the
following theorem.” It is seen anecdotally as stated by von Neumann to begin a classroom lecture.
Inventing is the intellectual bicycle that he rides each day.
Reported without quotation marks, describing James West, by Timothy L. O’Brien, in 'Not Invented here: Are U.S. Innovators Losing Their Competitive Edge?', New York Times (13 Nov 2005), B6.
It frequently happens that two persons, reasoning right on a mechanical subject, think alike and invent the same thing without any communication with each other.
As quoted by Coleman Sellers, Jr., in his Lecture (20 Nov 1885) delivered at the Franklin Institute. Printed in Coleman Sellers, Jr., 'Oliver Evans and his Inventions', Journal of the Franklin
Institute (Jul 1886), 122, No. 1, 15.
It is quite possible that mathematics was invented in the ancient Middle East to keep track of tax receipts and grain stores. How odd that out of this should come a subtle scientific language that
can effectively describe and predict the most arcane aspects of the Universe.
Epigraph in Isaac Asimov’s Book of Science and Nature Quotations (1988), 265.
It is, of course, a bit of a drawback that science was invented after I left school.
In Observer (23 Jan 1983).
It was necessary to invent everything. Dynamos, regulators, meters, switches, fuses, fixtures, underground conductors with their necessary connecting boxes, and a host of other detail parts, even
down to insulating tape.
Concerning the electrical system to power his customers’ electric lights.
It would seem at first sight as if the rapid expansion of the region of mathematics must be a source of danger to its future progress. Not only does the area widen but the subjects of study increase
rapidly in number, and the work of the mathematician tends to become more and more specialized. It is, of course, merely a brilliant exaggeration to say that no mathematician is able to understand
the work of any other mathematician, but it is certainly true that it is daily becoming more and more difficult for a mathematician to keep himself acquainted, even in a general way, with the
progress of any of the branches of mathematics except those which form the field of his own labours. I believe, however, that the increasing extent of the territory of mathematics will always be
counteracted by increased facilities in the means of communication. Additional knowledge opens to us new principles and methods which may conduct us with the greatest ease to results which previously
were most difficult of access; and improvements in notation may exercise the most powerful effects both in the simplification and accessibility of a subject. It rests with the worker in mathematics
not only to explore new truths, but to devise the language by which they may be discovered and expressed; and the genius of a great mathematician displays itself no less in the notation he invents
for deciphering his subject than in the results attained. … I have great faith in the power of well-chosen notation to simplify complicated theories and to bring remote ones near and I think it is
safe to predict that the increased knowledge of principles and the resulting improvements in the symbolic language of mathematics will always enable us to grapple satisfactorily with the difficulties
arising from the mere extent of the subject.
In Presidential Address British Association for the Advancement of Science, Section A., (1890), Nature, 42, 466.
Junior high school seemed like a fine idea when we invented it but it turned out to be an invention of the devil. We’re catching our boys in a net in which they’re socially unprepared. We put them in
junior high school with girls who are two years ahead of them. There isn’t a thing they should have to do with girls at this age except growl at them.
As quoted in interview with Frances Glennon, 'Student and Teacher of Human Ways', Life (14 Sep 1959), 147.
Last night I invented a new pleasure, and as I was giving it the first trial an angel and a devil came rushing toward my house. They met at my door and fought with each other over my newly created
pleasure; the one crying, “It is a sin!” - the other, “It is a virtue!”
In Kahlil Gibran: The Collected Works (2007), 21.
Learning how to access a continuity of common sense can be one of your most efficient accomplishments in this decade. Can you imagine common sense surpassing science and technology in the quest to
unravel the human stress mess? In time, society will have a new measure for confirming truth. It’s inside the people-not at the mercy of current scientific methodology. Let scientists facilitate
discovery, but not invent your inner truth.
Let me arrest thy thoughts; wonder with me, why plowing, building, ruling and the rest, or most of those arts, whence our lives are blest, by cursed Cain’s race invented be, and blest Seth vexed us
with Astronomy.
Metals are the great agents by which we can examine the recesses of nature; and their uses are so multiplied, that they have become of the greatest importance in every occupation of life. They are
the instruments of all our improvements, of civilization itself, and are even subservient to the progress of the human mind towards perfection. They differ so much from each other, that nature seems
to have had in view all the necessities of man, in order that she might suit every possible purpose his ingenuity can invent or his wants require.
From 'Artist and Mechanic', The artist & Tradesman’s Guide: embracing some leading facts & principles of science, and a variety of matter adapted to the wants of the artist, mechanic, manufacturer,
and mercantile community (1827), 16.
Of all the sciences that pertain to reason, Metaphysics and Geometry are those in which imagination plays the greatest part. … Imagination acts no less in a geometer who creates than in a poet who
invents. It is true that they operate differently on their object. The first shears it down and analyzes it, the second puts it together and embellishes it. … Of all the great men of antiquity,
Archimedes is perhaps the one who most deserves to be placed beside Homer.
From the original French: “La Métaphysique & la Géométrie sont de toutes les Sciences qui appartiennent à la raison, celles où l’imagination à le plus de part. … L’imagination dans un Géometre qui
crée, n’agit pas moins que dans un Poëte qui invente. Il est vrai qu’ils operent différemment sur leur objet; le premier le dépouille & l’analyse, le second le compose & l’embellit. … De tous les
grands hommes de l’antiquité, Archimede est peut-être celui qui mérite le plus d’être placé à côté d’Homere.” In Discours Preliminaire de L'Encyclopedie (1751), xvi. As translated by Richard N.
Schwab and Walter E. Rex, Preliminary Discourse to the Encyclopedia of Diderot (1963, 1995), xxxvi. A footnote states “Note that ‘geometer’ in d’Alembert’s definition is a term that includes all
mathematicians and is not strictly limited to practitioners of geometry alone.” Also seen in a variant extract and translation: “Thus metaphysics and mathematics are, among all the sciences that
belong to reason, those in which imagination has the greatest role. I beg pardon of those delicate spirits who are detractors of mathematics for saying this …. The imagination in a mathematician who
creates makes no less difference than in a poet who invents…. Of all the great men of antiquity, Archimedes may be the one who most deserves to be placed beside Homer.” This latter translation may be
from The Plan of the French Encyclopædia: Or Universal Dictionary of Arts, Sciences, Trades and Manufactures (1751). Webmaster has not yet been able to check for a verified citation for this
translation. Can you help?
One feature which will probably most impress the mathematician accustomed to the rapidity and directness secured by the generality of modern methods is the deliberation with which Archimedes
approaches the solution of any one of his main problems. Yet this very characteristic, with its incidental effects, is calculated to excite the more admiration because the method suggests the tactics
of some great strategist who foresees everything, eliminates everything not immediately conducive to the execution of his plan, masters every position in its order, and then suddenly (when the very
elaboration of the scheme has almost obscured, in the mind of the spectator, its ultimate object) strikes the final blow. Thus we read in Archimedes proposition after proposition the bearing of which
is not immediately obvious but which we find infallibly used later on; and we are led by such easy stages that the difficulties of the original problem, as presented at the outset, are scarcely
appreciated. As Plutarch says: “It is not possible to find in geometry more difficult and troublesome questions, or more simple and lucid explanations.” But it is decidedly a rhetorical exaggeration
when Plutarch goes on to say that we are deceived by the easiness of the successive steps into the belief that anyone could have discovered them for himself. On the contrary, the studied simplicity
and the perfect finish of the treatises involve at the same time an element of mystery. Though each step depends on the preceding ones, we are left in the dark as to how they were suggested to
Archimedes. There is, in fact, much truth in a remark by Wallis to the effect that he seems “as it were of set purpose to have covered up the traces of his investigation as if he had grudged
posterity the secret of his method of inquiry while he wished to extort from them assent to his results.” Wallis adds with equal reason that not only Archimedes but nearly all the ancients so hid
away from posterity their method of Analysis (though it is certain that they had one) that more modern mathematicians found it easier to invent a new Analysis than to seek out the old.
In The Works of Archimedes (1897), Preface, vi.
Pure mathematics and physics are becoming ever more closely connected, though their methods remain different. One may describe the situation by saying that the mathematician plays a game in which he
himself invents the rules while the while the physicist plays a game in which the rules are provided by Nature, but as time goes on it becomes increasingly evident that the rules which the
mathematician finds interesting are the same as those which Nature has chosen. … Possibly, the two subjects will ultimately unify, every branch of pure mathematics then having its physical
application, its importance in physics being proportional to its interest in mathematics.
From Lecture delivered on presentation of the James Scott prize, (6 Feb 1939), 'The Relation Between Mathematics And Physics', printed in Proceedings of the Royal Society of Edinburgh (1938-1939), 59
, Part 2, 124.
Pure mathematics is much more than an armoury of tools and techniques for the applied mathematician. On the other hand, the pure mathematician has ever been grateful to applied mathematics for
stimulus and inspiration. From the vibrations of the violin string they have drawn enchanting harmonies of Fourier Series, and to study the triode valve they have invented a whole theory of
non-linear oscillations.
In 100 Years of Mathematics: a Personal Viewpoint (1981), 3.
Scientific education is a training in mental integrity. All along the history of culture from savagery to modern civilization men have imagined what ought to be, and then have tried to prove it true.
This is the very spirit of metaphysic philosophy. When the imagination is not disciplined by unrelenting facts, it invents falsehood, and, when error has thus been invented, the heavens and the earth
are ransacked for its proof.
From address (1 Oct 1884), at inauguration of the Corcoran School of Science and Arts, Columbian University, Washington, D.C. Published in 'The Larger Import of Scientific Education', Popular Science
Monthly (Feb 1885), 26, 455.
Some of my youthful readers are developing wonderful imaginations. This pleases me. Imagination has brought mankind through the Dark Ages to its present state of civilization. Imagination led
Columbus to discover America. Imagination led Franklin to discover electricity. Imagination has given us the steam engine, the telephone, the talking-machine and the automobile, for these things had
to be dreamed of before they became realities. So I believe that dreams—day dreams, you know, with your eyes wide open and your brain-machinery whizzing—are likely to lead to the betterment of the
world. The imaginative child will become the imaginative man or woman most apt to create, to invent, and therefore to foster civilization. A prominent educator tells me that fairy tales are of untold
value in developing imagination in the young. I believe it.
Opening paragraph of preface, 'To My Readers', The Lost Princess of Oz (1917), 13.
Someone poring over the old files in the United States Patent Office at Washington the other day found a letter written in 1833 that illustrates the limitations of the human imagination. It was from
an old employee of the Patent Office, offering his resignation to the head of the department His reason was that as everything inventable had been invented the Patent Office would soon be
discontinued and there would be no further need of his services or the services of any of his fellow clerks. He, therefore, decided to leave before the blow fell.
Written jokingly, to contrast with the burgeoning of American inventions in the new century. In 'Nothing More to Invent?',
Scientific American
(16 Oct 1915), 334. Compare that idea, expressed in 1915, with the classic myth still in endless recirculation today, “Everything that can be invented, has been invented,” for example, in Chris
Morgan and David Langford,
Facts and Fallacies
(1981), on the
Charles Duell Quotations
page on this website, which includes references debunking the myth.
Sometimes I wonder whether there is any such thing as biology. The word was invented rather late—in 1809—and other words like botany, zoology, physiology, anatomy, have much longer histories and in
general cover more coherent and unified subject matters. … I would like to see the words removed from dictionaries and college catalogues. I think they do more harm than good because they separate
things that should not be separated…
In The Forest and the Sea (1960), 6-7.
Symbolism is useful because it makes things difficult. Now in the beginning everything is self-evident, and it is hard to see whether one self-evident proposition follows from another or not.
Obviousness is always the enemy to correctness. Hence we must invent a new and difficult symbolism in which nothing is obvious. … Thus the whole of Arithmetic and Algebra has been shown to require
three indefinable notions and five indemonstrable propositions.
In International Monthly (1901), 4, 85-86.
The distinctive Western character begins with the Greeks, who invented the habit of deductive reasoning and the science of geometry.
In 'Western Civilization', collected in In Praise of Idleness and Other Essays (1935), 161.
The importance of a result is largely relative, is judged differently by different men, and changes with the times and circumstances. It has often happened that great importance has been attached to
a problem merely on account of the difficulties which it presented; and indeed if for its solution it has been necessary to invent new methods, noteworthy artifices, etc., the science has gained more
perhaps through these than through the final result. In general we may call important all investigations relating to things which in themselves are important; all those which have a large degree of
generality, or which unite under a single point of view subjects apparently distinct, simplifying and elucidating them; all those which lead to results that promise to be the source of numerous
consequences; etc.
From 'On Some Recent Tendencies in Geometric Investigations', Rivista di Matematica (1891), 44. In Bulletin American Mathematical Society (1904), 444.
The most technologically efficient machine that man has invented is the book.
Quoted, without citation as epigraph in Claus Grupen, Astroparticle Physics (2005), ix. Need primary source. Can you help?
The only way to get rid of the [football] combats of gorillas which now bring millions to the colleges will be to invent some imbecility which brings in even more. To that enterprise, I regret to
have to report, I find myself unequal.
From American Mercury (Jun 1931). Collected in A Mencken Chrestomathy (1949, 1956), 372.
The radical invents the views. When he has worn them out, the conservative adopts them.
In Albert Bigelow Paine (ed.), Mark Twain's Notebook (1935, 1971), Chap. 31, 344, (1898 entry).
The significant thing about the Darbys and coke-iron is not that the first Abraham Darby “invented” a new process but that five generations of the Darby connection were able to perfect it and develop
most of its applications.
In Essays on Culture Change (2003), Vol. 2, 200.
There is a noble vision of the great Castle of Mathematics, towering somewhere in the Platonic World of Ideas, which we humbly and devotedly discover (rather than invent). The greatest mathematicians
manage to grasp outlines of the Grand Design, but even those to whom only a pattern on a small kitchen tile is revealed, can be blissfully happy. … Mathematics is a proto-text whose existence is only
postulated but which nevertheless underlies all corrupted and fragmentary copies we are bound to deal with. The identity of the writer of this proto-text (or of the builder of the Castle) is
anybody’s guess. …
In 'Mathematical Knowledge: Internal, Social, and Cultural Aspects', Mathematics As Metaphor: Selected Essays (2007), 4.
This [the fact that the pursuit of mathematics brings into harmonious action all the faculties of the human mind] accounts for the extraordinary longevity of all the greatest masters of the Analytic
art, the Dii Majores of the mathematical Pantheon. Leibnitz lived to the age of 70; Euler to 76; Lagrange to 77; Laplace to 78; Gauss to 78; Plato, the supposed inventor of the conic sections, who
made mathematics his study and delight, who called them the handles or aids to philosophy, the medicine of the soul, and is said never to have let a day go by without inventing some new theorems,
lived to 82; Newton, the crown and glory of his race, to 85; Archimedes, the nearest akin, probably, to Newton in genius, was 75, and might have lived on to be 100, for aught we can guess to the
contrary, when he was slain by the impatient and ill mannered sergeant, sent to bring him before the Roman general, in the full vigour of his faculties, and in the very act of working out a problem;
Pythagoras, in whose school, I believe, the word mathematician (used, however, in a somewhat wider than its present sense) originated, the second founder of geometry, the inventor of the matchless
theorem which goes by his name, the pre-cognizer of the undoubtedly mis-called Copernican theory, the discoverer of the regular solids and the musical canon who stands at the very apex of this
pyramid of fame, (if we may credit the tradition) after spending 22 years studying in Egypt, and 12 in Babylon, opened school when 56 or 57 years old in Magna Græcia, married a young wife when past
60, and died, carrying on his work with energy unspent to the last, at the age of 99. The mathematician lives long and lives young; the wings of his soul do not early drop off, nor do its pores
become clogged with the earthy particles blown from the dusty highways of vulgar life.
In Presidential Address to the British Association, Collected Mathematical Papers, Vol. 2 (1908), 658.
To learn is to incur surprise—I mean really learning, not just refreshing our memory or adding a new fact. And to invent is to bestow surprise—I mean really inventing, not just innovating what others
have done.
In How Invention Begins: Echoes of Old Voices in the Rise of New Machines (2006), 217.
Two extreme views have always been held as to the use of mathematics. To some, mathematics is only measuring and calculating instruments, and their interest ceases as soon as discussions arise which
cannot benefit those who use the instruments for the purposes of application in mechanics, astronomy, physics, statistics, and other sciences. At the other extreme we have those who are animated
exclusively by the love of pure science. To them pure mathematics, with the theory of numbers at the head, is the only real and genuine science, and the applications have only an interest in so far
as they contain or suggest problems in pure mathematics.
Of the two greatest mathematicians of modern tunes, Newton and Gauss, the former can be considered as a representative of the first, the latter of the second class; neither of them was exclusively
so, and Newton’s inventions in the science of pure mathematics were probably equal to Gauss’s work in applied mathematics. Newton’s reluctance to publish the method of fluxions invented and used by
him may perhaps be attributed to the fact that he was not satisfied with the logical foundations of the Calculus; and Gauss is known to have abandoned his electro-dynamic speculations, as he could
not find a satisfying physical basis. …
Newton’s greatest work, the Principia, laid the foundation of mathematical physics; Gauss’s greatest work, the Disquisitiones Arithmeticae, that of higher arithmetic as distinguished from algebra.
Both works, written in the synthetic style of the ancients, are difficult, if not deterrent, in their form, neither of them leading the reader by easy steps to the results. It took twenty or more
years before either of these works received due recognition; neither found favour at once before that great tribunal of mathematical thought, the Paris Academy of Sciences. …
The country of Newton is still pre-eminent for its culture of mathematical physics, that of Gauss for the most abstract work in mathematics.
In History of European Thought in the Nineteenth Century (1903), 630.
We have become a people unable to comprehend the technology we invent.
Report, Integrity in the College Curriculum (Feb 1985).
What is mathematics? What is it for? What are mathematicians doing nowadays? Wasn't it all finished long ago? How many new numbers can you invent anyway? Is today’s mathematics just a matter of huge
calculations, with the mathematician as a kind of zookeeper, making sure the precious computers are fed and watered? If it’s not, what is it other than the incomprehensible outpourings of
superpowered brainboxes with their heads in the clouds and their feet dangling from the lofty balconies of their ivory towers?
Mathematics is all of these, and none. Mostly, it’s just different. It’s not what you expect it to be, you turn your back for a moment and it's changed. It's certainly not just a fixed body of
knowledge, its growth is not confined to inventing new numbers, and its hidden tendrils pervade every aspect of modern life.
Opening paragraphs of 'Preface', From Here to Infinity (1996), vii.
When all the discoveries [relating to the necessities and some to the pastimes of life] were fully developed, the sciences which relate neither to pleasure nor yet to the necessities of life were
invented, and first in those places where men had leisure. Thus the mathematical sciences originated in the neighborhood of Egypt, because there the priestly class was allowed leisure.
In Metaphysics, 1-981b, as translated by Hugh Tredennick (1933). Also seen translated as “Now that practical skills have developed enough to provide adequately for material needs, one of these
sciences which are not devoted to utilitarian ends [mathematics] has been able to arise in Egypt, the priestly caste there having the leisure necessary for disinterested research.”
When I needed an apparatus to help me linger below the surface of the sea, Émile Gagnan and I used well-known scientific principles about compressed gases to invent the Aqualung; we applied science.
The Aqualung is only a tool. The point of the Aqualung—of the computer, the CAT scan, the vaccine, radar, the rocket, the bomb, and all other applied science—is utility.
In Jacques Cousteau and Susan Schiefelbein, The Human, the Orchid, and the Octopus: Exploring and Conserving Our Natural World (2007), 181.
When we consider all that Hipparchus invented or perfected, and reflect upon the number of his works, and the mass of calculations which they imply, we must regard him as one of the most astonishing
men of antiquity, and as the greatest of all in the sciences which are not purely speculative, and which require a combination of geometrical knowledge with a knowledge of phenomena, to be observed
only by diligent attention and refined instruments.
In Histoire de l’Astronomie Ancienne (1817), Vol. 1, 186. As translated in George Cornewall Lewis, An Historical Survey of the Astronomy of the Ancients (1862), 214. From the original French: “Quand
on réunit tout ce qu’il a inventé ou perfectionné, et qu’on songe au nombre de ses ouvrages, à la quantité de calculs qu’ils supposent, on trouve dans Hipparque un des hommes les plus étonnans de
l’antiquité, et le plus grand de tous dans les sciences qui ne sont pas purement spéculatives, et qui demandent qu’aux connaissances géométriques on réunisse des connaissances de faits particuliers
et de phénomènes dont l’observation exige beaucoup d'assiduité et des instrumens perfectionnés.”
In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view
from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time
something like that happened in politics or religion. (1987) --
Carl Sagan
Sitewide search within all Today In Science History pages:
Visit our
Science and Scientist Quotations
index for more Science Quotes from archaeologists, biologists, chemists, geologists, inventors and inventions, mathematicians, physicists, pioneers in medicine, science events and technology.
Names index: |
Z |
Categories index: |
Z | | {"url":"https://todayinsci.com/QuotationsCategories/I_Cat/Invent-Quotations.htm","timestamp":"2024-11-06T03:08:09Z","content_type":"text/html","content_length":"343174","record_id":"<urn:uuid:bf5a4a22-5181-44f8-81ef-28c90947cf6e>","cc-path":"CC-MAIN-2024-46/segments/1730477027906.34/warc/CC-MAIN-20241106003436-20241106033436-00391.warc.gz"} |
Math Exam Resources/Courses/MATH152/April 2022/Question B4 (a)/Solution 1
To compute the eigenvalues, first form the characteristic equation, then solve for its zeros.
To solve for the zeros, use
thus the eigenvalues are ${\textstyle \lambda _{1}=2+i}$ and ${\textstyle \lambda _{2}=2-i}$. Since the eigenvalues are complex conjugates of each other, we know that the eigenvectors are also
complex conjugates of each other, meaning we only need to compute one eigenvector to know both.
In question 17 we found the eigenvectors of a matrix ${\displaystyle A}$ by solving ${\textstyle A{\vec {v}}=\lambda {\vec {v}}}$ for the components or ${\textstyle {\vec {v}}}$ using basic algebra.
For this question we will solve that same system using row operations. Solving for ${\textstyle {\vec {v}}_{1}}$, we write the system as ${\textstyle (A-\lambda _{1}I){\vec {v}}_{1}={\vec {0}}}$, row
operations on the augmented system of equations gives
If ${\textstyle {\vec {v}}_{1}=[v_{1}\ \ v_{2}]^{T}}$, then we have ${\textstyle (1-i)v_{1}+v_{2}=0}$. Choosing (arbitrarily) ${\textstyle v_{1}=1}$, we get ${\textstyle v_{2}=-1+i}$, and the two
eigenvectors are | {"url":"https://wiki.ubc.ca/Science:Math_Exam_Resources/Courses/MATH152/April_2022/Question_B4_(a)/Solution_1","timestamp":"2024-11-14T01:02:46Z","content_type":"text/html","content_length":"48120","record_id":"<urn:uuid:69226447-a875-497c-8850-455b5d522352>","cc-path":"CC-MAIN-2024-46/segments/1730477028516.72/warc/CC-MAIN-20241113235151-20241114025151-00798.warc.gz"} |
Setting up Excel formula
Wow, your organization needs to hire an analyst! I am saying, that is a relatively easy problem for the modern organization. It is called the cost of doing business, and sometimes you need to pay for
the things that the business requires. Perhaps, a different hiring method needs to be utilized when hiring the back office in such an organization.
This is not a technical problem, but a legal one. You really need to consult a pro in your area to assist, as we are discussing taxes.
What happens when you tell the tax man that you plugged in an EXCEL formula you cut and pasted from CCM.NET? Do you thing he cares?
It's kind of fun to do the impossible! -Walter Elias Disney
Thank you for the reply
We do have an analyst. And I dont deal with taxation. Knowing how it works on excel will make my job easier for a report which is totally not related with taxation. I work at the front end, for
customer support. I hope someone could tell me if this is possible.. Thank you again
It is possible, it is just a very sensitive, important part of business, and typically you get what you pay for. Although I am 100% confident we can supply a calculation, it is a matter of if it is
correct for your region! I truly hope you understand, and Please forgive me if I came across harsh!
Thank you for replying. Took me a few hours but I figured out the calculations. It was really simple :-D
Thank you for your time.
Can you post here, so that others may see what your solution was, please.
Thank you for the feedback! | {"url":"https://ccm.net/forum/affich-1022289-setting-up-excel-formula","timestamp":"2024-11-06T01:43:39Z","content_type":"text/html","content_length":"108896","record_id":"<urn:uuid:a2ade5bc-7b23-4c63-9468-83ecd5ce24d0>","cc-path":"CC-MAIN-2024-46/segments/1730477027906.34/warc/CC-MAIN-20241106003436-20241106033436-00587.warc.gz"} |
The ellipse is one of the four classic
conic sections
created by slicing a cone with a plane. The others are the
, the circle, and the hyperbola. The ellipse is vitally important in
objects in periodic
around other celestial objects all trace out ellipses.
An ellipse is defined as the locus of all points in the plane for which the sum of the distances r[1] and r[2] to two fixed points F[1] and F[2] (called the foci) separated by a distance 2c, is a
given constant 2a.
Therefore, from this definition the equation of the ellipse is: r[1] + r[2] = 2a, where a = semi-major axis.
The most common form of the equation of an ellipse is written using Cartesian coordinates with the origin at the point on the x-axis between the two foci shown in the diagram on the left.
If we define the semi-minor axis, b^2 = a^2 – c^2, then the ellipse equation can be rewritten as:
The shape of the ellipse is described by its eccentricity. The larger the semi-major axis relative to the semi-minor axis, the more eccentric the ellipse is said to be. The eccentricity is defined
Another useful relation can be obtained substituting for b in the equation above:
This gives an interpretation of the eccentricity as the position of the foci as a fraction of the semi-major axis.
The position of a point on an ellipse can be specified by using polar coordinates, radial distance r and angle f, with the origin on one of the foci. This allows us to express (x,y) coordinates
The equation of the ellipse can also be written in terms of the polar coordinates (r, f). Substituting for x and y in the ellipse equation we get:
The circle is a special case of an ellipse with c = 0, i.e. the two foci coincide and become the circle’s centre. If we substitute for zero eccentricity in the equations above, we obtain a = b, so
both axes are equal to each other, and to the circle’s radius. | {"url":"https://astronomy.swin.edu.au/cosmos/E/ellipse","timestamp":"2024-11-08T05:21:05Z","content_type":"application/xhtml+xml","content_length":"12984","record_id":"<urn:uuid:f7029875-ee18-4c64-9bff-6b83e2383dbc>","cc-path":"CC-MAIN-2024-46/segments/1730477028025.14/warc/CC-MAIN-20241108035242-20241108065242-00523.warc.gz"} |
Fisher Equation
Exploring The Essential Aspects Of Fisher Equation
Fisher equation, named after its designer Irving Fisher, is a concept in Economics that defines the relationship between nominal interest rates and real interest rates under the influence of
inflation. This blog explores the different elements of the equation with examples, along with the pros and cons associated with it.
What Is The Fisher Equation?
The Fisher equation is a concept of economics stating the relationship between nominal interest rates and real interest rates. The bond given between the two is derived under the effect of inflation.
According to the Fisher equation, the nominal interest rate is equal to the sum of the real interest rate and inflation. The concept of the Fisher equation has great significance in the field of
finance and economics. This is because it is used in calculating returns on investments (ROI) or estimating the nature of nominal and real interest rates.
Also, the Fisher equation elucidates a state of affairs where investors or lenders demand an additional reward. The demand for an additional reward is justified to compensate for the loss of
purchasing power due to growing inflation. Moreover, the applications of the Fisher effect has been protracted considering its growing demand in the market. This method now successfully deals with
the analysis of the money supply and international trading of currencies. So, the designer of such a beautiful concept in the field of finance and economics was an excellent American economist,
Irving Fisher. Thus, the Fisher equation rapidly gained popularity in the market due to its unmatched work in the theory of interest.
myassignmenthelp.expert tutors can guide you to write your assignment on Fisher equation.
How Do You Calculate The Fisher Effect?
Fisher Equation Formula
The exact formula to justify the relationship between the real interest rate and nominal interest rate can be given as follows:
(1 + nominal interest rate) = (1 + real interest rate) * (1 + inflation rate)
In mathematical terms, the Fisher equation is broadly expressed using the formula given below:
(1 + i) = (1 + r) * (1 + Pi)
i = the nominal interest rate
r = the real interest rate
Pi = the inflation rate
Therefore, the approximate relationship between the real interest rate and the nominal interest rate can be shown as follows:
i ≈ r + Pi
Fisher Equation Examples
To understand the working of the Fisher equation, you can refer to the example shown as follows:
Suppose you own a firm having the real rate of return to 3.5% and expected inflation to 5.4%. According to the above formula, the approximate nominal rate of return can be calculated as 0.035 + 0.054
= 0.089, or 8.9%. Therefore, substituting the value of i and r in the formula for the Fisher equation, (1 + i) = (1 + r) * (1 + Pi), the value for the nominal rate of interest is 9.1%.
What Is The Inflation Rate?
The inflation rate is a measure of the price inflation comprehending the annual percentage change in the consumer price index (CPI). Thus, the inflation rate contributes to the development of an
economy as it compares an increase in the general price level of goods. It is imperative to monitor the inflation rate as an independent inflation rate can damage an economy severely. Moreover,
excessive growth in the liquidity can often lead to a higher rate of inflation which can further result in hyperinflation.
Subjects We Cover In Fisher Equation ?
Nominal interest rates Monetary policy Economic growth and development
Real interest rates Central banking Financial markets and investment
Inflation and inflation rates Inflation expectations Consumption and saving
What Is The Nominal Rate Of Interest?
The nominal rate of interest is the type of interest rate which is measured before considering the inflation in an economy. It is compared with the real interest rate before referring to inflation.
Therefore, the term nominal can also see the advertised or pre-fixed interest rate on loan. This pre-fixed interest rate does not have permission to take into account any fees or compounding of
interest. Moreover, the interest rate set by the Federal Reserve, also known as the federal funds rate, can also be identified as a nominal rate.
What Is The Relationship Between Nominal And Real Interest Rate?
A nominal interest rate elucidates the financial return earned by an individual in return of the deposited money. In the Fisher equation, the value of the nominal interest rate and the actual
interest rate is similar. It highlights the financial growth for a specific interval of time deciphering the total amount owed to a financial lender. On the contrary, a real interest rate refers to
the amount reflecting the buying capacity of the money borrowed over a specific time. The two interest rates work in the direction to identify the financial growth for a pre-defined interval of time.
Thus, the fundamental relationship among them can be determined by the nature of their work.
Fisher Equation Formula: Understanding The Quantity Theory Of Money
The Fisher equation formula and examples will always guide you through the challenges involved in the calculation. However, there’s more to it.
Are you aware of the concept of the quantity theory of money? This is said to be a significant aspect and one of the key elemental concepts associated with the Fisher effect equation. Here’s
everything you need to know.
• The supply of money comprises the quantity of money in existence, signified by (M), multiplied by the number of times the money changes hands.
• This is also considered as the velocity of the money, signified by (V).
• According to the Fisher equation formula, (V) is basically the transaction velocity of money which denotes the average number of times a unit of money turns over.
• In addition, one can carry out the equation on the basis of the average number of times the money changes hands during a particular period of time.
• Thus, (MV) signifies the net volume of money in circulation during a given period of time.
So, keep referring to such lucid explanations while going about the essentials of the quantity theory of money. If you would still find things difficult, then use an advanced Fisher effect equation
calculator to ease the burden.
Pros And Cons Of The Fisher Effect
Pros Of The Fisher Effect
• Fisher effect distinguishes between the nominal interest rate and the real interest rate giving a clear picture for these interest rates.
• It contributes to sustainable developments of the economy as it detects a situation where investors or lenders demand an additional reward.
Cons Of The Fisher Effect
• The elasticity of demand to interest rates: With the continuous rise in the price of the assets, the high-interest rates prove to be worthless in reducing demand. This gives rise in the central
banks the need to increase the real interest rate to affect.
• Liquidity Trap: It works on the concept of reducing nominal interest rates to influence the expenditure in favour of the business. Thus, to attract investment, the bank needs to increase the
interest rates and eliminate all the possibilities of failure.
Textbooks On Fisher Equation
It is common among the students to feel overwhelmed under the pressure of their academic curriculum. Especially it becomes quite difficult for the students in higher academic grades to maintain a
healthy balance between their academic and personal life. Therefore, this factor plays a crucial role in exposing students to numerous health and mental disorders is the pressure to sustain in the
competitive world. This is the reason that myassignmenthelp.expert needs to step in the scenario to rescue the students out of their misery. Consequently, it is critical for the students to deliver
an unmatched quality of assignment to ensure their sustainability in academics. The sense of urgency under a tight deadline also contributes to the mental pressure on students. It is not a piece of
cake to manage the schedule keeping a healthy balance between a student's personal and academic life. Thus, the need for the best online guiadance arises providing students with a helping hand.
Exceptional Services For Students In Australia
The tutors at myassignmenthelp.expert are dedicated to delivering you the best guidance you can get online. Moreover, the level of knowledge they possess regarding the subject of the Fisher equation
is unmatched. This contributes to the guidance through the best assignment service you can get online to help you achieve maximum grades. Also, we understand the need of every student and our
customer support team works day and night to deliver guide them with unexpected challenges. So, to make our consultation services more interactive, we have a customer support team available 24*7 to
guide you in the best way possible. myassignmenthelp.expert is the most popular writing and tutoring service among the students worldwide because of the full range of consultation service we provide.
Moreover, you can go through the sample assignments available on our website to get an idea of the guidance we offer. Once you upload your queries, our tutors begin to analyse and understand your
needs. Especially the students in the US, the UK, and Australia are facing severe trouble regarding assignment writing due to the strict guidelines followed by their universities.
Now, you don't need to worry even if you have not prepared your assignment with hours left for the submission. Our proficient tutors are highly capable of offering instant guidance that promises you
higher grades successfully.
Most Popular FAQs Searched By Students:
Ques1 - What is the Fisher effect equation?
Ans: The Fisher effect equation and formula is denoted by Rnom – Rreal +E[I], or nominal interest rate – real interest rate + expected rate of inflation.
Ques 2- How do you calculate Fisher's equation?
Ans: If you want to convert the nominal interest rates to real interest rates, then use:
• real interest rate ≈ nominal interest rate − inflation rate
If you want to find the real interest rate, then take the nominal interest rate and subtract the inflation rate.
Ques 3- Why Fisher's formula is called ideal formula?
Ans: Fisher’s formula is called ideal formula due to its accuracy and ease of calculation. The equation is really simple to perform and ensures nothing but flawless derivations.
Ques 4- What is a nominal and effective interest rate?
Ans: Nominal interest is also known as a stated interest rate. This interest works in accordance with the simple interest and does not consider the compounding periods.
On the other hand, the effective interest rate is the one that caters the compounding period during a payment plan.
Other Services Covered By Myassignmenthelp.expert
SAP Assignment Help finance planning assignment help accounting assignment help
Finance Assignment Help sas assignment help Effective Interest Rate
Family Branding Help corporate finance assignment help managerial accounting assignment help | {"url":"https://myassignmenthelp.expert/fisher-equation.html","timestamp":"2024-11-08T08:20:38Z","content_type":"text/html","content_length":"192781","record_id":"<urn:uuid:b80e4036-1188-4403-994f-0d1aa97ddc27>","cc-path":"CC-MAIN-2024-46/segments/1730477028032.87/warc/CC-MAIN-20241108070606-20241108100606-00250.warc.gz"} |
How to Make a Semi Logarithmic Graph in Excel - TechnoGigs.Net
How to Make a Semi Logarithmic Graph in Excel
Hello, Reader Technogigs! Are you having trouble plotting data on a graph with values that vary exponentially? Worry no more, as we introduce to you the semi logarithmic graph in Excel. This type of
graph allows for an appropriate representation of data with exponential variations. In this article, we will provide you with a step-by-step guide on how to create a semi logarithmic graph using
The Introduction
Excel is a versatile software that offers a wide range of capabilities, one of which is data visualization. While Excel offers many graph types, semi logarithmic graphs are an essential tool for
scientists, researchers, and statisticians for monitoring exponential trends. These graphs are used to conduct research, analyze data, and make predictions.
The semi logarithmic graph has two axes, where the horizontal axis displays data on a linear scale and the vertical axis on a logarithmic scale. This chart type is useful when there are significant
variations between data points. Consequently, the logarithmic axis visually compresses the data points and allows for accurate plotting of data with a huge range of values.
In this article, we will explore the benefits of using a semi logarithmic graph and the steps to create an effective one on Microsoft Excel.
Semi Logarithmic Graph Strengths
1. Clear Representation of Huge Datasets
One of the most important advantages of using a semi logarithmic graph is its ability to provide a clear representation of huge datasets. The graph does not squash all data values into one corner,
giving the user a visual idea of vast differences between data points.
2. The Ability to Monitor Exponential Trends
Another advantage of creating a semi logarithmic graph is the ability to monitor exponential trends. The vertical logarithmic axis allows for proportional data representation of various magnitudes.
The line slopes on the graph can provide an estimate of how the data is likely to change in the future, providing the user with reliable data for making informative decisions.
3. Effective Data Processing
The semi logarithmic graph also has the advantage of making data processing effective. The graph compresses the data to enable the easy plotting of widely varied values, making it an invaluable tool
for statisticians, researchers, and scientists.
Semi Logarithmic Graph Weaknesses
1. Limited to Exponential Data
One common disadvantage of the semi logarithmic graph is that it is limited to exponential data. The logarithmic scale is purely logarithmic, nearly logarithmic, or fully linear. Without exponential
variations, the graph may lose its significance.
2. Misinterpretation of Data
Semi logarithmic graphs’ compressed Y-axis might cause the user to misinterpret data. The visual representation of the graph may cause parts of the data to appear more significant or less significant
than what they are, leading to inaccurate or misleading findings.
3. Difficulty in Accurate Data Analysis
Correct interpretation of a semi logarithmic graph may lead to some difficulty. The logarithmic scaling on the vertical axis involves some mathematical interpretation, which thereby requires
mathematical interpretation techniques.
Steps to Create a Semi Logarithmic Graph on Excel
Here are the detailed steps to create a semi logarithmic graph on Excel.
Step 1: Data Selection Open your intended work on Excel and select your data. Your data should contain positive values only.
Step 2: Create Chart Select a chart type (Line Chart, Column Chart, or Scattered Chart), click to add a chart, then select the chart series you want to apply to your semi logarithmic chart.
Step 3: Secondary Axis Right-click on the chart series you want to include on the logarithmic scale, click Format Data Series, and then check the box for the Secondary Axis.
Step 4: Logarithmic Select the secondary axis scale, right-click on it, then select Format Axis. In the Format Axis dialogue box, check the box for logarithmic scale to create your semi
Scale logarithmic graph.
Step 5: Formatting Edit the chart format, fonts, and colors to create a high-quality semi logarithmic chart that accurately represents your data.
Step 6: Title and Labels Include a chart title and legend and add the secondary axis label reflections to the logarithmic scale to create an effective and self-explanatory chart.
Step 7: Save the Chart Save your wizardry as an image file for presentations or import it as an Excel object for further analysis and interpretation.
Frequently Asked Questions (FAQs)
1. What is a Semi Logarithmic Graph in Excel?
A Semi Logarithmic Graph in Excel is a graph that has one axis (usually Y-axis) with a logarithmic scale and another axis (usually the X-axis) with a linear scale.
2. What type of data is appropriate for a semi logarithmic graph?
Semi logarithmic graphs are appropriate for data that has exponential variations and a wide range of values.
3. What is a logarithmic scale?
A logarithmic scale is a scale used in graphs where the biggest numbers are not shown, and the lower and smaller values are amplified.
4. What is an exponential graph?
An exponential graph is a graph of an exponential function where the dependent variable (y) is raised to an exponent.
5. How does one create a semi logarithmic graph in Excel?
Creating a semi logarithmic graph in Excel involves data selection, creating the chart, secondary axis, logarithmic scale, formatting, and title and labels.
6. What is the disadvantage of a semi logarithmic graph?
The disadvantage of a semi logarithmic graph is that it is limited to exponential data and may cause users to misinterpret data.
7. What are the benefits of using a semi logarithmic graph?
The benefits of using a semi logarithmic graph include a clear representation of huge datasets, the ability to monitor exponential trends, and effective data processing, among others.
Semi logarithmic graphs are powerful tools for presenting exponential data in an organized and visually appealing way. They are useful for a range of applications, including science and mathematics.
Following the steps provided in this article, you are now equipped to create your semi logarithmic graph on Excel. So, what are you waiting for? Create your semi logarithmic graph today and get
accurate and informative representations of your data! | {"url":"https://technogigs.net/how-to-make-a-semi-logarithmic-graph-in-excel/","timestamp":"2024-11-14T17:43:56Z","content_type":"text/html","content_length":"45902","record_id":"<urn:uuid:9fadfdd8-56b1-423b-9712-89247c214347>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00873.warc.gz"} |
Advanced Solver
I shall explain my problem using the below example.
I have a column of 5 numbers - 345, 435,3567, 1423 & 975. The next column shows the contribution of the each number to the total. (Sum of 5 numbers is 6745, contribution of each number to the total
is 5%, 6%, 53%, 21% and 14% respectively).
What i want is this:
The Total (Sum of all numbers) is fixed. Now, if i change any percentage figure, all the values below it should change such that the sum is always 100%. From the above example, if I change 6% to 11%,
the values below 6% i.e 53%, 21% and 14% should change in such a way that total percentage is 100%. I should be able to set conditions as to what level those figures can change. Also, all the values
above the one should not change.
Is it possible to do this with Excel. I have tried using Solver, but could NOT find the solution.
There was an error in the last post..
please read the last line as "....... but could NOT find the solution"
Do you want the remaining pieces to maintain their relativity to each other or change evenly ?
I want top maintain their relativity. i should be able to set constraints for each of the below values..
for example (relating to the example used to describe my problem):
53% can change to any value from 49% to 56%. 21% can change to any value in the range 20% to 25%.
Can you give an example of how the numbers below the number you have changed will change
ok... continuing with the same example...
The numbers initially were 5, 6, 53, 21 and 14.
I have kept the first number same and changed the second number from 6 to 11.
And i have given the conditions for below cells in this way: 53 can change to any value from 49 to 56. 21 can change to any value in the range 20 to 25 and the last number 14 cannot be changed...
Now the sequence i got is 5, 11, 49, 20 and 14. This is just an example.
If instead of 6, i had changed 5 to 8. Here i shall add a condition that 6 can change from 6 to 12. then the sequence i got is 8, 6, 50, 21 and 14. In all the cases, the sum should be same (=99).
I hope I have managed to explain what i wanted.
Hi Bharat,
I have worked out the formulas for the changes, but have ignored the ranges that you set.
The calculation requires a number of helper columns and rows.
I have done this in Excel 2007, please let me know where I can upload the file for you.
Could you please mail me the file. My e-mail address is trbharat@gmail.com
Thank you..
Hi Bharat,
Glad to know it worked, have sent you a second file with a slightly more elegant solution
Could you guys post the excel file in this fourm it is highly appreciated
use rapidshare.com to post the files please
Hi Nagovind,
I am not able to access any of the share sites from my computer, they are all blocked. | {"url":"https://chandoo.org/forum/threads/advanced-solver.890/","timestamp":"2024-11-07T03:05:22Z","content_type":"text/html","content_length":"80645","record_id":"<urn:uuid:3a97e64a-3078-4ed2-a1b4-72f635f8f6e7>","cc-path":"CC-MAIN-2024-46/segments/1730477027951.86/warc/CC-MAIN-20241107021136-20241107051136-00083.warc.gz"} |
Motions of the Heart
To be emotionally stirred is to care, to be concerned. It is to be in a scene or subject not outside of it… The more anything, whether an object, scene, idea, fact or study, cuts into and across our
experience the more it stirs and arouses…
No amount of possession of facts and ideas, no matter how accurate the facts in themselves and no matter what the sweep of the ideas—no one of these in themselves secure culture. They have to take
effect in modifying emotional susceptibility and response before they constitute cultivation.
—John Dewey (1859–1952), Address to Harvard Teacher’s Association, March 21, 1931
Grand Confluences
We must look to our own faculty for discerning those fine connective things—community of aim, interformal analogies, structural similitudes—that bind all the great forms of human activity and
aspiration—natural science, theology, philosophy, jurisprudence, religion, art and mathematics—into one grand enterprise of the human spirit.
—Cassius Jackson Keyser (1862–1947), “The Humanization of the Teaching of Mathematics,” Science
Our brains are complicated devices, with many specialized modules working behind the scenes to give us an integrated understanding of the world. Mathematical concepts are abstract, so it ends up that
there are many different ways they can sit in our brains. A given mathematical concept might be primarily a symbolic equation, a picture, a rhythmic pattern, a short movie—or best of all, an
integrated combination of several different representations…
A whole-mind approach to mathematical thinking is vastly more effective than the common approach that manipulates only symbols.
—William P. Thurston (1946–2012), Foreword to Crocheting Adventures with Hyperbolic Planes and Foreword to The Best Writing on Mathematics 2010
“Every thing throws light upon every thing,” observed the “Yale Report of 1828”—the nineteenth-century’s strongest bulwark for retaining what has been called the classical curriculum prescribed for
all students attending college.^1 As discussed in Chapter 7, this curriculum was based on an extremely rugged ancient Greek and Roman core, and had come under increasingly intense criticism
throughout the 1820s as being completely out of touch with student needs of the day.^2
1828 Yale University Catalog Course of Instruction (pp. 24–25): “Livy, three books” is Roman history, “Adam’s Roman Antiquities” is Roman manners and customs, “Graeca Majora” is an anthology of
canonical scholarship in Greek, and “Fluxions” is calculus
The “Yale Report” was the Yale faculty’s passionate attempt to justify continuing with this curriculum, which in Yale’s case wasn’t 100% totally wedded to the far-distant past as was sometimes
claimed—with the faculty having added, for example, symbolic algebra, logarithms, calculus, and political economy to its roster, which were relatively modern fields of study for the era. But a large
portion of it was based on antiquity, and it certainly was a rigorous course of study to most students of the day, with many, if not a majority, growing to eventually despise it.^3 The more recent
mathematical courses in the curriculum only compounded the difficulty, and people were quite justified in questioning the relevance, arrangement, difficulty, and manner in which the entire course of
study was taught: just as they often are with the curricula of today.
The Yale faculty contended that the essence of the classical curriculum spoke to many recurring features of professional life, and though not always directly applicable to other areas, the broad
principles, techniques, and “strenuous exercise of the intellectual powers” honed by this course of study embraced what was “common to them all.”^4 Although the classical curriculum of 1828
eventually gave dramatic way to a far more diversified set of course offerings and majors by the century’s end, its most idealistic leanings of using a broad approach to education—through
illuminating and exploiting the connections between a wide array of disciplines and life in general—is still alive and well in some circles today.
And here is the same desire, embedded in the assertions cited at the beginning of the chapter by Keyser and Thurston, though they are separated by nearly a century. The mathematician Alvin White
called the application of this philosophy to mathematics “humanistic mathematics” and helped to jump start a robust network for this way of thinking about math as a human endeavor in the late
twentieth century and beyond. The refrain behind this way of thinking is that many important rhythms of life as experienced both individually and collectively by human beings manifest themselves in a
wide array of subjects—including mathematics—and that these different manifestations should be deliberately sought out, identified, and connected together. This pedagogical philosophy represents one
of the grandest of all the grand confluences in education, acting much like the conceptual superhighway from Chapter 8 to connect big ideas across a wide range of disciplines—both inside and outside
of the curriculum.
Though proponents and critics alike believe that an educational curriculum at any level should have a significant impact on the students passing through it, they vehemently disagree on the
particulars of what that curriculum should be or how to devise it. Specifically in the case of algebra, some passionately say that the significant and impactful thing that is happening to students
nowadays is actually in reverse of what it should be, believing that it harms those who are forced to study a subject that will be largely irrelevant to their professional lives and may prevent them
from advancing or completing their education. They remain firm in the stance that it simply must be cast aside as a general requirement, and replaced by something else.
Others defend algebra’s current place in secondary and adult education and the methods used to teach it, insisting that it is a necessary standard to develop students’ technical capacities, and that
the problem with algebra today is a dearth of qualified teachers, not the subject itself or standard instructional methods.
Still a third group agrees with the second that algebra should remain a required subject but is sympathetic to the concerns of the first, arguing for reforms to address the serious philosophical and
infrastructural problems in math education, such as a mountain of topics and an overemphasis on manipulating symbols, testing, and irrelevant practice problems. In their view, simply finding
better-qualified teachers is not enough to fix a fundamentally flawed situation, and we should focus our energies on developing new and compelling pedagogical methodologies that make the subject far
more understandable and appealing to the majority of students required to take it—methodologies that reflect the true potency and beauty in the subject. This is also a hope often expressed by more
than a few mathematics professionals over the past two centuries.
To use a crude military analogy, the first group’s stance is somewhat akin to abandoning troop positions in ambiguously held territory and redeploying them to more secure locations, in the belief
that adequate supply lines do not exist and can never be established. Thus, making the current positions too dangerous for the majority of troops, save, perhaps, for a comparatively few specialized
units. Those who argue for improving status quo methods can be viewed as wanting to maintain these positions in the belief that adequate supply lines do exist, but are failing due to incompetent or
inadequately trained staff and troops. The third camp, advocating for reform, accordingly believe that by reinforcing the troops and creating additional, alternate routes within a preexisting broad
network of supply lines, their position need not be abandoned—and, moreover, can be strengthened. Keyser’s and Thurston’s statements most naturally align with those in the third camp.
Viewed purely from a military point of view, all three possibilities may make sense depending on the circumstances in which an army in the field finds itself. But what of the educational
circumstances that legions of students find themselves facing in an algebra class?
I have adopted the viewpoint of the third camp and have devoted a substantial portion of this book to opening such pathways into existing supply lines for algebraic illumination, insight, and
understanding. In this concluding chapter, we’ll summarize some of the forms that these paths have taken, but it remains for you to judge for yourself whether these attempts have been successful.
Just as arithmetic gives us a precise quantitative vocabulary to express notions such as one collection being larger than another collection, algebra allows us to give shape and personality to our
interactions with numerically variable quantities. This is not insignificant, taking full advantage of certain capital features of nature. Consider that though one can write the name of a town with
pencil, ink, or chalk, it is also possible to spell the same word using toothpicks, bricks, shrubbery, contrails from an airplane, sand, tape, dominos, people, Play-Doh, and so on. Although its
letters can be formed from dramatically different materials—even those not designed for writing—the order of the letters and relationships between them are paramount and are what continue to allow us
to recognize the word.
Relationships that we establish between objects, concepts, and quantities can translate to a broad spectrum of materials and circumstances, enabling us to connect them to a broader network of ideas
and scenarios. Algebra is inherently relational, helping us to express, maneuver, and transform a wide array of quantitative relationships in extremely efficient and often emergent ways. Two of the
most important ways in which algebra does this have been characterized in this book as the two dramas, with the first drama roughly corresponding to what can be captured by variable expressions and
the second drama corresponding to what is capturable as equations. A third way—involving graphical representations—has not been critically examined in this book, but is nevertheless extremely
important in its own right.
In the first two dramas, relationships between numerically varying quantities are translated into symbolic relationships between the letters that represent them, thus rendering variable situations
into a visual and operational format. This represents another grand confluence because once we take variable phenomena and capture them through the lens of visible symbols, it allows us to sometimes
make surprising connections in algebraic writing between situations that on the surface may not look similar at all, as occurred in the section “Algebraic Songs” in Chapter 7 and throughout Chapter 8
These translations to symbolic representations can be likened to the way spectral analysis allows us to identify the constituent material components of astronomical objects by analyzing the light
they emit or absorb—or to how detectives can link a person to the scene of a crime by comparing the unique ridges and curves of their fingerprints with those at the scene. In algebra, it is the
visible symbols and the relationships they express that facilitate these connections. The transfer of variable situations into their notational renderings really do serve as a type of algebraic
But algebra offers more than just the symbolic fingerprinting of variable behavior. Consider that, of all the physical materials we mentioned to form a word, the Play-Doh variant is probably the most
pliable and easiest to manipulate. Play-Doh has memory and can represent and hold to a certain shape, but it is also malleable and can easily be molded into other shapes. Algebra and arithmetic as we
practice them today are similar insofar as the symbols we use can both hold a certain form and also be conveniently reconfigured into other useful forms.
For instance, in arithmetic, we may have six collections of 22, 57, 28, 45, 23, and 25 items, respectively, whose sizes we are able to write down with numerals—and that may be all that is needed,
depending on what we want to do with the information. In this case, the symbols act as an aid in remembering the amount in each collection. However, these numerals contain far more content than just
the ability to record information. As we know, they can be combined and maneuvered to give new insights. We can start by setting up the addition of 22 + 57 + 28 + 45 + 23 + 25. This can, of course,
be calculated in the traditional vertical fashion, but we can also reorganize the problem as (22 + 28) + (57 +23) + (45 + 25), which allows us to even more quickly condense the expression into 50 +
80 + 70 to obtain 200. This computational feature, where the numerals transform—according to certain well-established rules—into new values that match what we actually observe, is an example of when
the symbols act in a malleable fashion.
It was a revolutionary discovery in arithmetic that certain types of numerals could actually be made to conveniently and reproducibly transform in this way. That is, these numerals were not static
vessels for storing information, but dynamic vehicles that could be maneuvered by users into making nontrivial, extensive calculations singly on their own in writing unassisted by a mechanical
instrument. For most ancients, notations such as Roman numerals and hieroglyphic numerals were primarily used to record quantitative information with the calculations being performed on a computing
device like an abacus, but the ancient Indians found a way to unify both information storage and calculational functionality into one set of numerals—the Hindu-Arabic numerals—and the rest, as they
say, is history.
A similar and equally dramatic revolution occurred in algebra, but it took mathematicians centuries to come to this realization about the possibilities with the symbols used there, with the old
rhetorical methods expressed in words giving dramatic way to the more operational symbolic ones developed in the watershed sixteenth and seventeenth centuries.
Firstly, modern symbolic algebra inherits all of what representational and computational arithmetic offers, then scales and intensifies it to represent infinitely many possible versions of an
arithmetic statement or action by a single grand variable expression. Secondly, it allows us to capture and separate out all of the different types of variations in a situation, combining those that
are the same and separating those that aren’t, simultaneously managing variation on multiple channels. When handled properly, these procedures of algebra become strategic and decisive deployments not
just pedestrian manipulations, all of which imbue algebra with the power to process and organize the symbolic representation of many types of variations that occur in nature—rendering it
indispensable to fields such as science, business, statistics, and data science.
On Saturday afternoons in the fall, sports bars across the nation may have on as many as a dozen or more different Division I college football games, each one flavored by the history, traditions, and
unique fan bases of both teams on the field. Some of these games will be remarkably one-sided affairs, as a powerhouse team takes on a much weaker opponent, whereas others will go down to the wire
and may even result in an upset.
Yet, despite the variety of possible matchups and outcomes, all of the games will still have enough in common that we can easily recognize them all for what they are—college football games. Changing
channels from game to game, we can see that in spite of the variation between contests, they each feature 60 minutes of regulation play, a system of downs, a line of scrimmage for each play, players
clad in protective helmets and pads with numbered jerseys, referees, a brown ball with pointed ends, and other distinctive rules and positions. The simple ability to change TV stations from game to
game, or to view them on multiple screens, provides a sports example of the dynamic interplay that is possible between variable elements at work around a strong core of stability.
This is but one illustration of many such productive interactions between variation and stability that occur in many aspects of nature and society—others include the following:
• Spoken languages:
° Variables: There are more than 6000 spoken languages in active use worldwide.^5
° Constants: Languages share the common goal of facilitating structured communication with words that convey meaning in speech, gestures, or writing.
• People:
° Variables: The global human population numbers in the billions, but each person is an individual with a unique personality, physical characteristics, talents, skills, and ambitions.
° Constants: Humans are characterized by common anatomical features, including a complex brain, heart, bipedalism, and opposable thumbs, among other mammalian traits.
• Nations:
° Variables: There are nearly 200 different nations in the world.
° Constants: Every nation has a territory, population, laws, and a system of government.
• Automobiles:
° Variables: There are hundreds of different models of automobiles in service today.
° Constants: Automobiles share many common characteristics, including an engine or motor, energy source, brakes, and tires.
Sometimes, this intricate dance between variability and stability can be of a much more quantitative nature, which can help us articulate more detailed and precise mathematical descriptions. In this
book, we’ve discussed examples that include
• businesses, with varying costs and revenues, yet common methods to represent and locate their break-even situations;
• course instructors, with varying assignment categories and weights, yet common methods to represent and compute their course grade averages;
• students, with varying course loads and academic performance, yet common methods for schools to compute their grade point averages;
• investors, with portfolios of diversified investments at varying levels of appreciation or depreciation, yet common ways to calculate their overall return on investment.
Algebra provides a powerful way to comprehensively treat these latter quantitative situations, using symbols to organize and coordinate the variable components and the more stable ones. We’ve
identified these more consistent or stable components in this book as scenario variables—stable within a given scenario, but variable from scenario to scenario.
The existence of scenario variables and the need to distinguish them from traditional unknowns was probably the most valuable of the major advancements in algebra during the 1500s—which is saying
something, as it was a banner century for algebra. As we discussed in Chapter 4, scenario variables are more commonly called parameters and were definitively introduced in the late sixteenth century
by French mathematician François Viète.
A little over 40 years later in 1637, French mathematician and philosopher René Descartes modified Viète’s ideas in his treatise La Géométrie by using letters early in the alphabet for parameters and
letters later in the alphabet for traditional unknowns, or regular variables.^6 Though Descartes protocol is often followed in elementary algebra instruction, it can be much more inconvenient to
adhere to in ensuing applications, as we saw in Chapter 8.
These two types of variable quantities—parameters and regular variables—allow us to transform single-instance algebra into what we have termed “big algebra,” illustrating how algebraic insight
gleaned from one problem can be scaled to a wider range of applications. For instance, to find the break-even point for various businesses, we may have to solve an individual equation such as 5x = 3x
+ 20000 or 752x = 534x + 987000 or 15.65x = 7.82x + 72000. As we witnessed firsthand in Chapter 4, parameters then enable us to represent all three of these equations, and thousands more like them,
by the single all-encompassing equation Px = Cx + F, where P, C, and F take on particular constant values in the context of a specific problem, but change values to reflect different scenarios. This
single equation with parameters establishes a holistic, structural connection between all break-even problems that share the same constraints, and individual equations specific to a given scenario
become particular instances of that general equation. For example, in the first and second cases, respectively, we have P = 5, C = 3, F = 20000 and P = 752, C = 534, F = 987000.
We considered a similar case in Chapter 8 where we saw that for the three assessment categories of student homework, tests, and final exam scores, we could represent all course average calculations
with the single big algebra formula ax + by + cz. Here, the letters a, b, and c serve as parameters and capture the contribution values—or weight—of each category, which remain consistent for a
particular instructor in a given class, but may change from class to class or from instructor to instructor.
Moreover, algebra is capable of far more than only containing a multitude of situations in a single formula. Like Play-Doh, it can render variable expressions malleable enough to maneuver and
transform them into radically different shapes and forms that generate novel insights. One especially pronounced instance of this capacity is visible in quadratic equations, where we can represent a
galaxy of such equations with the single big algebra formula ax^2 + bx + c = 0. From this we can apply the technique for solving each such individual equation, once and for all, to this single
super-equation and derive the famous quadratic formula:
(See Appendix 1 for more details.) This formula holds the collective results of infinitely many individual acts in suspended animation, showing through the spectacular use of the parameters—a, b, and
c—the final form that all of the specific instances can end up taking. We also saw the potential of big algebra in the various interpretations of the bill denominations problem from Chapter 11.
Significant scientific laws and processes have historically been captured by algebraic formulas capable of handling a wide array of different inputs—including mass, charge, the coefficient of
friction, the spring constant, electrical resistivity, and electrical conductivity—through the use of parameters. Similarly, in real-life financial situations, parameters can stand in for fixed
numerical information such as the sales tax in various towns, the interest rates at a given time, a principal amount invested, the price of gas per gallon on a given day, or the hourly wage of
various workers. Although these constant quantities may be fixed in a particular location, for a certain period of time, or concerning a specific person, they can vary depending on the unique
circumstances of the problem. In tuning our parameters from scenario to scenario, we become like patrons at the algebraic sports bar where—instead of changing channels between football games—we
change channels from scenario to scenario identifying their similarities and differences, their constants and variables.
As breathtaking as it may be at first sight, the Grand Canyon becomes all the more impressive once we understand its dimensions, what it contains, and how it was slowly carved out by the Colorado
River over millions of years. The realization that some of the same smaller-scale processes at work in the erosion you witness in your backyard or at a local municipal park along the river also
created this immense natural wonder is a spectacular and powerful grand confluence of ideas.
Emergent viewpoints in geology—such as understanding the relationship between micro and macro processes—makes much of what we observe on Earth more comprehensible and less mysterious. Moreover, these
viewpoints provide even nonexperts, who have some understanding and awareness of them, an entire framework within which to place and analyze new and unfamiliar landscapes that they happen upon. Such
awareness can also lead individuals to acquire a greater appreciation and awareness of their natural environment, which may ultimately lead them to become even less intimidated by the subject of
geology itself. The same can be said for astronomical knowledge. As Bernard de Fontenelle stated, “Nature… is never so admirable, nor so admired as when it is known.”^7
Consider how we might apply the same principle to large swaths of basic numeration and even some aspects of geometry. Most people can tell you very little about the nuances of land surveying but, at
the same time, are often quite comfortable with basic geometric concepts such as length, angles, area, and volume. Moreover, those same people can successfully apply those concepts to calculating the
distance between two towns, the heights of people or structures, the square footage of a house or room, or the area of a garden.
How might we frame such a relationship between micro and macro algebra? What would it look like—and is it even possible—for someone with a rudimentary understanding of variable quantities, and a
passing familiarity with algebra from a distant course or two, to extrapolate that basic proficiency to new situations involving variable phenomena? Variation and all that it entails is a much more
abstract idea, evidenced by the fact that most people readily internalize elementary arithmetic, whereas conceptual retention of fundamental algebraic principles is orders of magnitude lower in the
general population.
Algebra in a sense does for arithmetic what arithmetic does for the general notions of the size of a collection, measurement, and ordering. That is, algebra offers a set of rules for manipulating
mathematical symbols that represent objects and operations from arithmetic, a subject that itself offers a set of rules for manipulating symbols that represent numerical quantities. A second level of
symbolization and a second level of generalization can be tough to master, but symbols at both levels serve a powerful purpose.
One such power of symbolism is that symbols enable us to speak about things in their absence.^8 This is equally true of drawings, photographs, and maps. In many cases such as with military units,
sports, or travel, such representations allow us to better understand the things being represented while probing them for weakness or limitations and gleaning new insights. So too is it with the
alphabetic, diagrammatic, and graphical symbols we use in algebra.
As art education scholar Elliot Eisner wrote in The Arts and the Creation of the Mind, “Ideas and images are very difficult to hold onto unless they are inscribed in a material that gives them at
least a kind of semipermanence.”^9 Yet, how can we present algebra in such a way that its symbols and methods illuminate and expand our mathematical knowledge, rather than obscure and obstruct it?
This is one of the central problems in algebra education—and it has proven to be a tougher nut to crack than for arithmetic.
What do people remember about or take away from the other classes they take? Though undoubtedly not as much as their teachers might hope, students do perhaps take general lessons away with them into
their future coursework and professional lives. They may even learn some of these lessons outside of class.
Take science classes, for instance. Former science students are likely to be at least somewhat familiar with the concepts of atoms, planets, stars, power, and forces, as well as physical phenomena
they personally can experience like electricity, gravity, velocity, and acceleration. Some can also recall the names of a few of the famous scientists associated with major discoveries. From
chemistry, even a student who has forgotten how to balance an equation is likely to know that mixing unknown substances together could produce dangerous gases or even cause explosive reactions. From
biology, they know that tiny microorganisms can carry contagious diseases and that airborne pathogenic microbes can infect us.
What do people think about when they recall algebra? Common responses may involve letters, equations, and manipulations, but rarely with an appreciation of what those elements are really about. If
students leaving algebra classrooms can’t articulate why algebra is conceptually significant, even at the most basic level, this indicates a breakdown in algebra education relative to other subjects
in the secondary school or college curriculum—something that has made it a topic of ongoing discourse in math education. This book has been an attempt to contribute a few ideas to that discourse
while simultaneously fostering a greater appreciation of the magic and wonder of algebra in general—one of many possible higher callings of algebra educators.
William Thurston once wrote that “it is easy to forget that mathematics is primarily a tool for human thought,”^10 and it’s true that the perspective that’s often lost in translation in the algebra
classroom is that algebra can shape the way that we think, both inside and outside the context of a specific problem. An algebraic way of thinking seeks a more global and comprehensive understanding
of quantitative variable behavior in its various guises, and seeks to consolidate that understanding in productive, formulaic, and operational ways—including variable expressions, equations, tables,
and graphs. This way of thinking actually transcends algebra, but the potential exposure to it for most students receives a golden opportunity in an algebraic setting.
Though teaching algebra as a way of thinking rather than as a means to an end may be difficult to achieve in the current educational environment, a student outcome that achieves a more holistic
understanding of algebra—and emphasizes the purposes and meaning behind the procedures being taught—would be a step in the right direction and is a worthwhile goal in and of itself. I believe that
Daniel Willingham is correct in his claim that, though many of the complaints against algebra involve questions of relevance outside of the classroom, the far greater concern is that many students
simply don’t understand the rationale behind the calculations they are performing.^11 The unfortunate reality that most of them find no cohesion—no conceptual organizing principle either within the
subject itself or in their efforts—doesn’t help matters either.
If students understood the purpose of algebra from the beginning, they may leave their studies with both a better feeling toward the subject and a better sense of how they might make use of what
they’ve learned. This is by no means a trivial thing, amounting to what John Dewey calls having a worthwhile experience (as discussed in the introduction).^12 However, this is not a comprehensive
picture of what may be possible. Students certainly will encounter quantitative variation elsewhere in life—what would be some of the things that they could think about when they encounter it?
One of the things we’ve touched on several times throughout the book is that numerical variation in everyday life is not always transparent, and that it can take some work to even be aware of its
presence. When we encounter quantitative variation in the wild, it is often as a specific instance of a numerical value. Sometimes this particular value may be all that we are interested in, just
like sometimes we only want to know the specific temperature and weather conditions on a certain day.
However, more is available if we want. Just as a person can learn much more about a geographical region by being aware of the range of temperatures and weather over a period of time—its climate—so
too can the algebraic way of thinking help us to better understand the climate of a particular phenomenon. This can be done in part by having a better feel for the range of values it can take on; so,
when we encounter a particular number for a particular type of behavior, it may be productive to look at that value as a particular instance—like a particular temperature—of something more general.
Questions we could ask include: What type of algebraic climate could produce these values? What patterns can we identify that will tell us more about it?
Think of it this way. An alien coming to Earth might first see children, young adults, and the elderly as distinctly different species of people, not understanding the aging process or that one group
morphs into another group over time. However, after much observation over time, they could eventually reach this conclusion on their own by studying the relationships and interactions between each
Encountering specific instances of variation is a bit like this. Modeling scenarios algebraically gives us the ability to tie together situations that we may not initially understand or see as
connected. Alternatively, if a range of values are what is first encountered, then we can go the other way and ask if there is some core mechanism that ties them together in a formulaic way:
Algebra’s investigative properties work both ways. As we discussed in Chapter 9, part of understanding that core mechanism may include trying to find out if it easily splits into scenario variables
and regular variables and identifying what those are. This can be a useful organizing principle even when a detailed, technical understanding is not attainable.
As a mathematician educator, I’ve found that developing this kind of higher-order algebraic awareness tends to be easier for adult students. Adults are trying to weave much more complicated
tapestries in their understanding than children who are still developing; this instinct can be leveraged and built upon through a humanistic approach to mathematics that connects with their own
experiences. In my teaching, I aim to give my students a sense of the bigger picture of algebra’s contribution to our collective understanding, which can mean giving older students a productive new
perspective that alters or evolves the way they see the world and what they already know about it. One of my goals in writing this book has been to capture the magic and impact that such a global
shift in perspective has had for my adult students—and though there are many different ways to teach algebra and my approach may not necessarily be the most effective for the high-school classroom,
my hope in this final movement of our algebraic symphony is that you will close this book with a better sense of what algebra has to offer us. I may not have convinced you that the algebraic way is
“fun,” but I hope you’ll agree that algebra can be interesting, accessible, and full of possibilities.
Figuring out how to successfully incorporate topics into an algebraic setting can be likened to figuring out how to incorporate various ingredients into cooking a good meal. We know what needs to be
added—some ingredients essential and others optional—but it is the proper mixing of these—along with proper amounts of heat and time—that turn our efforts into a good meal or not. As just one cook in
a kitchen that features a wide assortment of recipes and cooking styles, I hope you have enjoyed my offerings.
We’ve thought about algebra throughout this book as a vast continent of knowledge, containing both areas that we already know fairly well and tracts of less penetrated terrain brimming with unused
potential for readers to explore. It is a grand subject whose ability to exploit a remarkable property of nature is key—that property being that it is possible to represent, describe, mimic, and
transform a wide array of phenomena using symbolic systems that obey certain protocols.
Paradoxically, it is exactly these protocols that are often looked upon as being among the most monotonous of the features of algebra, no doubt contributing in part to the subject’s large PR problem.
Yet, it is exactly these procedures—along with the fact that they were acquired to deal with one situation but are capable of being continually reused to deal with other situations—that account for
some of the most intense aspects of the beauty of the subject. Imagine a retail store gift card with a zero balance. Such a card can be looked upon as being a valueless rectangular piece of plastic
or as an object having a lot of potential. This potential can be realized through recharging or reloading the card by adding money to its balance. Once this has been done, a wide assortment of
possible purchases emerges.
Similarly, the symbols and protocols of algebra can be looked upon as being completely devoid of value, the many manipulations just so much arbitrary, meaningless ritual. However, like the empty gift
card, these protocols and rituals have the potential to be given immense value. Algebraic expressions and operational procedures can be continually “charged up” to represent and say important things
about a wide array of quantitative variations, including the ability to take these charged-up representations and make spectacular transformations of form to find out unknown, new information and
insights almost like no other discipline that preceded it or that isn’t presently underwritten by it. In other words, the apparently mindless ritual can be electrified to great purpose—acquiring
immense worth. In this, it shares great similarities to computer science, natural science, and engineering.
Thus, elementary algebra when viewed from a certain perspective can contain in miniature some demonstration of how these other disciplines contribute to the advancement of human knowledge and our
understanding of the universe around and beyond us. It is a subject with a fraught pedagogical history, at one time having its secrets completely masked from public view, like a half-mythical
impenetrable forest, and yet at the present time having many of its secrets hidden from the public in plain sight, with most people unable to appreciate the algebraic forest now for its many trees.
Algebra is a heritage that belongs to every one of us—truly one of the intellectual wonders of the ancient and modern world, and though probably not perched as high, by discipline, as one of the top
seven such wonders, it certainly has helped bankroll some of those in the top spots.
Regardless of where it sits, algebra is a vast, scenic, wide-ranging continent of possibilities that provides conceptual fuel for mathematics, as well as much of science, engineering, and a host of
other disciplines vital to modern life. It was already a very big deal during its modern symbolic ascent back in the age of printing presses, Mercator projections, armadas, Kepler, and slide rules,
and it still remains a big deal in this current era of the internet, global positioning systems, carrier battle groups, data science, and computers.
Algebra the Beautiful—fertile, electrical soil indeed.
If you find an error or have any questions, please email us at admin@erenow.org. Thank you! | {"url":"https://erenow.org/exams/algebra-beautiful-an-ode-maths-least-loved-subject/13.php","timestamp":"2024-11-04T13:32:54Z","content_type":"text/html","content_length":"57071","record_id":"<urn:uuid:69c28bdb-0f35-4c2f-9497-e08d13fc6d7c>","cc-path":"CC-MAIN-2024-46/segments/1730477027829.31/warc/CC-MAIN-20241104131715-20241104161715-00834.warc.gz"} |
Turbo Forms, Ruby on Rails Drag-Drop: Pt.1
Turbo Forms & Drag and Drop in Ruby on Rails: Part 1
Much like the Drag and Drop Uploader I built, I've been finding that you don't need to use JS plugins to build a lot of common functionality these days. It is easier to just roll your own solution.
The DOM API is modern and easy to use.
In this series of posts we're going to build a Drag and Drop feature to add music tracks to playlists. The end result will look something like:
We'll be using Turbo so that means the majority of this will be done with minimal to no Javascript (and certainly no Typescript).
In this post we're focusing on setup and the new playlist form interaction, just setting everything else up for the next post which is the main drag and drop functionality.
The final repository is here.
Getting Started
I bootstrapped the demo drag and drop rails application using my Rails Starter. That means I have shadcn-ui so I get a great component library and some other defaults that'll make getting started
fast. In fact, this first step took me 15 minutes. I'm not going to go over all the UI stuff but what you need to know is:
• A Playlist has_many playlist_tracks.
• A Playlist has_many tracks through playlist_tracks.
• A Track has_many playlist_tracks.
• A Track has_many playlists through playlist_tracks.
So we have 2 main models, Playlist, and Track, and they are joined by PlaylistTrack. We've got a Tracks controller and our main view is going to be to list out all the tracks with our playlists on
the sidebar. You can check out the main view and browse the code at the start of the application.
Creating a New Playlist
The first feature we're going to implement is creating a new playlist. It'll look like this:
The plan is to use turbo frames for this but after the fact, I think turbo streams would be a better solution. However, using turbo_frames led to some interesting patterns to get it to work elegantly
so I thought I would cover that approach and then in a later post, show how to refactor it to turbo streams.
Showing the New Playlist Form
The first step is to build a link that will drive the turbo_frame to load the new playlist form.
<%= render_button as: :link, href: new_playlist_path, data: {turbo_frame: "new_playlist"},
variant: :ghost, class: "px-2" do %>
+ Add
<% end %>
The important think about this link is that it will drive the navigation of a turbo frame with an id of new_playlist. That means when we click on this link, the source of that frame will change to
this links href. So the next step is to add that turbo_frame to the view.
<div class="px-3"><%= turbo_frame_tag "new_playlist" %></div>
If we click on that link now we'll get an error that says Content Missing. That's because we need to build the view that will load into that place. The important part about that view is that it
contains a turbo_frame with id of new_playlist.
In the PlaylistsController, the new action will instantiate an instance of Playlist and store it in @playlist.
Here's what the view for that action looks like:
<%= turbo_frame_tag "new_playlist" do %>
<%= render_form_for(@playlist) do |form| %>
<div class="my-2">
<%= form.text_field :name %>
<div class="flex justify-between items-center">
<%= form.submit "Create", class: "text-sm px-2 py-1" %>
<%= render_button "Cancel", variant: :ghost, class: "text-sm px-2 py-1" %>
<% end %>
<% end %>
With that, clicking on the Add link should load this form, sans any javascript.
Submitting the New Playlist Form
There are two features we need to account for when submitting the form. The first is re-render the form with validation errors if the playlist doesn't contain a name.
The create action in the PlaylistsController will handle the validation, re-rendering our new.html.erb if it fails validation along with sending the correct status code. If the form is valid, we can
render the create.html.erb instead of the normal flow of redirecting. The reason why we'll do this is to create the next feature, which is to show the newly created playlist within a turbo frame.
def create
@playlist = Playlist.new(playlist_params)
render :new, status: 422 unless @playlist.save
Validation works now because the form field is getting an error class attached to it on the field that fails validation from form_for (or render_form_for with shadcn). The error class is defined in
shadcn and is just a red border.
The next step is to render the create.html.erb view. We want the newly created playlist to render within the list of playlists in the view. To do this we'll use another turbo frame in the view to
show all the playlists.
<div class="px-3"><%= turbo_frame_tag "new_playlist" %></div>
<div dir="ltr" class="relative px-1">
<div class="h-full w-full rounded-[inherit]">
<div style="min-width: 100%; display: table">
<%= turbo_frame_tag "playlists" do %>
<div data-controller="playlists">
<%= render collection: Playlist.all, partial: "playlists/playlist" %>
<% end %>
By having turbo_frame_tag "playlists" in the index view, if we include a similar playlist turbo frame in the create.html.erb view, it will render the newly created playlist in the list of playlists
and replace the playlists frame.
<%= turbo_frame_tag "playlists" do %>
<%= render collection: Playlist.all, partial: "playlist" %>
<% end %>
The effect works pretty well.
The only issue is that the form for the playlist persists after the playlist is created instead of disappearing.
I can think of a lot of ways to solve this without reaching for Stimulus, the most proper being turning the form into a turbo stream and using append and remove directives. But I found an interesting
way of doing it that doesn't bother me too much but will probably bother a good amount of people.
Inline Javascript to the Rescue
This is what I did, don't judge me.
<%= turbo_frame_tag "playlists" do %>
<%= render collection: Playlist.all, partial: "playlist" %>
<% end %>
That's right. I added an inline script tag in create.html.erb that does exactly what I want it to do, it removes the new_playlist form. I can't really think of a problem with this approach other than
the eww factor.
Look, when you use turbo stream directives, you're still adding behavior in the form of html tags to your html. You're still essentially calling that JS because there is no magic, you're just doing
it through the turbo stream abstraction. You are still referring to some DOM element by ID, you're just doing it through the turbo stream name. This is just a more direct way of saying this view
comes with instructions.
The dangers of this sort of code, such as the document not being ready or the element not existent don't apply in this use-case. It works really well, it's simple, it's direct, I'm buying it.
Update: Nate Matykiewicz correctly states that the issue with inline code has to do with Content Security Policies not style.
Wrapping Up New Playlist
With that we're able to create new playlists through a nifty form and we've setup the view and the models for the actual functionality we're interested in, the drag and drop. Unfortunately, this post
got a little long and the next part is long too so I'm going to publish this as part 1 and we'll continue the drag and drop implementation in part 2.
Did you find this article valuable?
Support Avi Flombaum by becoming a sponsor. Any amount is appreciated! | {"url":"https://code.avi.nyc/turbo-forms-drag-and-drop-in-ruby-on-rails-part-1","timestamp":"2024-11-02T09:31:00Z","content_type":"text/html","content_length":"250125","record_id":"<urn:uuid:1b50d475-6fa4-43b9-a33a-406ce61c544b>","cc-path":"CC-MAIN-2024-46/segments/1730477027709.8/warc/CC-MAIN-20241102071948-20241102101948-00112.warc.gz"} |
Least to Greatest Calculator Fractions - GEGCalculators
Least to Greatest Calculator Fractions
Least to Greatest Fractions Calculator
Enter a list of fractions separated by commas:
Sorted fractions:
Q: How do you order fractions from least to greatest? A: To order fractions from least to greatest, compare their values. The fraction with the smallest value comes first, and then arrange the rest
in increasing order of value.
Q: What is 2 3 3 5 as a fraction? A: The numbers 2, 3, 3, and 5 don’t form a valid fraction on their own. To express them as a fraction, you would need a numerator and a denominator.
Q: Which calculator is best for fractions? A: There are various calculators that are suitable for working with fractions, including scientific calculators and online calculators that specifically
handle fractions. Look for calculators with fraction capabilities and user-friendly interfaces.
Q: Which is in order from least to greatest? A: You would need to provide a list of numbers or fractions for this question.
Q: What is the proper order from least to greatest for 2 3 7 6 1 8 9 10? A: The proper order from least to greatest for these numbers is: 1, 2, 3, 6, 7, 8, 9, 10.
Q: How do you find the least to greatest fractions with different denominators? A: To compare fractions with different denominators, find a common denominator and then compare the numerators.
Q: What is 5 8 2 3 in fraction form? A: 5 8 2 3 is not a clear representation of numbers or fractions. It seems to be a sequence of numbers separated by spaces.
Q: What is 3 8 times 2 5 in fraction form? A: 3 8 times 2 5 can be expressed as a fraction: (3/8) * (2/5) = 6/40, which simplifies to 3/20.
Q: What is 2 3 times 4 5 in fraction form? A: 2 3 times 4 5 can be expressed as a fraction: (2/3) * (4/5) = 8/15.
Q: How do I use a calculator for fractions? A: To use a calculator for fractions, enter the fractions using appropriate keys or buttons, and then perform the desired mathematical operations.
Q: What is the best calculator for 5th grade? A: For 5th grade, a basic scientific calculator that can handle addition, subtraction, multiplication, division, and fractions should be sufficient.
Q: What calculator do schools use? A: Schools often use a variety of calculators depending on grade level and curriculum. Basic scientific calculators and graphing calculators are common choices.
Q: What is the proper order from least to greatest for 1 2 5 6 2 7 4 2? A: The proper order from least to greatest for these numbers is: 1, 2, 2, 2, 4, 5, 6, 7.
Q: How do you compare and order fractions? A: To compare and order fractions, find a common denominator, compare the numerators, and then arrange them in ascending or descending order.
Q: How do you arrange fractions in descending order? A: To arrange fractions in descending order, compare their values and list them in decreasing order.
Q: Which of the following is the greatest 1 2 2 3 4 5 7 8? A: The greatest number in this list is 8.
Q: How do you order fractions from least to greatest with mixed numbers? A: To order fractions with mixed numbers, convert the mixed numbers to improper fractions, compare their values, and then
arrange them.
Q: What is the order of fractions from smallest to largest 1 4 2 3 4 7 1 2? A: The order of fractions from smallest to largest is: 1/4, 1/2, 2/3, 4/7.
Q: How do you arrange fractions from least to greatest Grade 2? A: In Grade 2, students typically learn basic fractions. To arrange fractions from least to greatest, they would need to compare the
numerators and denominators.
Q: How do you arrange fractions in ascending and descending order? A: To arrange fractions in ascending order, compare their values and list them in increasing order. To arrange them in descending
order, list them in decreasing order.
Q: How do you order fractions on a number line? A: To order fractions on a number line, first find a common denominator, convert the fractions to equivalent fractions with that denominator, and then
place them on the number line based on their values.
Q: Which is the largest fraction 5 8 2 3 7 9 3 5? A: To determine the largest fraction, convert these mixed numbers to improper fractions and then compare their values.
Q: Which is the smallest fraction 1 2 3 7 3 5 4 9? A: To determine the smallest fraction, convert these mixed numbers to improper fractions and then compare their values.
Q: Which of the following are proper fractions 1 2 3 5 10 7 2 15 8 16 16 10 11 23 10? A: Proper fractions are fractions where the numerator is smaller than the denominator. Among the listed numbers,
1/2, 3/5, 7/15, and 10/16 are proper fractions.
Q: What is 3 7 times 2 5 in fraction form? A: 3 7 times 2 5 can be expressed as a fraction: (3/7) * (2/5) = 6/35.
Q: What is 7 8 2 3 as a fraction? A: 7 8 2 3 is not a clear representation of a mixed number or a fraction. It seems to be a sequence of numbers separated by spaces.
Q: What is 8 9 — 2 3 in fraction form? A: 8 9 — 2 3 is not a clear representation of a mixed number or a fraction. It seems to have formatting issues.
Q: What is 1 4 times 5 in fraction form? A: 1 4 times 5 can be expressed as a fraction: (1/4) * (5/1) = 5/4.
Q: What is 1 3 times 5 in fraction form? A: 1 3 times 5 can be expressed as a fraction: (1/3) * (5/1) = 5/3.
Q: What is 1 2 times 2 5 in fraction form? A: 1 2 times 2 5 can be expressed as a fraction: (1/2) * (2/5) = 2/10, which simplifies to 1/5.
Q: What is 1 2 2 3 in fraction form? A: 1 2 2 3 is not a clear representation of a mixed number or a fraction. It seems to be a sequence of numbers separated by spaces.
Q: How to do fractional math without calculator? A: To perform fractional math without a calculator, you can use paper and pencil to perform operations like addition, subtraction, multiplication, and
division using the rules of fractions.
Q: How to simplify a fraction? A: To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator, and then divide both by the GCD.
Q: Can 7th graders use a calculator? A: Yes, many 7th graders are introduced to calculators as part of their math education. However, they should also learn how to perform calculations manually to
build a solid foundation.
Q: Should 7th graders use calculators? A: Using calculators can be beneficial for 7th graders in certain situations, especially for complex calculations. However, it’s important for them to also
develop mental math skills and understand the underlying concepts.
Q: Do you use a calculator in 6th grade? A: The use of calculators in 6th grade varies based on educational standards and curriculum. Some topics may introduce calculators, but students should still
focus on understanding concepts and mental math.
Q: Can 8th graders use a calculator? A: Yes, 8th graders often use calculators as part of their math education. However, it’s important for them to balance calculator use with manual calculation
Q: What kind of calculator does a 10th grader need? A: A scientific calculator with additional features like trigonometric functions and statistics capabilities is usually suitable for a 10th grader.
Q: What calculator do freshman need? A: Freshmen in high school typically need a scientific calculator with features like logarithms, exponentials, trigonometric functions, and possibly basic
graphing capabilities.
GEG Calculators is a comprehensive online platform that offers a wide range of calculators to cater to various needs. With over 300 calculators covering finance, health, science, mathematics, and
more, GEG Calculators provides users with accurate and convenient tools for everyday calculations. The website’s user-friendly interface ensures easy navigation and accessibility, making it suitable
for people from all walks of life. Whether it’s financial planning, health assessments, or educational purposes, GEG Calculators has a calculator to suit every requirement. With its reliable and
up-to-date calculations, GEG Calculators has become a go-to resource for individuals, professionals, and students seeking quick and precise results for their calculations.
Leave a Comment | {"url":"https://gegcalculators.com/least-to-greatest-calculator-fractions/","timestamp":"2024-11-05T08:55:26Z","content_type":"text/html","content_length":"175787","record_id":"<urn:uuid:fdcf3a3f-e8b4-42d2-8682-7d486a1790b0>","cc-path":"CC-MAIN-2024-46/segments/1730477027878.78/warc/CC-MAIN-20241105083140-20241105113140-00427.warc.gz"} |
Integration by Parts Exam Solutions (examples, videos, worksheets, activities)
Related Topics:
More Lessons for A Level Maths Math Worksheets
Examples, videos, solutions, activities and worksheets that are suitable for A Level Maths.
How to answer questions on integration by parts?
A-Level Maths Edexcel C4 June 2008 Q2a
This question is on integration by part.
(a) Use integration by parts to find ∫xe
A-Level Maths Edexcel C4 June 2008 Q2b
This question is on integration by parts.
(b) Hence find ∫x
Integration (8) - Integration By Parts (C4 Maths A-Level)
How to integrate functions by using integration by parts (reverse product rule)?
1. Find ∫x cos x dx.
2. Find ∫x
ln x dx.
3. Find ∫x
4. Find ∫ ln x dx.
Integration by Parts
1. Find ∫x
cos 2x dx.
2. Find ∫x e
3. Find ∫x ln x dx.
4. Find ∫e
sin 3x dx.
Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page. | {"url":"https://www.onlinemathlearning.com/integration-by-parts-questions-2.html","timestamp":"2024-11-07T23:45:57Z","content_type":"text/html","content_length":"37794","record_id":"<urn:uuid:6c95d5e0-51be-4149-b355-93e2c9a1b94f>","cc-path":"CC-MAIN-2024-46/segments/1730477028017.48/warc/CC-MAIN-20241107212632-20241108002632-00085.warc.gz"} |
RS Aggarwal Solutions Class 6 Chapter-3 Whole Numbers (Ex 3E) Exercise 3.5 - Free PDF
Free PDF download of RS Aggarwal Solutions Class 6 Chapter-3 Whole Numbers (Ex 3E) Exercise 3.5 solved by Expert Mathematics Teachers on Vedantu. All Exercise 3.5 Questions with Solutions for Class 6
Maths RS Aggarwal to help you to revise complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other Engineering entrance exams. Every NCERT Solution
is provided to make the study simple and intresting on vedantu. You can also register Online for NCERT Class 6 Science tuition on Vedantu to score more marks in CBSE board examination.
FAQs on RS Aggarwal Solutions Class 6 Chapter-3 Whole Numbers (Ex 3E) Exercise 3.5
1. What are the few interesting things in the Whole Number?
The concept of the Whole Number is a basic one in Mathematics. There are some interesting things about the Whole Number. They are as follows:
• A Whole Number can both be an integer or a natural number
• There is nothing called the largest Whole Number since if W is a Whole Number W+1 is also a Whole Number and there is no end in this series. However there is the smallest Whole Number which is
zero. So this is a set of numbers which has no largest but smallest number.
2. Which book is best for Class 6 Maths Chapter 3?
RS Aggarwal and RD Sharma are both well recommended books for Maths in any standard. However it has been seen that RS Aggarwal Maths book usually gives more importance in slow and steady development
of concepts. A Class 6 student will find it easy to understand the different topics in Maths with comparatively easy Examples in RS Aggarwal. The students will also find it easy to start their
practicing with easy Exercises of RS Aggarwal. Vedantu also helps with the ready-made solutions for all the Exercises to guide the students when they are not able to attempt a few questions.
3. What are the properties of Whole Numbers?
The variety of properties of Whole Numbers help the students to conduct a lot of operations on Whole Numbers. The properties are in fact the characteristics of Whole Numbers. The properties can be
clubbed a follows:
• W is the symbol used for representation of Whole Number
• Closure property states that if two Whole Numbers are added or multiplied the product is always a Whole Number
• Associative property states that the result of sum or product of three Whole Numbers are always same irrespective of the way they are arranged or grouped
• Commutative property states that the result of addition or multiplication of any two Whole Numbers is always the same even after interchanging their order.
• Distributive property states that if three Whole Numbers a,b,c are expressed as a* (b+c) then this is equal to a*b+a*c.
4. Under which operations are the Whole Numbers closed?
Whole Numbers are closed under addition and multiplication only. If two Whole Numbers are added or multiplied the result is always a Whole Number. However if two Whole Numbers are subtracted the
result may or may not be a Whole Number. The result of subtraction of two Whole Numbers can be a negative integer which is not a Whole Number. Similarly the result of division of two Whole Numbers
can be a fraction or decimal which is not a Whole Number.
5. Why is zero considered a Whole Number?
The concept of Whole Number is not only important but also interesting. It is interesting to find zero in the set of Whole Numbers. The reason or logic behind this can be well justified. Whole Number
includes all non-negative integers. Zero satisfies this criteria. It can be argued that if all positive integers are Whole Numbers then how zero is a Whole Number. However the former justification
that it is non-negative integer is stronger than the latter one. Hence zero is a Whole Number. | {"url":"https://www.vedantu.com/rs-aggarwal-solutions/class-6-maths-chapter-3-exercise-3-5","timestamp":"2024-11-12T13:55:08Z","content_type":"text/html","content_length":"175304","record_id":"<urn:uuid:27c244ae-9268-4059-bdf1-0b62234209e8>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.45/warc/CC-MAIN-20241112113320-20241112143320-00872.warc.gz"} |
MAT is our flagship contest series. The Summer MAT has 3 sets of 3 problems, each set to be done in 30 minutes, along with a tiebreaker set - so in total, 4 sets of 3. The difficulty ranges from
mid-AMC 10 to late AIME, with most of the difficulty variation occurring within a set and less of it between sets (though there is an increase between sets). It is typically held in the summer.
An easier version of the MAT is held in the winter. The Winter MAT also has 3 sets of 3 problems, but it does not have a tiebreaker and the time limit for each set is 20 minutes.
mapm is the software which Math Advance uses to create its contests. The principle purpose of mapm is to modularize problems into individual files which allows them to be programatically composed
into a contest. My personal website contains a demonstration of the problem mapm was designed to fix. The Math Advance mapm contest archives may be of interest.
Of course, mapm is open source. It is licensed with 3-Clause BSD.
This fall, we are teaching an AIME course. Applications are due September 3rd, and classes tentatively begin the Sunday after. Pricing is $100 for a semester of 10 lectures, plus potential guest | {"url":"https://mathadvance.org/projects","timestamp":"2024-11-09T22:30:40Z","content_type":"text/html","content_length":"2788","record_id":"<urn:uuid:4249bcf3-b722-4476-a951-045d6bad8734>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.10/warc/CC-MAIN-20241109214337-20241110004337-00549.warc.gz"} |
Optimal profile design for acoustic black holes using Timoshenko beam theory
We revisit the problem of constructing one-dimensional acoustic black holes. Instead of considering the Euler-Bernoulli beam theory, we use Timoshenko's approach, which is known to be more realistic
at higher frequencies. Our goal is to minimize the reflection coefficient under a constraint imposed on the normalized wavenumber variation. We use the calculus of variations to derive the
corresponding Euler-Lagrange equation analytically and then use numerical methods to solve this equation to find the "optimal"height profile for different frequencies. We then compare these profiles
to the corresponding ones previously found using the Euler-Bernoulli beam theory and see that in the lower range of the dimensionless frequency ω (defined using the largest height of the plate), the
optimal profiles almost coincide, as expected.
Bibliographical note
Publisher Copyright:
© 2023 Acoustical Society of America.
Dive into the research topics of 'Optimal profile design for acoustic black holes using Timoshenko beam theory'. Together they form a unique fingerprint. | {"url":"https://vbn.aau.dk/en/publications/optimal-profile-design-for-acoustic-black-holes-using-timoshenko-","timestamp":"2024-11-10T07:49:40Z","content_type":"text/html","content_length":"61696","record_id":"<urn:uuid:5c16ad2a-a2c3-4917-92bc-dadbd69a8208>","cc-path":"CC-MAIN-2024-46/segments/1730477028179.55/warc/CC-MAIN-20241110072033-20241110102033-00036.warc.gz"} |
Usually, when comparing a fit to data, one should first plot the data, and then the PDF. In this case, the PDF is automatically normalised to match the number of data events in the plot. However,
when plotting only a sub-range, when e.g. a signal region has to be blinded, one has to exclude the blinded region from the computation of the normalisation.
In this tutorial, we show how to explicitly choose the normalisation when plotting using NormRange().
import ROOT
# Make a fit model
x = ROOT.RooRealVar("x", "The observable", 1, 30)
tau = ROOT.RooRealVar("tau", "The exponent", -0.1337, -10.0, -0.1)
expo = ROOT.RooExponential("expo", "A falling exponential function", x, tau)
# Define the sidebands (e.g. background regions)
x.setRange("full", 1, 30)
x.setRange("left", 1, 10)
x.setRange("right", 20, 30)
# Generate toy data, and cut out the blinded region.
data = expo.generate(x, 1000)
blindedData = data.reduce(CutRange="left,right")
# Kick tau a bit, and run an unbinned fit where the blinded data are missing.
# ----------------------------------------------------------------------------------------------------------
# The fit should be done only in the unblinded regions, otherwise it would try
# to make the model adapt to the empty bins in the blinded region.
expo.fitTo(blindedData, Range="left,right", PrintLevel=-1)
# Clear the "fitrange" attribute of the PDF. Otherwise, the fitrange would be
# automatically taken as the NormRange() for plotting. We want to avoid this,
# because the point of this tutorial is to show what can go wrong when the
# NormRange() is not specified.
# Here we will plot the results
canvas = ROOT.TCanvas("canvas", "canvas", 800, 600)
canvas.Divide(2, 1)
# Wrong:
# ----------------------------------------------------------------------------------------------------------
# Plotting each slice on its own normalises the PDF over its plotting range. For the full curve, that means
# that the blinded region where data is missing is included in the normalisation calculation. The PDF therefore
# comes out too low, and doesn't match up with the slices in the side bands, which are normalised to "their" data.
print("Now plotting with unique normalisation for each slice.\n")
plotFrame = x.frame(Title="Wrong: Each slice normalised over its plotting range")
# Plot only the blinded data, and then plot the PDF over the full range as well as both sidebands
expo.plotOn(plotFrame, LineColor="r", Range="full")
expo.plotOn(plotFrame, LineColor="b", Range="left")
expo.plotOn(plotFrame, LineColor="g", Range="right")
# Right:
# ----------------------------------------------------------------------------------------------------------
# Make the same plot, but normalise each piece with respect to the regions "left" AND "right". This requires setting
# a "NormRange", which tells RooFit over which range the PDF has to be integrated to normalise.
# This means that the normalisation of the blue and green curves is slightly different from the left plot,
# because they get a common scale factor.
print("\n\nNow plotting with correct norm ranges:\n")
plotFrameWithNormRange = x.frame(Title="Right: All slices have common normalisation")
# Plot only the blinded data, and then plot the PDF over the full range as well as both sidebands
expo.plotOn(plotFrameWithNormRange, LineColor="b", Range="left", NormRange="left,right")
expo.plotOn(plotFrameWithNormRange, LineColor="g", Range="right", NormRange="left,right")
expo.plotOn(plotFrameWithNormRange, LineColor="r", Range="full", NormRange="left,right", LineStyle=10)
[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'full' created with bounds [1,30]
[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'left' created with bounds [1,10]
[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'right' created with bounds [20,30]
[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'fit_nll_expo_expoData_left' created with bounds [1,10]
[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'fit_nll_expo_expoData_right' created with bounds [20,30]
[#1] INFO:Fitting -- RooAbsPdf::fitTo(expo_over_expo_Int[x|left,right]) fixing normalization set for coefficient determination to observables in data
[#1] INFO:Fitting -- using CPU computation library compiled with -mavx2
[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_expo_over_expo_Int[x|left,right]_expoData) Summation contains a RooNLLVar, using its error level
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization
[#1] INFO:Plotting -- RooAbsPdf::plotOn(expo) only plotting range 'full', curve is normalized to data in given range
[#1] INFO:Plotting -- RooAbsPdf::plotOn(expo) only plotting range 'left', curve is normalized to data in given range
[#1] INFO:Plotting -- RooAbsPdf::plotOn(expo) only plotting range 'right', curve is normalized to data in given range
[#1] INFO:Plotting -- RooAbsPdf::plotOn(expo) only plotting range 'left'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(expo) p.d.f. curve is normalized using explicit choice of ranges 'left,right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(expo) only plotting range 'right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(expo) p.d.f. curve is normalized using explicit choice of ranges 'left,right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(expo) only plotting range 'full'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(expo) p.d.f. curve is normalized using explicit choice of ranges 'left,right'
Now plotting with unique normalisation for each slice.
Now plotting with correct norm ranges: | {"url":"https://root.cern.ch/doc/master/rf212__plottingInRanges__blinding_8py.html","timestamp":"2024-11-12T22:33:49Z","content_type":"application/xhtml+xml","content_length":"18804","record_id":"<urn:uuid:adb737b1-9dce-482b-b5d0-1f08eda8c597>","cc-path":"CC-MAIN-2024-46/segments/1730477028290.49/warc/CC-MAIN-20241112212600-20241113002600-00765.warc.gz"} |
Application of Statistical Design of Experiment and Numerical Optimization in Optimizing the Effects of Selected Input Variables on the Period of Oscillation in an Unsteady Flow Through Surge Chamber
Ilaboya, I. R., University of Benin; Department of Civil Engineering, Faculty of Engineering, PMB 1154, Benin City, Nigeria.
Oti, E. O., University of Benin; Department of Civil Engineering, Faculty of Engineering, PMB 1154, Benin City, Nigeria.
Atikpo E., Department of Civil Engineering, Igbinedion University, Okada, Edo State, Nigeria.
Enamuotor, B. O., Department of Civil Engineering, Delta State University, Abraka, Nigeria.
Umukoro, L. O., Department of Civil Engineering, Igbinedion University, Okada, Edo State, Nigeria. | {"url":"http://openscienceonline.com/journal/archive2?journalId=716&paperId=634","timestamp":"2024-11-14T02:15:10Z","content_type":"text/html","content_length":"44072","record_id":"<urn:uuid:bf3422e1-d226-4647-9501-92c310f14535>","cc-path":"CC-MAIN-2024-46/segments/1730477028516.72/warc/CC-MAIN-20241113235151-20241114025151-00493.warc.gz"} |
Tutorial: Rainy/Snowy Day Max: Spirographics | Cycling '74
Rainy/Snowy Day Max: Spirographics
I'm sure a lot of you are going to look at this picture and be transported to childhood (either your own, or one of your own children or younger friends): The Spirograph. This deceptively simple
collection of geared rings and wheels and pens were the source of hours of drawing fun; You pinned down the big ring, grabbed a little gear full of holes, put your pen in the hole of your choice, and
your pen magically drew these amazing curves and shapes inside or outside of the toothed ring as you moved the little wheel on its circular path... that is, unless your hand slipped and the wheel
came loose, in which case you started again and learned a little coordination as well as creating cool designs!
For this seasonally-appropriate edition of Rainy Day Max, we're going to revisit those exciting days of drawing by implementing a version of the Spirograph with Jitter using Javascript — we'll walk
you how to conceptualize the mathematics of the hypotrochoids and epitrochoids (those are the fancy Maths names for the curves you drew inside or outside of the geared ring back in the day), and show
you how to create a patch that lets you explore doing the drawing yourself without making any of those gear-slipping errors that made you crazy when you were a kid. Let's get started!
download the patches used in this tutorial
Here's our Spirograph tutorial patch: The Spirograph_lcd.maxpat patch lets us set some drawing variables and produce Spirographic output, and contains a Max js (Javascript) object whose code
calculates drawing our curves:
The basics of this patch are pretty straight-ahead: a set of four parameters are needed to control the drawing:
• Two radii that set the relative size of the two rings used to create the drawing
• A value (theta) that sets a ratio between the two rings
• A number that specifies the number of points to plot when we render our results
So, how does our Spirograph work? Simply put, the Spirograph consists of the interaction between two circles. In the real world of a Spirograph set, there’s a large toothed wheel, and a smaller one
that can roll around the inside of the larger one (a hypotrochoid) or the outside (epitrochoid) of the larger wheel.
The drawing magic derives from the fact that the gears have differing numbers of teeth, so they spin at different rates. In addition, the smaller wheel contains holes for your pen, which are spaced
at equal intervals outward from the center of the smaller wheel, which gives you curves of varying intensity.
We need to start creating our Spirograph patch by getting a handle on the mathematics for calculating the curves, and then translate that understanding into creating some Javascript code to do that
for us. A little quality googling time really paid off - there is a beautifully explained online article on creating Spirograph drawings using Javascript by by Chris Maissan. Reading through it
wasn’t only inspiring – it gave me a clear starting point for the calculations I needed to perform. Here are the basics (and I’d like to thank Chris for his permission to use the snapshots from his
interactive web page).
To draw the inner circle, you can use this formula to plot x and y values within a range of 0. To 2π. The values of cx and cy are the center point of the circle
image courtesy of Chris Maissan
The outer circle should have its center on the outer edge of the inner circle. To do that, we use the value of the initial calculation as the center point for the outer circle
x = cx + radius1 × cos(θ) + radius2 × cos(θ)
y = cy + radius1 × sin(θ) + radius2 × cos(θ)
image courtesy of Chris Maissan
The next calculation is where the magic happens – to simulate the different number of teeth in the inner and outer wheels of the Spirograph, we replace the theta value for the second circle by a
ratio. The result is that the ratio determines the number of “spins” of the gear of the Spirograph.
x = cx + radius1 × cos(θ) + radius2 × cos(θ × ratio)
y = cy + radius1 × sin(θ) + radius2 × cos(θ × ratio)
image courtesy of Chris Maissan
I’d strongly encourage you to visit Chris' website to see the interactive versions of these images and watch them in action for yourself. They were an invaluable starting point for realizing these
Armed with this knowledge, it's time to fire up the Max js object and try to implement this in Max.
Formulas to Code
We're going to create some Javascript code that takes the four parameters from the parent patch and calculates the points to plot as our virtual inner/outer wheel "turns."
To do that, we'll need to do some basic Javascript housekeeping: We set our code to automatically update when it’s saved, and create an object with a single inlet and a single outlet.
Following that, we need to create a constant for use in our calculations, and declare the global variables we’ll be working with.
In the visualization examples we were looking at on Chris Maissan's website, everything was calculated in the range 0. – 2∏ (6.28318), so we'll need to work with that value. Javascript’s math library
only includes Math.Pi as a constant, but that’s not problem. We can calculate the value by multiply the Javascript constant Math.PI by two and declare it as a constant.
// Max js object setup
autowatch = 1;
inlets = 1;
outlets = 1;
// constants
var TWOPI = 2 * Math.PI;
Next, we’ll set default values for the size of the radius of the large (outer) and small (inner) circles/wheels for our spirograph. As you'll see, calling them "large" and "small" isn't exactly
right, since - as we'll see later on - or "large" parameter value can be smaller than the "small" parameter value and produce interesting results.
In addition, we’ll add a default value (smallRatio) we’ll use for a number of the functions we’ll use to set our plotting values.
The renderpoints variable represents the number of points we’re going to draw to graph our spirograph. In the data visualizations we saw above, the calculations were done at a high resolution. For
our patch, we’re going to choose the number of points we’ll use to plot the spirograph. While we obviously would normally use a high number for the number of rendering points, there are some
interesting things we can do by experimenting with different resolutions, too.
Knowing the number of render points also allows us to set the amount by which we increment/offset each point calculation as we make our way from 0 to 2π. We calculate that amount (the variable
renderstep) by dividing the range (2∏) by the number of points we want to render, and we’ll add use that amount as an increment in the for() loop that does our calculation of each point to render.
Here's a listing of the global values we're going to be working with (along with the defaults we set for them):
// global variables
var largeRad = .70;
var smallRad = .15;
var smallRatio = 10;
var renderpts = 1000;
var renderstep = TWOPI / renderpts;
The body of the program itself is a function – bang() – that takes the current settings for our global variables and outputs a set of x/y vector locations in the range of -1.0 to 1.0. The number of
vector locations in the output is set by the renderpts variable.
Inside the bang() function, we’ve got several sets of variables used for the function’s calculations
• A pair of variables that represented the last calculated x/y output position
• The variables used for the drawing calculations (tmp and the theta value that sets the number of “gears in the wheel”
• The starting points for the calculation (stx, sty), calculated based on the size of the small and large radii
• A flag set when the calculations are started
// the bang function renders the current settings into a set
// of vector locations in the ranges of -1.0 thru 1.0
function bang() {
var x, y; // calculated dimensions
var tmp, theta; // variables for drawing calcs
var stx, sty; // variables containing the starting points
var started = 0; // 'first time' flag
To calculate the coordinate values we need to plot our output, we're going to use a for() loop. Using the computed renderstep value as an increment, the loop starts by outputting the message 0, point
, followed by the calculated x/y coordinates. Calculating those x/y coordinates will look familiar to you if you’ve looked at Chris Maissan’s web page equations. Here’s the version from his website
x = cx + radius1 × cos(θ) + radius2 × cos(θ × ratio)
y = cy + radius1 × sin(θ) + radius2 × cos(θ × ratio)
And here’s the for() loop code from the js object that does the calculation
for (theta=0; theta<TWOPI; theta+=renderstep) {
// calculate the drawing position
tmp = theta * smallRatio;
x = largeRad * Math.cos(theta) + smallRad * Math.cos(tmp);
y = largeRad * Math.sin(theta) + smallRad * Math.sin(tmp);
if (started) {
// send out the current point
outlet(0, 'point', x, y);
} else {
started = 1;
// send out the start message along with the
// first drawing location (the start point)
outlet(0, 'start', x, y);
// store the start point for later
stx = x;
sty = y;
// send out the end message along with the
// original start point (to complete the drawing)
outlet(0, 'end', stx, sty);
Whenever the bang() function is triggered (i.e whenever one of the four input parameters from the parent patch is changed), a starting message is sent out of "outlet 0" (the first/only outlet) from
the js object as a message in the form:
start <first-stxvalue> <first-sty-value>
That calculated pair of coordinate values is stored as the stx and sty variables for use at the end of drawing. Then, as the for() loop runs, the result of each of the calculations is sent out the js
object as a message in the form:
point <x-coordinate> <y-coordinate>
When the incremented renderstep value exceeds 2∏, a final message in the form:
end <last-stxvalue> <last-sty-value>
is output, using the stored positions, to complete the drawing and return us to the starting point.
The rest of the Javascript code contains a number of small functions used to set the radius of the “small” and “large” rings and constrain those input values to a reasonable size, a simple function
that sets and constrains the actual ratio of the small ring rotations per large ring rotation, and the function that calculates the number of steps/points to render (calculated by dividing the number
of points by 2∏ (6.28318). Here's an example of one of those functions:
// set the radius of the 'large' ring
function setLargeRadius(v) {
if ((v > 0.01) && (v < 0.99)) {
largeRad = v;
Doing a Little Drawing
Now that we've got our Javascript code set up, let's walk through the Spirograph_lcd.maxpat patch.
Each of the four variables our patch uses are sent to a pak object, which will output a four-item list whenever any of the input variables changes. The resulting list is sent to the p Spirographics
subpatcher. Here's the inside of the subpatcher:
The trigger object takes the four-item list from the parent patch and unpacks the list, setting each of the variables (LargeRadius, SmallRadius, ThetaRatio and RenderPoints) used in our Javascript
code. After that's all unpacked, the trigger object sends a bang message to the js spiro.js object, which does all of our calculations for us.
The js spiro.js object outputs one of three slightly different messages that we use in plotting our results:
• A start message, whose co-ordinates are always the same (start
• A point message for each of the rendering steps which contains the x and y coordinates of the point to plot
• An end message whose co-ordinate are also always the same (start, etc.)
The messages for each point to plot from the js object are sent out the route object’s point output, where the list output constructs a lineto message that draws a line between the previous point and
the new one. However, there’s one bit of housekeeping we’ll need to attend to for a good plot to the jit.lcd object: The output of our Javascript code produces x and y coordinates in the range of
-1.0 to 1.0. Since that will produce a really tiny output image for a jit.lcd object, we’ll need to scale our output lists to plot the output over a more easily visible range. The coord-scale
abstraction handles us for that using a vexpr object to process the list input to provide output in a more visible range (400 points, in this case).
The messages for each point to plot from the js object are sent out the route object’s point output, where the list output constructs a lineto message that draws a line between the previous point and
the new one.
However, there’s one bit of housekeeping we’ll need to attend to for a good plot to the jit.lcd object: The output of our Javascript code produces x and y co-ordinates in the range of -1.0 to 1.0.
Since that will produce a really tiny output image for a jit.lcd object, we’ll need to scale our output lists to plot the output over a more easily visible range. The coord-scale abstraction handles
us for that using a vexpr object to process the list input to provide output in a more visible range (400 points, in this case).We use the first of those now-scaled output messages (the start
message) to set up our jit.lcd object to begin drawing. When a start message is received, we output the message brgb 0 0 0, frgb 255 0 0, pensize 1 1, clear, moveto $1 $2 to do the following:
• We set the background and foreground colors for our display using brgb and frgb messages respectively
• We set the size of the line drawn in the display using the pensize message
• We clear the current display
• We set the point to begin plotting our output with the moveto $1 $2 messageThe end of the js object’s calculation sequence draws a line segment to the point where the original calculation started
to complete the drawing
The output of the p Spirographics subpatcher is then sent to the jit.lcd external we use to do our drawing and display. Here's how the sequence of start, point, and end drawing commands to the
jit.lcd object work: We use the first of those now-scaled output messages (the start message) to set up our jit.lcd object to begin drawing. When a start message is received, we output a series of
messages (separated by commas in the message box) the message brgb 0 0 0, frgb 255 0 0, pensize 1 1, clear, moveto $1 $2 to do the following:
• The messages brgb 0 0 0 and frgb 255 0 0 set the background and foreground colors for our display.
• The message pensize 1 1 sets the size of the line drawn from point to point in the display.
• The message clear clears the current display
• The message moveto $1 $2 draws a line to the current coordinate point.
After that, the messages for each further point to plot in the form moveto $1 $2 draws a line to the next coordinate point.
The end of the js object’s calculation sequence draws a line segment to the point where the original calculation started to complete the drawing.
Using the Spirograph
We've now got a working Spirograph. It's time to experiment with the parameters available to us! You'll be surprised at the range of possible outputs. Here are a few interesting things to consider:
Your ability to set different theta values lets you control the number of "loops" in the spirograph output. To specify a particular number of loops, just add 1 to the number of loops you want, and
set the theta to that number:
You can experiment with setting the number of render points for your calculations (Remember: the calculation will be executed in the low-priority queue, to setting a very high number of render points
will slow down your output). You might want to experiment with the relationship between the theta values and a lower number of plotting points.
While we've used the terms "Small Ring Radius" and "Big Ring Radius," they're actually independent values - explore reversing the parameter values, or using the same value for both radii:
You could also modify your patch to set up two separate drawing passes (i.e. two js spiro.js sets of calculations) drawn to the same jit.lcd object with different color pens....
You get the idea. Have some fun! Next time out, we're going to investigate implementing a Spirograph using OpenGL, and add a third dimension to our visuals. See you then!
by Darwin Grosse on December 1, 2021 | {"url":"https://cycling74.com/tutorials/rainysnowy-day-max-spirographics","timestamp":"2024-11-02T02:34:51Z","content_type":"text/html","content_length":"227676","record_id":"<urn:uuid:c1a1ebc8-2330-4970-851c-10149359e424>","cc-path":"CC-MAIN-2024-46/segments/1730477027632.4/warc/CC-MAIN-20241102010035-20241102040035-00732.warc.gz"} |
Guide to Essential Biostatistics XIX: Linear regression (PROBIT)
Probit (“probability unit”) models were developed by American biologist and statistician Chester Bliss in 1934, as a method to evaluate dose response in pesticide data.
Probit allows researchers to convert mortality (effect) percentages to probit values, which approximate a straight line function between the logarithm of the dose and effect, and which can be
analyzed by simple linear regression methods.
Probit is thus the transformation of the sigmoid dose-response curve to a straight line.
The Probit model was further adapted and tabulated at Rothamsted by British statisticians D. J. Finney and W. L. Stevens in 1948 to avoid having to work with negative probits in an era before the
ready availability of electronic computing.
It is these Probit tables that even today ensure that dose-response fitting to evaluate dose-response relationships may be conveniently performed when statistical software packages are not available,
and experimenters do not have a background in mathematics.
Probit analysis may be conducted using tables to determine the probits and fitting the relationship by eye or through linear regression, or by using a statistical package.
The process for evaluating dose-response relationships through the Probit analysis by hand, or by using a spreadsheet, are outlined in the following:
▶︎ Step 1: log transform the doses.
▶︎ Step 2: Convert % response to probits (short for probability unit).
Probits are generally calculated in the range where the sigmoidal response increases linearly i.e. from approximately 10-20% to 80-90% of maxima and should ideally contain three points within this
linear phase.
If control (untreated) response is more than 10%, Schneider-Orelli’s correction (see previous chapter) may be used.
Probits for a given percentage effect may be determined using Finney’s table:
Figure 1: Finney’s table for the transformation of response percentages to probits.
In our example, for a 25% response the corresponding probit is 4.33, for 58% effect probit=5.20 and for 88% effect probit=6.18:
Figure 2: Dose-response data table, log-transformed doses and transformation of response percentages to probits.
▶︎ Step 3: Graph the probits versus the log of the concentrations and perform a linear regression, by hand or using a spreadsheet (Figure 3).
▶︎ Step 4: Determine the ED50.
In our example, using values from a herbicide dose-response curve, the ED50 value may be fitted by eye as logED50= 1.36 from which the dose may be determined as ED50= 10^1.36= 22.91g ai/Ha:
Figure 3: Linear fit of dose-response data, probits versus the log of the concentrations: visual estimation of ED50.
Alternatively, if the linear function has been calculated (in our example as y= 1.85x + 2.48) the ED50 may be calculated as:
…where 2.48 is the intercept (at x=0) and 1.85 is the slope. The Probit value is 5 for ED50 (in Finney’s table, Figure 1, for a 50% response (ED50) the corresponding probit is 5):
Figure 4: Linear fit of dose-response data, probits versus the log of the concentrations: calculation of ED50.
In our example, logED50= 1.364 from which the dose may be determined as ED50= 10^1.364= 23.146g ai/Ha.
An alternative method of calculating Effective Dose levels (EDx) is Logit, which can be performed through a similar process to that described for Probit.
The key difference between logit and probit models lies in the assumption of the distribution of the errors, where for probit the errors are assumed to follow a Normal distribution. In practice, both
generally lead to the same conclusions and both are thus considered appropriate.
In our example, for both non-linear (sigmoidal) regression (see previous chapter) and linear (Probit) regression, both ED50 values are almost equal, and visual estimates were relatively accurate. For
data with more scatter around the regression line, visual determination of ED50 becomes less precise.
As for non-linear regression, a further advantage of using statistical packages is that the goodness-of-fit of the data to the regression curve can be quantified.
Are you a student, researcher or science leader looking for an overview of the essential principles of Biostatistics?
Guide To Essential Biostatistics is an easily accessible primer for scientists and research workers not trained in mathematical theory, but who have previously followed a course in Biological
This book provides a readily accessible overview on how to plan, implement and analyse experiments without access to a dedicated staff of statisticians.
Guide To Essential Biostatistics contains few calculations (the “how” of Biostatistics) but instead provides a plain-English overview of the “why” – what is it the numbers are telling us, and how can
we use this to plan trials, understand our data and make decisions.
Designed to fit in a lab coat pocket for easy access, Guide To Essential Biostatistics compiles some of the most-used biostatistical techniques, approximations and rules-of-thumb used in the design
and analysis of biological experiments.
Buy this book to obtain an overview of essential aspects of Biostatistics! By purchasing the print edition of this book on AMAZON, you are eligible for a FREE download of the eBook version, providing
access to high-resolution, zoomable color images.
A little about myself
I am a Plant Scientist with a background in Molecular Plant Biology and Crop Protection.
20 years ago, I worked at Copenhagen University and the University of Adelaide on plant responses to biotic and abiotic stress in crops.
At that time, biology-based crop protection strategies had not taken off commercially, so I transitioned to conventional (chemical) crop protection R&D at Cheminova, later FMC.
During this period, public opinion, as well as increasing regulatory requirements, gradually closed the door of opportunity for conventional crop protection strategies, while the biological crop
protection technology I had contributed to earlier began to reach commercial viability.
I am available to provide independent Strategic R&D Management as well as Scientific Development and Regulatory support to AgChem & BioScience organizations developing science-based products.
For more information, visit BIOSCIENCE SOLUTIONS – Strategic R&D Management Consultancy.
This site uses Akismet to reduce spam. Learn how your comment data is processed. | {"url":"https://biocomm.eu/2019/04/03/guide-to-essential-biostatistics-i-the-scientific-method-probit/","timestamp":"2024-11-14T12:19:42Z","content_type":"text/html","content_length":"64856","record_id":"<urn:uuid:14ab4ddb-dbc7-4973-b833-03095c6de585>","cc-path":"CC-MAIN-2024-46/segments/1730477028558.0/warc/CC-MAIN-20241114094851-20241114124851-00402.warc.gz"} |
SSC Higher Math Assignment 2021 Answer - Jagobahe
SSC Higher Math Assignment 2021 Answer
SSC Higher Math Assignment 2021 Answer
SSC Higher math 2021 assignment question publish on the website of dshe.gov.bd. So, we collect the assignment question from them and going to publish on our website. Even though, we are not going to
publish ssc higher math assignment question only. We also publish ssc higher math assignment 2021 solution on our website. So if you are a students of SSC Higher math and looking for ssc higher math
assignment solution pdf just continue reading the whole article till last.
So, you already get inform about your ssc higher math assignment solution. In this post we’ll write about SSC Ucchotor Gonit Assignment answer. Alongside all ssc higher math all week question and
answer, we’ll also discuss about every details on SSC higher Math Assignment. Now without waste your time anywhere in the internet just start reading the Article.
Biology All Week SSC Assignment Answer 2021
Physics All Week SSC Assignment Answer 2021
Chemistry All Week SSC Assignment Answer 2021
SSC Higher Math Assignment 2021 5th Week Question
SSC Higher Math Assignment 2021 5th Week Answer
SSC Higher Math Assignment 2021 4th Week Question
SSC Higher Math 4th week assignment is already publish on our website. This is the 4th week assignment for exam 2021. But the important information is that this is the SSC Higher Math Assignment 2
no. Because there is not assignment on 2nd week for Higher Math. So, now we’ll discuss about the Higher Math 4th week assignment question 21.
Now we can see the question from the below image. You can also download the image from the link. Now talk about the 4th week higher math question 2021. The higher math question is for SSC 21 is স্থানাঙ্ক
জ্যামিতির মধ্যে সরল রেখা সংক্রান্ত সমস্যা সমাধান. So, this is the practical relation assignment work. Follow below for assignment answer.
Download SSC Higher Math Assignment 2021 4th Week Question
SSC Higher Math Assignment 2021 4th Week Answer
So the question is স্থানাঙ্ক জ্যামিতির মধ্যে সরল রেখা সংক্রান্ত সমস্যা সমাধান. As you can see from the question that this is the question from the 11th chapter from the Higher Math Text Book. So, Open your book. See
some example as like this higher math assignment question of 2021. Then start solving the assignment from beginning.
For your Help, we already made a question solution from the ssc math assignment question 21. You just need to download the whole question paper. See all the instruction and start download the answer
from the below. After writing check the whole assignment answer 2021. That’s it.
Download SSC Higher Math Assignment 21 4th Week Answer
SSC Higher Math Assignment 2021 2nd Week Question
Due to corona virus, school and college are remain closed. So, students are getting bored and they are loosing their academic year. So, ministry of education publish the assignment system of SSC
class. So, they publish 2nd week Higher Math Assignment question on their website. In this post we are going to publish all the update about SSC Higher Math 2nd week assignment
From this question we can easily see the SSC Higher Math SSC Assignment Question for 2nd week. This is actually a question of geometry. So, open your SSC Higher Math 11th chapter and check the
examples of the question. In below check for whole details.
Download SSC Higher Math Assignment 2021 1st Week Question
SSC Higher Math Assignment 2021 2nd Week Answer
So, we can see that, this is the SSC Math assignment question for the SSC Exam 21. Now in this section we’ll make a higher math question solution for 2nd week. Though this is the 2nd week assignment.
But this is the higher math assignment first. So, carefully answer all the question.
In the section below we already attach the higher math assignment 1. We already make the solution from the higher math text book. So, you can easily download this question from the link below. Then
write the assignment to your assignment paper.
Leave a Comment | {"url":"https://jagobahe.com/ssc-higher-math-assignment-2021-answer","timestamp":"2024-11-03T12:10:18Z","content_type":"text/html","content_length":"130264","record_id":"<urn:uuid:b30b7ca0-0e19-42f4-a60d-97e0f8de0d59>","cc-path":"CC-MAIN-2024-46/segments/1730477027776.9/warc/CC-MAIN-20241103114942-20241103144942-00636.warc.gz"} |
UChicago Instructional Physics Laboratories
Table of Contents
Faraday's Law and Measuring Earth's Magnetic Field
This lab is devoted to understanding how to use the concept of magnetic induction to design and test a method of measuring the ambient magnetic field in the lab (which will be pretty close to the
value of the Earth's magnetic field in Chicago).
You will use Faraday's Law to measure the induced emf ($\epsilon$) in a coil of wire. Part of the lab is ensuring you know how to use the apparatus at your disposal to create a magnetic field of
known value and then measure that known field using Faraday's Law. This exercise will give you the knowledge you need to devise a way of using a coil of wire to measure the horizontal and vertical
components of the ambient field in the lab. Once you have a plan for measuring the ambient field, you will verify your technique by again creating a magnetic field of known value and measuring it in
the same manner as you plan to use for the ambient field measurement. Once you have established that your technique is sound and produces the results you expect, then you will proceed to make the
final measurement of the ambient field.
Pedagogically speaking, measuring the ambient field is not the point of the lab. It is the end point of the experimental task you have been given. But what we are teaching you is how to figure out
for yourself how to use your physics knowledge (i.e. Faraday's Law) and common lab apparatus to design, test and execute an experiment without being told explicitly what to do every step of the way.
Said another way, we are teaching how to do physics.
Induced Current In A Loop
Ampere's Law can be used to show that passing an electrical current ($I$) through a loop of wire with radius $R$ produces a magnetic field ($\vec B $) given by,
$\vec B = \frac{\mu_{o} I}{2R}$
where $\mu_{o} = 4\pi \times 10^{-7} Tm/A$.
This seemingly simple phenomena can be found in a wide range of applications ranging from production and detection of magnetic fields, to the wireless chargers now available for charging you phone.
Faraday's Law shows how a time varying magnetic flux ($\Phi$) induces an electro magnetic force ($\epsilon$) in $N$ loops of wire as,
$\epsilon = -N \frac{d\Phi}{dt}$
where $\Phi = \int B \cdot dA$.
This photo shows what the apparatus at your station looks like and what your station should look like at the end of lab.
You have the following equipment at your disposal.
• A DC power supply.
• A Heath Coil.
• An iOLab device and computer loaded with the software to use the iOLab to collect data.
• An approximately 20cm to 30cm length of wire.
IOlab Magnetic Sensor Location
It may be useful to know the precise location of the magnetometer in the iOLab device. The image below gives that information.
If you took the PHYS141 labs last quarter you are already familiar with the iOLab device and software. If you need a refresher here is a link to the iOLab device introduction page.
In addition there are various ring stands, rods, clamps, spools of wire and string, tape, rulers, etc in the room which you can make use of.
Here is the link to the Google Doc for this lab.
Two Ways To Measure B
Let us now consider how to use magnetic induction in a wire loop as part of an experiment to measure the strength of the horizontal and vertical components of the Earth's magnetic field here in
The Earth's $\vec B$ field is constant, at least on time scales relevant to this lab. According to Faraday's Law the induced $\epsilon$ is proportional to $\frac{d\Phi}{dt}$ where $\Phi = \int B \
cdot dA$. So if $\vec B$ is constant we need to find a way to vary the area $A$ of our loop in order to induce an $\epsilon$.
Here are some tips to get you started.
Not only does the iOLab have the differential input amplifier (inputs G- and G+) for reading the small induced $\epsilon$ from a wire loop, it also has built in three gyroscopes on three axes. Using
these two features along with the fact that the device uses wireless transmission to the computer opens up some interesting possibilities. The built in gyroscopes can be used to measure the
rotational motion of the body of the iOLab. If a coil of wire is wrapped around the body of the device, which is then spun with angular velocity $\omega$ around an axis orthogonal to the axis of the
magnetic field component you want to measure, the time dependent dot product of the magnetic field and area vectors becomes $\Phi = B A cos(\omega t)$. Differentiating Faraday's Law with respect to
time then yields $\epsilon = ωNBA sin(ωt)$. The peak emf $\epsilon_{peak}$ occurs when $sin(\omega t)$ = 1. Therefor if one can record the induced emf and the angular velocity of the coil about an
axis orthogonal to the normal vector of the area $\vec{A}$, $B$ can be found given Knowledge of $N$ and $A$.
Based on the above, one way to measure a constant magnetic field would be to rotate the wire loop while simultaneously measuring the induced $\epsilon$ and angular velocity $\omega$.
Another way to approach the problem is to rotate the iOLab in the $\vec B$ field between two known angles $\theta_{1}$ and $\theta_{2}$. If we rotate the coil from $\theta = 0^\circ$ to $theta = 180^
\circ$ integrating Faraday's law gives $ \int^{t_{2}}_{t_{1}} \epsilon dt = - \int{ \frac{d \phi}{dt}dt} = NBA( cos(\theta(t1)) - cos(\theta(t2))$. If we rotate the iOLab from $\theta (t1) = 0^\circ$
to $\theta (t2) = 180^\circ$ we get $ \int^{t_{2}}_{t_{1}} \epsilon dt = 2NAB$.
Using the above if you can record $\epsilon$ while rotating the coil between two known angular positions and then integrate $\epsilon$ you can get the magnitude of $\vec B$.
Now work out a plan for how you intend to measure both the horizontal and vertical components of the net magnetic field in the lab. The field in the lab should be close to that of the Earth's
magnetic field in Chicago, whose approximate value is given later in this wiki. You may have to use different techniques for each component of the field. In addition to the apparatus at your station,
you should feel free to use other items in the lab such as ring stands, clamps, additional wire, etc.
Once you have a plan in place for both measurements you need to test your planed technique using a magnetic field of known strength. Use the Heath coil to produce a constant magnetic field of known
strength. Use your planned technique(s) to measure the known field in order to verify that your plan will work, compare your measured field to the known value.
Measurement of Earth's Magnetic Field
Now that you are familiar with how magnetic fields can be created and detected by current carrying loops of wire, use this knowledge to come up with a technique for measuring the vertical and
horizontal components of the Earth's magnetic field using one or more loops of wire connected to the G- and G+ inputs on the IOlab.
In order to estimate the uncertainty in your measured values try to make use of more than one measurement technique for each component of the Earth's magnetic field as well as averaging multiple
The Earth's magnetic field in Chicago can be estimated using the NOAA Magnetic Field Calculator https://www.ngdc.noaa.gov/geomag/calculators/magcalc.shtml?#igrfwmm as shown in the screen shot below.
Assignment submission and grading
Make sure to submit your lab notebook by the end of the period. Download a copy of your notebook in PDF format and upload it to the appropriate spot on Canvas. Only one member of the group needs to
submit to Canvas, but make sure everyone's name is on the document!
Your individual summary and conclusions are due 48 hours after the end of the lab. | {"url":"http://physlab-wiki.com/phylabs/lab_courses/phys-140-wiki-home/winter-experiments/faradays-law-lab/start","timestamp":"2024-11-13T07:56:43Z","content_type":"text/html","content_length":"21899","record_id":"<urn:uuid:145d11cc-2d75-49dd-83c8-f35626f7f074>","cc-path":"CC-MAIN-2024-46/segments/1730477028342.51/warc/CC-MAIN-20241113071746-20241113101746-00078.warc.gz"} |
Radix sort–Punch card sorting
“The oldest algorithm ever invented. Simpler and very useful. Used in mechanical devices even. So this is even before computers are invented. Involves pure mathematics and works for any numeral
and text systems. The oldest method used to sort dictionaries”
See Also
This is one of the oldest method and some what easy to understand until you get the point clear. The main idea behind this sort is: if there is array of digits, if you sort array from the least
significant to most significant number, you finally get a sorted array.
Similarly, in a dictionary in which you sort the words lexicographically, Most significant character to least significant character sorting is done.. All these are Radix sorts.. It gives a good
performance benefit as well, i.e, around O(n).
This sort is not so important. But gives as an idea about why stable sorting is important in certain cases. Radix sort will not work out if the order of the elements is not maintained while putting
the elements at the sorted spot.
Radix sort supports all bases starting from 2.. But the algorithm we wrote and tested is only for base 10 for simplicity. We take each digit and sort the whole array around it.
For example,
On first sorting around the least significant digit, should yield,
Sort just the digits picked from 1’s place, 10’s place and 100th place. Even though intermediate steps looks like unsorted, You finally get a sorted array out of it. This is achieved just because the
order of elements in maintained through out the iterations.
The above example illustrates only an array of integers with equal number of digits. This will also work for integers sizes < 3. The best way to start radix sort is to find out the maximum value and
count the digits in it or to decide on the number of max digits.
Usually, in a mechanical punching card where this algorithm is used, they have static 12 digit number imprinted over it and sort starting from LSD to MSD.
Two kinds of radix sort is clearly visible now: LSD radix sort, MSD radix sort. MSD is mostly used for dictionary sort. We will discuss LSD sort in this article.
The simple algorithm is like this,
1. For 0 to number of digits
2. Sort the digits in a stable way in the main array
#define BASE 10
void counting_sort_radix(int*& arr, int k, int size)
int *B, *C;
C = (int*) malloc(sizeof(int)*BASE);
B = (int*) malloc(sizeof(int)*(size+1));
for(int i=0;i<BASE; i++) C[i] = 0;
// only the last digit need to be used
// for sorting
for(int i=0;i<size;i++){
int val = arr[i]/k;
int idx = val%BASE;
for(int i=1;i<BASE;i++) C[i] += C[i-1];
for(int j=size-1;j>=0;j--) {
int val = arr[j]/k;
int idx = val%BASE;
B[C[idx]] = arr[j];
for(int i=0; i<size; i++) arr[i] = B[i+1];
void radix_sort(int* arr, int d, int size)
//d = number of digits
// must calculate d from the max val in array
for(int i=0;i<d; i++) {
counting_sort_radix(arr, pow((float) BASE, (float) i), size);
void main()
int A[] = {329,457,657,89,46,720,355};
radix_sort(A, 3, 7);
Important points
• We have reused counting sort as the base sorting algorithm for our radix sort algorithm
• We go from 1st place to 100th place in above code.. it will run until 3 digits. So, input can only have max 3 digits
• BASE is only tested for 10. It can be base 2, base 8(octet), base 16(hex).
• We need to read different digit in different iterations. That’s why we have to modify the counting sort and get k=10^d as argument which is used to evaluate arr[j]/k and val%BASE. These two gives
you the exact digit at necessary place we are looking for
• The 10^d loop decides the place around which counting sort needs to be applied
• B[] as usual requires size+1 since we never get a zero digit count. So, we copy from B[1] –> A[0] to balance it.
• THE MOST IMPORTANT BUG FIX IN THIS CODE IS STABILITY!!.. The last loop which creates the B[] must run from length to 0 rather than running from 0 to length. If we run from 0 to length, we just
get all elements in reverse order instead of forward order.
• Why when we run from 0 to length, we get the order of elements in reverse ? Because cumulative sum is taken from front to back, denoting all the other elements go below that index from back to
front. So, we must go in reverse to get the correct order
• Without this stability condition, we will never get a sorted list from radix sort. Stability of the sorting used to sort digits is very important in radix sort method
• Any stable sorting method can be used to sort the digits, not just counting sort. | {"url":"http://analgorithmaday.blogspot.com/2011/03/radix-sortpunch-card-sorting.html","timestamp":"2024-11-04T23:32:14Z","content_type":"text/html","content_length":"93173","record_id":"<urn:uuid:1c10855a-45c1-4e62-b903-fec31752b255>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.84/warc/CC-MAIN-20241104225856-20241105015856-00887.warc.gz"} |
Math Contest Repository
CSMC 2021 Part A - Question 6, CEMC UWaterloo
(Canadian Senior Mathematics Contest 2021, Part A, Question 6, CEMC - UWaterloo)
In the diagram, $PABCD$ is a pyramid with square base $ABCD$ and with $PA = PB = PC = PD$. Suppose that $M$ is the midpoint of $PC$ and that $\angle BMD = 90^{\circ}$. Triangular-based pyramid $MBCD$
is removed by cutting along the triangle defined by the points $M$, $B$ and $D$. The volume of the remaining solid $PABMD$ is $288$. What is the length of $AB$?
Answer Submission Note(s)
Your answer should be of the form "x * sqrt(y)".
Please login or sign up to submit and check if your answer is correct.
flag Report Content
You should report content if:
• It may be offensive.
• There is something wrong with it (statement or difficulty value)
• It isn't original.
Thanks for keeping the Math Contest Repository a clean and safe environment! | {"url":"https://mathcontestrepository.pythonanywhere.com/problem/csmc21a6/","timestamp":"2024-11-04T05:12:55Z","content_type":"text/html","content_length":"10413","record_id":"<urn:uuid:22740c4c-e89b-4316-9e0a-f1e98023acc5>","cc-path":"CC-MAIN-2024-46/segments/1730477027812.67/warc/CC-MAIN-20241104034319-20241104064319-00788.warc.gz"} |
Mathematics Storm
By Susam Pal on 15 May 2011
From Freenode IRC #math channel this morning:
<oops> I have a confusion. the calculation that was giving
me 2 bits earlier is not giving me 2 bits now. :( please help.
<oops> 4 equally probable symbols: so 4 * (1/4) * log(1 / 1/4), right?
<antonfire> yeah math changes sometimes.
<antonfire> probably a math storm
<antonfire> wait a few minutes and try again
<_Ray_> try logging out and back in
<oops> so, so 1 * log(4) = 2
<oops> oh it is giving me 2 bits again
<mariano|syzygy> hmmm, actually he was not his advisor
<oops> thanks, nvm.
<sig^> try switching math off and on again
<thermoplyae> haha
<_Ray_> yeah, it was the router | {"url":"https://susam.net/mathematics-storm.html","timestamp":"2024-11-02T11:00:46Z","content_type":"text/html","content_length":"2305","record_id":"<urn:uuid:53600cd3-c2c3-4402-bee2-294b3374a747>","cc-path":"CC-MAIN-2024-46/segments/1730477027710.33/warc/CC-MAIN-20241102102832-20241102132832-00622.warc.gz"} |
class sherpa.data.Filter[source] [edit on github]
Bases: object
A class for representing filters of N-Dimensional datasets.
The filter does not know the size of the dataset or the values of the independent axes.
Attributes Summary
mask Mask array for dependent variable
Methods Summary
apply() Apply this filter to an array
notice(mins, maxes, axislist[, ignore, ...]) Select a range to notice or ignore (remove).
Attributes Documentation
Mask array for dependent variable
Return type:
bool or numpy.ndarray
Methods Documentation
apply(array: None) None[source] [edit on github]
apply(array: Sequence[float] | ndarray) ndarray
Apply this filter to an array
array (array_like or None) – Array to be filtered
Return type:
ndarray or None
sherpa.utils.err.DataErr – The filter has removed all elements or there is a mismatch between the mask and the array argument.
notice(mins: Sequence[float] | ndarray, maxes: Sequence[float] | ndarray, axislist: Sequence[Sequence[float] | ndarray], ignore: bool = False, integrated: bool = False) None[source] [edit on
Select a range to notice or ignore (remove).
The axislist argument is expected to be sent the independent axis of a Data object - so (x, ) for one-dimensional data, (xlo, xhi) for integrated one-dimensional data, (x0, x1) for
two-dimensional data, and (x0lo, x1lo, x0hi, x1hi) for integrated two-dimensinal data. The mins and maxes must then be set to match this ordering.
○ mins (sequence of values) – The minimum value of the valid range (elements may be None to indicate no lower bound). When not None, it is treated as an inclusive limit, so points >=
min are included.
○ maxes (sequence of values) – The maximum value of the valid range (elements may be None to indicate no upper bound). It is treated as an inclusive limit (points <= max) when
integrated is False, and an exclusive limit (points < max) when integrated is True.
○ axislist (sequence of arrays) – The axis to apply the range to. There must be the same number of elements in mins, maxes, and axislist. The number of elements of each element of
axislist must also agree (the cell values do not need to match).
○ ignore (bool, optional) – If True the range is to be ignored, otherwise it is included. The default is to include the range.
○ integrated (bool, optional) – Is the data integrated (we have low and high bin edges)? The default is False. When True it is expected that axislist contains a even number of rows,
where the odd values are the low edges and the even values the upper edges, and that the mins and maxes only ever contain a single value, given in (None, hi) and (lo, None) ordering.
Select points in xs which are in the range 1.5 <= x <= 4:
>>> f = Filter()
>>> f.mask
>>> xs = [1, 2, 3, 4, 5]
>>> f.notice([1.5], [4], (xs, ))
>>> f.mask
array([False, True, True, True, False])
Filter the data to select all points with x0 >= 1.5 and x1 <= 4:
>>> f = Filter()
>>> x0 = [1, 1.4, 1.6, 2, 3]
>>> x1 = [2, 2, 4, 4, 6]
>>> f.notice([1.5, None], [None, 4], (x0, x1))
>>> f.mask
array([False, False, True, True, False])
For integrated data sets the lower and upper edges should be sent separately with the max and min limits, along with setting the integrated flag. The following selects the bins that cover the
range 2 to 4 and 1.5 to 3.5:
>>> xlo = [1, 2, 3, 4, 5]
>>> xhi = [2, 3, 4, 5, 6]
>>> f = Filter()
>>> f.notice([None, 2], [4, None], (xlo, xhi), integrated=True)
>>> f.mask
array([False, True, True, False, False])
>>> f.notice([None, 1.5], [3.5, None], (xlo, xhi), integrated=True)
>>> f.mask
array([ True, True, True, False, False]) | {"url":"https://sherpa.readthedocs.io/en/latest/data/api/sherpa.data.Filter.html","timestamp":"2024-11-07T18:55:10Z","content_type":"text/html","content_length":"36038","record_id":"<urn:uuid:9a2ddba3-2ca1-42b0-8722-3db9b8c84963>","cc-path":"CC-MAIN-2024-46/segments/1730477028009.81/warc/CC-MAIN-20241107181317-20241107211317-00122.warc.gz"} |
Third mini-project: Edge-connectivity in graphs solved
I. MEASURES OF CONNECTIVITY A measure of the robustness of a network is the number of edges whose failure prevents network-wide communications. A network is modeled as a graph. The edge-connectivity
of a network is the minimum size of a set of edges the removal of which prevents the network from being connected. The edge-connectivity of a network is a global parameter. In order to compute the
edge-connectivity of a network, we may start by analyzing the edge-connectivity between pairs of nodes. Oftentimes, the edge-connectivity between pairs of nodes is interesting in its own right. A set
of edges separates a source node from a destination node if every path from the source to the destination contains at least one edge belonging the set. It is well-known that the minimum number of
edges that separates a source node from a destination node equals the maximum number of edge-disjoint paths from the source to the destination. A set of paths is edge-disjoint if the paths do not
share an edge. II. YOUR ASSIGNMENT What you have to do. • Design and implement an algorithm to compute the minimum number of edges that separates a source node from a destination node. The network is
given in a file where each line identifies an edge. The source and destination nodes are given online. You may assume that there are no more than 100 nodes with identifiers between 0 and 99. (50% of
the grade.) • Given a network in the format above, produce the complementary cumulative distribution of the minimum number of edges that separates one node from another. That is, for every natural
number k, compute the fraction of pairs of nodes such that more than k edges separates the first node from the second. (25% of the grade.) • Given a network in the format above, compute the
edge-connectivity of the network. In order to convince a user of your program that the value presented is the correct one, you should exhibit a set of edges that prevents the network from being
connected. (25% of the grade.) What do you have to deliver, how, and when. • You have to deliver your code and a report with a cover page and no more than three other pages containing a text
explanation of your algorithms, their pseudo-codes, their asymptotic complexities, the statistics required, and a short discussion. • The code and the report should be sent in a .zip file to my email
address with subject p3..zip where is your group number. 2 • The deadline is December 2, 2016, 23:59. How I will evaluate your assignment. • Write your report and your pseudo-code clearly, and
present a commented code. • Be sure to test your code for correctness. I will take into consideration the efficiency of your algorithms. • I will have a discussion with you about your report and will
test your code at the end of the semestre, jointly with the other assignments. | {"url":"https://codeshive.com/questions-and-answers/third-mini-project-edge-connectivity-in-graphs-solved/","timestamp":"2024-11-14T08:56:02Z","content_type":"text/html","content_length":"98868","record_id":"<urn:uuid:ca0116d9-7bd0-42a1-a0b8-bc039752bae8>","cc-path":"CC-MAIN-2024-46/segments/1730477028545.2/warc/CC-MAIN-20241114062951-20241114092951-00058.warc.gz"} |
How to Find the Empirical Formula - Understand with Examples
The simplest chemical representation that denotes the ratio of elemental atoms of a compound in the form of positive integers is called empirical formula. So how does one go about finding the
empirical formula? This ScienceStruck article will provide you with some easy steps for calculating this ratio, along with a few examples and practice problems.
Did You Know?
Formaldehyde, glucose, and acetic acid, all have the same empirical formula, i.e., CH2O, but varying molecular formulas and structures, and also belong to different classes of chemical compounds.
The concept of empirical formula in the field of chemistry is very useful in finding out the elemental ratios of compounds that are similar in composition. It can be used as a standard value when
several ionic compounds are compared regarding their atomic structure, chemical properties, and percentage of elemental composition. This formula does not signify any similarity between the
structures of two compounds which have the same atomic ratio. In other words, isomeric compounds (the ones having same molecular formula, but different atomic structure) are not studied under this
You can use the empirical formula calculator given below to get instant empirical formula results of different compounds.
Empirical Formula Calculator
The empirical formula is also useful in the field of physics on a limited scale, especially for forecasting effects or results from an equation that is developed beforehand. The wavelength values of
the Lyman series (transitional line denoting UV radiations) were predicted using the empirical ratios of the waves. Thus, the spectral lines of different chemical elements were found out using the
Rydberg formula, along with the Lyman series.
Steps for Calculation
Step 1
The empirical ratios of a compound can be calculated when the percentages of each of the elements that makes up the compound are known. For simplicity, the summation of all the percentages is equal
to 100. Equate the percentages of each component as the gram weight of that specific element (the total weight of the compound will be 100 grams).
Step 2
Divide each weight value with the atomic weight of the particular element. The atomic weights can be found by referring to a periodic table of the elements. This division gives us the value in moles
or molar mass of each component of the compound. Note down every reading and arrange them in the given manner: (X, Y, and Z).
Step 3
Note down the smallest value of the molar masses, and divide every molar amount with this value, including itself. This gives us the atomic ratio, which is represented in a particular linear form,
i.e., X:Y:Z. This mathematical entity is quite useful for comparing the quantity of every element in the compound, in the simplest manner.
Step 4
Multiply the ratio by a particular number in order to convert it into whole numbers. This is done so that if the ratio consists of a few fractions, then simplifying them is required for writing down
the empirical formula. The number can be decided only by the trial-and-error method, and rounding off the digits to the nearest whole number is required in some cases.
Step 5
After the multiplication, write down the empirical formula in the same linear form, (X2Y5Z7). This is the simplest way by which the compound can be written by denoting the least number of molecules.
The compounds X4Y10Z14 and X6Y15Z21 have the same empirical formula as mentioned above.
Example # 1
Let’s say a compound consists of 68.31% carbon, 8.78% hydrogen, and 22.91% oxygen. We need to find out the empirical formula of this compound. As the total percentage of the compound is equal to
hundred, write the elemental weights as being equal to the percentage values.
Thus, the gram weight of each component is:
Carbon (C) = 68.31 gm
Hydrogen (H) = 8.78 gm
Oxygen (O) = 22.91 gm
The atomic weights can be referred from a periodic table, and they are – C (12.01), H (1.008), and O (16). Divide the gram values by the atomic weights to get the molar masses.
C = 68.31÷12.01 = 5.68 mol
H = 8.78÷1.008 = 8.71 mol
O = 22.91÷16 = 1.43 mol
The smallest molar value is 1.43, that belongs to oxygen. Dividing every molar amount by this value will give us the atomic ratio. This is represented as:
C = 5.68÷1.43 = 3.97
H = 8.71÷1.43 = 6.09
O = 1.43÷1.43 = 1
The atomic ratio is written as C:H:O = 3.97:6.09:1. The amount of oxygen is the least in this compound. In most cases, this ratio needs to be multiplied by a number to give a series of whole number
ratio. But, as two fractions are present in the series that are very close to whole numbers, the ratio can be rounded off, i.e., C:H:O = 4:6:1. Thus, the empirical formula of the compound is written
Example # 2
A compound consists of 58.26% carbon, 6.52% hydrogen, 8.73% nitrogen, and 26.49% of oxygen. We need to find out the empirical formula of this compound, if the atomic weights of each component are
given. These weights are: carbon (12.01), hydrogen (1.008), nitrogen (14), and oxygen (16). The values in grams of each element are written as follows:
Carbon (C) = 58.26 gm
Hydrogen (H) = 6.52 gm
Nitrogen (N) = 8.73 gm
Oxygen (O) = 26.49 gm
Dividing these values by the respective atomic masses, the molar weights of the elements are written as follows:
C = 58.26÷12.01 = 4.85 mol
H = 6.52÷1.008 = 6.46 mol
N = 8.73÷14 = 0.62 mol
O = 26.49÷16 = 1.65 mol
The least molar mass is 0.62 moles of nitrogen. By diving all the masses by this value, the atomic ratio is represented as:
C = 4.85÷0.62 = 7.82 ~ 8
H = 6.46÷0.62 = 10.41 ~ 10
N = 0.62÷0.62 = 1
O = 1.65÷0.62 = 2.66 ~ 3
From the above values, the atomic ratio is represented as: C:H:N:O = 7.82:10.41:1:2.66. As most of the digits are fractions, they can be rounded off to the nearest whole number (if less fractions are
present in the ration, then they should be multiplied by an integer to get a whole number). This is denoted by the sign ‘~’ in the above representation.
Thus, after rounding off the values, the empirical formula of this compound is written in the following form:
Practice Problems
Solve the following problems in order to thoroughly understand the concept of finding out the empirical formula in analytical chemistry.
• Calculate the empirical formula of a compound that has the following components: 64% carbon, 8% hydrogen, and 28% oxygen by weight. The atomic weights are: C (12.01), H (1.008), and O (16).
• A compound forms due to the reaction of ammonia with phosphate, and consists of 30.2% nitrogen, 19.4% phosphorous, 8.5% hydrogen, and 41.9% oxygen. Calculate the empirical formula. Atomic mass
numbers are: phosphorous (31), hydrogen (1.008), nitrogen (14), and oxygen (16).
• Calculate the empirical formula of a compound that consists of 34.42 % sulfur, 30.35 % oxygen, and 35.23% fluorine. Atomic weights of sulfur and fluorine are 32.06 and 19, respectively.
• Calculate the empirical formula of a compound that consists of 22.70% potassium, 38.76% manganese, and 38.54% oxygen. Atomic mass numbers of potassium and manganese are 30.97 and 54.93,
• Citric acid consists of 33.51% C, 11.20% H, and 55.29% O. Determine the empirical formula of this acid solution.
Always remember to keep a periodic table with you whenever calculating empirical formula or any such chemistry-related problems, as you will find all the important aspects of the elements described
in the table. | {"url":"https://sciencestruck.com/how-to-find-empirical-formula-understand-with-examples","timestamp":"2024-11-08T07:47:21Z","content_type":"text/html","content_length":"168101","record_id":"<urn:uuid:ff2ed91b-7699-4889-a48c-aa36e02c5cc5>","cc-path":"CC-MAIN-2024-46/segments/1730477028032.87/warc/CC-MAIN-20241108070606-20241108100606-00038.warc.gz"} |
Using MathQuestionsforKids - Concepts for Kids
If You Read Nothing Else Today, Read This Report on Math Questions for Kids
You can aid your kids by stating the issue in a different way. Most likely, kids will learn something as a result of abundance of games accessible to cater to all types of characteristics. Teaching
math to 5 to 15 yrs old kids is something that you can do only if you’re certain you know what it is that you are doing. Just make sure that they are challenged. When both kids have the very same
weight and stationary, the plank is going to be level. Even young kids can answer the majority of the questions.
Sometimes kids can be extremely nasty to the students that are trying and working hard. Out of the numerous subjects in school that your children take, math has ever been among the subjects that most
students appear to seek out difficult and hate. Unfortunately, though most kids eventually learn how to read and do the math required to carry them through life, many don’t learn to choose the tests
that SHOW they’ve learned the reading and math.
Finding Math Questions for Kids Online
Children first have to develop their brains in order to do mathematical computations independently. After doing the evaluation to figure out where your child ranks with respect to math, you must
learn specifically what type of problems they face. Instead of sitting down with a worksheet or textbook, he or she can use your home computer to enter an interactive learning environment that
provides the tools they need to grasp basic math concepts. Children should know their teacher cares about them and isn’t just attempting to give them lots of hard work. They will think that they are
playing a game, but in reality are actually learning math. For parents who need to assist their children who struggle in math or for people who need to guarantee success for their children in math
later on, there’s a manner.
The Start of Math Questions for Kids
Every parents dream of ensuring their kid is ready for the future. Fortunately, many parents accompany their elementary kids with their homework to figure out where the challenge is precisely. They
can assist with developing a lot of the fundamental skills needed for children to succeed in math when they attend school. They should make sure the elementary math teacher is knowledgeable and is a
good teacher. Parents that are positively involved with their kids and want the very best for them will make certain their children are keeping up with their math abilities and are successful in
The Do’s and Don’ts of Math Questions for Kids
To learn math students will need to take part in discovery learning. If you’ve never had your students take part in a math contest like this, you’ll be astonished at the enthusiasm it can generate.
It might be possible for some students not to find the response in the very first, second, or even the third effort.
If you wish to succeed at math, you must quit focussing only on the content and begin focusing on your learning strategy. Vedic math isn’t nearly solving the fundamental calculations as with Vedic
math an individual may also be in a position to address complex geometrical theorems, calculus sums and algebraic difficulties. Math is just one type of intelligence. Math is a rather intriguing
subject. Math is a tough subject for a lot of people. Bedtime Math also has a completely free app with the exact same daily math difficulties. As stated on their site, Bedtime Math is to aid kids
love math how they love playtime or dessert.
You may try out breaking the issue into simpler parts. Other than this, it’s important to comprehend the steps involved with solving a Math problem. Standard math word problems are just a combo of
specific language tricks and easy calculations.
The questions meant for adults may not suit kids. Then Twenty Questions” may be precisely the distraction you’re looking for. They tend to contain all the information we need to solve the problem. So
let’s jot down a few really hard questions and boost our general understanding. Beware this game will also ask you to prepare a whole lot of questions beforehand. If you believe this isn’t enough,
then don’t hesitate to post some more hard questions in the box.
Want to Know More About Math Questions for Kids?
Questions are almost always interesting to ask especially once you know the reply. Next step is to read the full question again and analyze all the appropriate information which can aid you in
solving the issue. However tricky and hard the questions are, folks try their very best to get to the conclusion of the maze. Likewise a question that’s actually meant for kids will hardly increase
the excitement of a game involving adults. | {"url":"https://conceptsforkids.us/2017/12/29/using-mathquestionsforkids/","timestamp":"2024-11-07T05:41:35Z","content_type":"text/html","content_length":"141662","record_id":"<urn:uuid:69f7563a-7f84-4e67-a52c-f1428e5984e8>","cc-path":"CC-MAIN-2024-46/segments/1730477027957.23/warc/CC-MAIN-20241107052447-20241107082447-00798.warc.gz"} |
Density Determination
Marcea Anderson Thornton Township High School
150th & Broadway Ave.
Harvey, Il. 60426
(for jr. or sr. high school)
Purpose is to learn and practice techniques and calculations for determining
volume and density of a substance.
Apparatus Needed:
Double pan balance, can of coke, can of diet coke, two evaporating dishes,
sugar. (demo.)
Density vial. (demo.)
Recommended strategy:
Start by having a density vial sitting on the front desk for the students
to look at when entering the classroom. There are several kinds of denisty vials
that you can make for the classroom. A density vial uses several different
solutions and objects in one container, each having a different density they
will sink to their own level. Start with a plastic liter bottle or jar or a
large graduated cylinder. Pour in small amounts of the liquid solutions first
in the following order: syrup (1.36 g/cc), glycerine (1.26 g/cc), ethylene
glycol (1.11 g/cc), colored water (1.0 g/cc), oil (.9 g/cc),colored alcohol (.79
g/cc). Now, slide in the solid objects, they will sink to their level of
density within the solutions: lead piece (11.3 g/cc), rubber stopper (1.2
g/cc), plastic piece (.9 g/cc), oak (.9 g/cc), cork .2 (g/cc).
Give the students time to look carefully at the vial to notice the
different levels of the solutions and the objects placed in the vial. Ask the
students questions about the vial. "What do you see in the vial? Why is the
cork floating near the top and the copper piece is near the bottom?" Continue
asking questions until the students come to some conclusion that the solutions
and objects have different densities. You may change this lesson some what by
making the density vial as a demonstration. At this point, set the density vial
off to the side and tell the students that we will come back to this later in
the class period.
Bring out your double pan balance and soda cans. Ask the students about
the mass and volume of the two sodas. Then place the two cans on the balance,
the regular coke should be heavier. Ask the students why the regular coke is
heavier. Ask them what is in the coke that is not in the diet coke. (Hint:
nutrisweet is 200 times sweeter than sugar, so they only use a small amount of
it in diet coke.) Coke has a very sweet taste to it because of all of the sugar
added to it. Then ask the students ways to determine how much sugar is in coke
that is not in diet coke. Hopefully, the students will tell you to put sugar on
top of the diet coke can. You can do this by placing an evaporating dish on top
of each can, then add sugar to the dish on the diet coke can until the two cans
are balanced, this will give you equal mass of the two cans. Ask the students
questions about the soda cans. "What happened to the mass of each can? What
happened to the volume of the two cans? What do you suppose that this can of
each variable is telling us?"
At this point in the lesson, it will be necessary to explain the concept of
density. Talk about the variables in density and the formula for solving for
density. Go back to the denisty vial. Once again ask the students questions
about the vial, this time relating them towards the denisty of the various
solutions and objects. Your "recipe" for the density vial should list the
various densities of the solutions and objects to be used.
Return to Chemistry Index | {"url":"https://smileprogram.info/ch9001.html","timestamp":"2024-11-14T18:28:22Z","content_type":"text/html","content_length":"4248","record_id":"<urn:uuid:3e9a80a2-0de2-4622-b89c-0ac4103360ee>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00273.warc.gz"} |
[QSMS Seminar 2022-12-2] N=2 supersymmetric W algebras from Hamiltonian reduction
• Date : 2022-12-2 (Fri), 15:00 ~ 16:00
• Place : 127-116 (SNU)
• Speaker : Eric Ragoucy (LAPTh, CNRS)
• TiTle : N=2 supersymmetric W algebras from Hamiltonian reduction
• Abstract :
I will review the formalism of classical Dirac brackets in the context of W algebras and superalgebras. Dirac brackets allow to deal with a Poisson bracket when constraints are imposed in the phase
space. In the context of Wess-Zumino models, this amounts to consider an Hamiltonian reduction of the model, leading to Toda models and W algebras. When considering a special class of Lie
superalgebras, it leads to supersymmetric W algebras. In that case, one can introduce a super-field formalism to make the N=1 supersymmetry manifest. For a sub-class of these Lie superalgebras, it
leads to N=2 supersymmetric W algebras. I will present these different cases, the last case opening the possibility of a procedure dealing with N=2 super-fields. | {"url":"https://qsms.math.snu.ac.kr/index.php?mid=board_sjXR83&order_type=asc&page=3&l=ko&sort_index=title&document_srl=2395","timestamp":"2024-11-07T20:33:08Z","content_type":"text/html","content_length":"66459","record_id":"<urn:uuid:9120a52e-7c71-45ef-968f-862dabe639da>","cc-path":"CC-MAIN-2024-46/segments/1730477028009.81/warc/CC-MAIN-20241107181317-20241107211317-00373.warc.gz"} |
The parameters under Plane defines the power plane pair characteristics.This is simulated using the two parameters CAP and ESR. Capacitance and DC resistance. Enter CAP in micro Farad (uF) and ESR in
To determine the right values to use for CAP and ESR, the best thing obviously is measurements. The next best thing is some simple formulas.
Capacitance (CAP)
The capacitance of a parallel plate capacitor of area A and with a distance between the plates of d is given by this formula.
$C=\epsilon_0 \epsilon_r \cfrac{A}{d}$
$\epsilon_0$is 8.85418782E-12 F/m (the permittivity in vacuum)
$\epsilon_r$is the relative permittivity or dielectric constant (often called DK or Dk) of the PCB material
Prepreg Dk um 50×100 mm 100×100 mm 100×200 mm 200×200 mm
106 4.0 50 3.6 nF 7.3 nF 14.5 nF 29 nF
1080 4.2 63 2.9 nF 5.8 nF 11.5 nF 23 nF
2125 4.3 100 1.8 nF 3.6 nF 7.3 nF 14.5 nF
2116 4.4 125 1.5 nF 2.9 nF 5.8 nF 11.6 nF
Conversion help: 1nF = 0.001uF, 25.4 mm = 1″ and 25.4um = 1 mil
Note the dielectric constant is not really a constant, as it varies with frequency, temperature and other parameters. This is illustrated by the below example graph. You should find the values in the
datasheet for the actual material used.
Equivalent Series Resistance (ESR)
Can often be set to 0 ohm.
3 thoughts on “Plane”
1. Rolf,
For your PDN Tool it would be nice if you could include a plane to plane capacitor calculator.
Examples online include:
best regards,
Randy Clemmons CID+
2. An observation: The more plane capacitance, the lower the plane resonance frequency. This leads me to think, that if we can reduce capacitance (eg. by reducing plane area) while keeping ESL low
(short via length, optimal footprints), we’ll get the best results. What are your thoughts on this, Rolf?
□ In some way right, but you also have a minimum amount of charge needed for the ICs at every switching event. This charge will (initially) have to come from the on-die/package and PCB plane
capacitance. This sets the minimum plane capacitance required.
Please Add Your Ideas and Suggestions | {"url":"https://www.pdntool.com/faq/plane","timestamp":"2024-11-06T19:51:45Z","content_type":"text/html","content_length":"52416","record_id":"<urn:uuid:550feae0-d496-4e8c-aee4-a7e6aabc9938>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.47/warc/CC-MAIN-20241106194801-20241106224801-00822.warc.gz"} |
class menpo.model.LinearVectorModel(components)[source]¶
Bases: Copyable
A Linear Model contains a matrix of vector components, each component vector being made up of features.
components ((n_components, n_features) ndarray) – The components array.
A particular component of the model.
index (int) – The component that is to be returned.
component_vector ((n_features,) ndarray) – The component vector.
Generate an efficient copy of this object.
Note that Numpy arrays and other Copyable objects on self will be deeply copied. Dictionaries and sets will be shallow copied, and everything else will be assigned (no copy will be made).
Classes that store state other than numpy arrays and immutable types should overwrite this method to ensure all state is copied.
type(self) – A copy of this object
Creates a new vector instance of the model by weighting together the components.
weights ((n_weights,) ndarray or list) –
The weightings for the first n_weights components that should be used.
weights[j] is the linear contribution of the j’th principal component to the instance vector.
vector ((n_features,) ndarray) – The instance vector for the weighting provided.
Creates new vectorized instances of the model using all the components of the linear model.
weights ((n_vectors, n_weights) ndarray or list of lists) –
The weightings for all components of the linear model. All components will be used to produce the instance.
weights[i, j] is the linear contribution of the j’th principal component to the i’th instance vector produced.
ValueError – If n_weights > n_available_components
vectors ((n_vectors, n_features) ndarray) – The instance vectors for the weighting provided.
Enforces that the union of this model’s components and another are both mutually orthonormal.
Both models keep its number of components unchanged or else a value error is raised.
linear_model (LinearVectorModel) – A second linear model to orthonormalize this against.
ValueError – The number of features must be greater or equal than the sum of the number of components in both linear models ({} < {})
Enforces that this model’s components are orthonormalized, s.t. component_vector(i).dot(component_vector(j) = dirac_delta.
Projects the vector onto the model, retrieving the optimal linear reconstruction weights.
vector ((n_features,) ndarray) – A vectorized novel instance.
weights ((n_components,) ndarray) – A vector of optimal linear weights.
Returns a version of vector where all the basis of the model have been projected out.
vector ((n_features,) ndarray) – A novel vector.
projected_out ((n_features,) ndarray) – A copy of vector with all basis of the model projected out.
Returns a version of vectors where all the basis of the model have been projected out.
vectors ((n_vectors, n_features) ndarray) – A matrix of novel vectors.
projected_out ((n_vectors, n_features) ndarray) – A copy of vectors with all basis of the model projected out.
Projects each of the vectors onto the model, retrieving the optimal linear reconstruction weights for each instance.
vectors ((n_samples, n_features) ndarray) – Array of vectorized novel instances.
weights ((n_samples, n_components) ndarray) – The matrix of optimal linear weights.
Project a vector onto the linear space and rebuild from the weights found.
vector ((n_features, ) ndarray) – A vectorized novel instance to project.
reconstructed ((n_features,) ndarray) – The reconstructed vector.
Projects the vectors onto the linear space and rebuilds vectors from the weights found.
vectors ((n_vectors, n_features) ndarray) – A set of vectors to project.
reconstructed ((n_vectors, n_features) ndarray) – The reconstructed vectors.
property components¶
The components matrix of the linear model.
(n_available_components, n_features) ndarray
property n_components¶
The number of bases of the model.
property n_features¶
The number of elements in each linear component. | {"url":"http://docs.menpo.org/en/stable/api/model/LinearVectorModel.html","timestamp":"2024-11-14T23:40:35Z","content_type":"text/html","content_length":"28993","record_id":"<urn:uuid:43ece4f0-7310-4133-a6d1-03485de6f42b>","cc-path":"CC-MAIN-2024-46/segments/1730477397531.96/warc/CC-MAIN-20241114225955-20241115015955-00207.warc.gz"} |
Multiple Choice Normalization in LM Evaluation
Let $x_{0:m}$ be the prompt, and $x_{m:n_i}$ be the $i$th possible continuation with a token length of $n_i - m$. There are several ways to use a language model to rank multiple possible
continuations to a prompt. Since the language model only gives (log) probabilities for the next token given the context (i.e $\log \mathbb P(x_i|x_{0:i})$), there is ambiguity in handling scoring for
arbitrary continuations. The following are several possible ways to resolve this problem:
• Unnormalized: The score of continuation $i$ is determined using $\sum_{j=m}^{n_i - 1} \log \mathbb P(x_j|x_{0:j})$. Intuitively, this is the probability of a generation sampled from the prompt
containing the continuation in question. While this is the simplest method, problems arise when there are significant differences in length between different continuations, as longer
continuations tend to have lower log probabilities, thus biasing the language model towards picking shorter continuations. This approach is used by eval harness in all multiple choice tasks and
presented as acc.
• Token-length normalized: The score of continuation $i$ is determined using $\sum_{j=m}^{n_i - 1} \log \mathbb P(x_j|x_{0:j}) / (n_i - m)$. This approach attempts to normalize for length by
computing average log probability per token; however, this approach is not tokenization agnostic, and as such two models with different tokenization that assign the same log likelihood to every
single input string will have different token-length normalized scores. This approach is used by GPT-3 in most tasks. Eval harness does not report this score because it violates the design
principle that all tasks should be tokenization independent.
• Byte-length normalized: The score of continuation $i$ is determined using $\sum_{j=m}^{n_i - 1} \log \mathbb P(x_j|x_{0:j}) / \sum_{j=m}^{n_i - 1} L_{x_j}$, where $L_{x_j}$ is the number of bytes
represented by the token $x_j$. This approach attempts to normalize for length by computing average log probability per character, which ensures that it is tokenization agnostic. This approach is
also used by eval harness in all multiple choice tasks and presented as acc_norm.
• Unconditional likelihood normalized: The score of continuation $i$ is determined using $\sum_{j=m}^{n_i - 1} \log \mathbb P(x_j|x_{0:j}) - \log \mathbb P(x_j)$. Intuitively, this approach
measures the amount that the prompt increases the model's probability of outputting each continuation from the probability of the model unconditionally producing that continuation. This approach
is used by GPT-3 in select tasks (ARC, OpenBookQA, and RACE), though no justification for why only these tasks in particular use this method is provided other than that this improves performance.
The unnormalized, token-length normalized, and byte-length normalized metrics can be computed without additional LM calls. The unconditional likelihood normalized metric requires an additional LM
call to obtain the unconditional likelihood. | {"url":"https://blog.eleuther.ai/multiple-choice-normalization/","timestamp":"2024-11-07T16:58:44Z","content_type":"application/xhtml+xml","content_length":"12698","record_id":"<urn:uuid:7199814d-cbec-4b99-85f9-2ee879c6eaac>","cc-path":"CC-MAIN-2024-46/segments/1730477028000.52/warc/CC-MAIN-20241107150153-20241107180153-00462.warc.gz"} |
Pascal's Triangle
Pascal's triangle is a triangular array of counting numbers. It begins with a first line of 1. The elements of subsequent rows are found by adding the two elements diagonally above in the preceding
row (e.g., 10 is the sum of the 4 and 6 above it). The outermost elements of each row are always 1, because there is no second number above to contribute to the sum.
There are many ways to derive the values in the triangle. See Ask Dr. Math: FAQ: Pascal's Triangle for a discussion of the triangle and several methods for generating it. See the links from that page
to learn more about Pascal's Triangle. Also look at Ladja's Report on Pascal's Triangle and Algebra Through Problem Solving, Chapter 1: The Pascal Triangle.
For help generating pictures of the remainder patterns see: | {"url":"https://www2.edc.org/makingmath/mathtools/pascal/pascal.asp","timestamp":"2024-11-01T18:44:25Z","content_type":"text/html","content_length":"11234","record_id":"<urn:uuid:112f5186-6131-4876-8350-3d5cd1a14678>","cc-path":"CC-MAIN-2024-46/segments/1730477027552.27/warc/CC-MAIN-20241101184224-20241101214224-00463.warc.gz"} |
Numbers in Scientific Notation – Explanation & Examples
Scientists perform calculations involving large or very small numbers by using scientific notations. What are then scientific notations? Why and how do we use it. How is scientific notation done?
Well, this article is going to discuss and answer these questions in detail.
What is Scientific Notation?
To start with, scientific notation is a form of expressing very small or large numbers in a simpler form. It is sometimes referred to as standard index form.
The general representation of scientific notation is: a x 10^b where 1 ≤ a < 10 and b can be any integer. The number b is known as the order of magnitude while the number a is referred to as the
mantissa or significand. The number a is the coefficient of the scientific notation and is normally greater than or equal to 1 and less than 10.
How to do Scientific Notation?
To write a number in scientific notation, the following steps are followed:
• If the given number is greater or equals to 10, the decimal point is moved to the left of the number and so, the power of 10 becomes positive. For example, 6000 in scientific notation is 6 × 10^3
• When the scientific notation of any large numbers is expressed, then we use positive exponents for base 10. For example:
20000 = 2 x 10^5, where 5 is the positive exponent
• If the given number is less than 1, the decimal point is moved to the right, and so the power of 10 becomes negative. For example, 0.006 in scientific notation is 6 × 0.001 = 6 × 10^-3
• When expressing small numbers in scientific notation, we use negative exponents for the base of 10. For example, 0.00002 = 2 x 10^-5, where -5 is the negative exponent.
Example 1
Convert 0.000000046 into scientific notation.
• The number is less than 1, therefore the decimal point is moved to the right up to 8 places
• The decimal point is moved 8 steps to form 4.6 because, the number 4.6 is greater than 1 and less than 10.
• The power of base 10 will be a negative exponent since we moved to the right.
• Therefore, the scientific notation of 0.00000046 ⇒6 × 10^-7
Example 2
Convert 4000000000 in scientific notation.
• 4000000000 is more 10, therefore, move the decimal point to the left 9 places.
• All the zeros are removed and the number multiplied by 10 raised to 9
• Now the number becomes 4 x 10^9
• In this case a positive exponent is used because the decimal point I moved to the left.
• Hence, 4 × 10^9 is the scientific notation of the number.
Example 3
Convert 4.306 × 10^7 to standard notation.
• Already 4.306 × 10^7is in scientific notation, so to change it to standard notation;
• Multiply 4.306 by 10000000
• 306 × 10^7= 14.306 × 10000000 = 43,060,000
Practice Questions
1. Which of the following shows the scientific notation of $0.0125$?
2. Which of the following shows the scientific notation of $2,000,000,000$?
3. Which of the following shows the scientific notation of $796,000$?
4. Which of the following shows the scientific notation of $872$?
5. Which of the following shows the scientific notation of $90$?
6. Which of the following shows the scientific notation of $27 \times 10^3$?
7. Which of the following shows the scientific notation of $281 \times 10^2$?
8. Which of the following shows the scientific notation of $0.0179$?
9. Which of the following shows the scientific notation of $0.000763$?
10. Which of the following shows the scientific notation of $168 \times 10^{-3}$?
11. The population of the world is around $7$ billion. Which of the following shows this in scientific notation?
12. The distance between the sun and the Earth is $93$ million miles. Which of the following shows this distance in scientific notation?
13. The speed of light is $1080$ million km/h. Which of the following shows its scientific notation?
14. An electron has a mass of $0.00000000000000000000000000000091093822$ kg. Which of the following shows it in scientific notation? | {"url":"https://www.storyofmathematics.com/numbers-in-scientific-notation/","timestamp":"2024-11-08T12:42:52Z","content_type":"text/html","content_length":"180037","record_id":"<urn:uuid:4f7b6b13-efee-4e12-a153-c202eeda3e45>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00203.warc.gz"} |
Transcendental number
From Encyclopedia of Mathematics
2020 Mathematics Subject Classification: Primary: 11J81 [MSN][ZBL]
A number that is not a root of any polynomial with integer coefficients. The domain of definition of such numbers is the field of either the real, complex or $p$-adic numbers. The existence and
explicit construction of transcendental numbers was provided by J. Liouville [1] on the basis of the following fact, noted by him. Irrational algebraic numbers do not have "very good" approximations
by rational numbers (see Liouville theorems). Similar considerations enable one to construct $p$-adic transcendental numbers. G. Cantor [2], after discovering the countability of the set of all
algebraic numbers and the uncountability of the set of all real numbers, thus proved that the transcendental real numbers form a set of the cardinality of the continuum. E. Borel [3], after
introducing the first concepts of measure theory, established that "almost all" real numbers are transcendental. It was later found that Liouville transcendental numbers form an everywhere-dense
subset of the real axis, having the cardinality of the continuum and zero Lebesgue measure. Despite the fact that already in the middle of the 18th century there arose the conjecture on the
transcendency of numbers such as $e$, $\pi$, $\log 2$, $2^{\sqrt2}$, etc., proofs of this could not be obtained. The transcendency of $e$ was proved by Ch. Hermite [4], that of $\pi$ and, more
generally, of logarithms of algebraic numbers by C.L.F. Lindemann [5], that of $2^{\sqrt2}$ by A.O. Gel'fond [6]; C.L. Siegel [7] developed a general method for proving transcendency and algebraic
independence of the values at algebraic points of entire functions of a specific class (the $E$-functions), satisfying a linear differential equation with polynomial coefficients (cf. Siegel method).
Gel'fond [8] and T. Schneider [9] simultaneously and independently proved that $\alpha^\beta$ is transcendental if $\alpha \ne 0,1$ is algebraic and $\beta$ is an algebraic irrational (the so-called
Hilbert's seventh problem); A. Baker [10] proved the transcendency of products of numbers of the form $\alpha^\beta$ under natural restrictions. Similar results have been obtained for $p$-adic
transcendental numbers (including Engel's theory of $E$-functions). The development of methods of the theory of transcendental numbers has proved to have a strong influence on new studies in
Diophantine equations [10], [11].
[1] J. Liouville, "Sur des classes de très étendues de quantités dont la valeur n'est ni algébrique, ni même réductible à des irrationelles algébriques" C.R. Acad. Sci. , 18 (1844) pp. 883–885;
[2] G. Cantor, "Gesammelte Abhandlungen mathematischen und philosophischen Inhalts" , G. Olms, reprint (1962) MR0148517 Zbl 0717.01007 Zbl 0441.04001 Zbl 0004.05401 Zbl 58.0043.01
[3] E. Borel, "Leçons sur les fonctions discontinues" , Gauthier-Villars (1898)
[4] Ch. Hermite, "Sur la fonction exponentielle" C.R. Acad. Sci. , 77 (1873) pp. 18–24; 74–79; 221–233; 285–293 Zbl 05.0248.01
[5] C.L.F. Lindemann, "Ueber die Zahl $\pi$" Math. Ann. , 20 (1882) pp. 213–225 MR1510165 Zbl 14.0369.04 Zbl 14.0369.02
[6] A.O. Gel'fond, "Sur les nombre transcendants" C.R. Acad. Sci. , 189 (1929) pp. 1224–1226
[7] C.L. Siegel, "Ueber einige Anwendungen diophantischer Approximationen" Abhandl. Preuss. Akad. Wiss., Phys. Kl. , 1 (1929) pp. 1–70 Zbl 56.0180.05
[8] A.O. Gel'fond, "Sur le septième problème de Hilbert" Dokl. Akad. Nauk SSSR , 2 (1934) pp. 4–6
[9] T. Schneider, "Transzendenzuntersuchungen periodischer Functionen I, II" J. Reine Angew. Math. , 172 (1934) pp. 65–69; 70–74
[10] A. Baker, "Transcendental number theory" , Cambridge Univ. Press (1975) MR0422171 Zbl 0297.10013
[11] V.G. Sprindzhuk, "Classical Diophantine equations in two unknowns" , Moscow (1982) (In Russian) MR0685430 Zbl 0523.10008
[12] N.I. Fel'dman, "Hilbert's seventh problem" , Moscow (1982) (In Russian)
The results of Gel'fond and Schneider imply that for any $\alpha,\beta \in \bar{\mathbf{Q}} \setminus \{0,1\}$, if $\log\alpha/\log\beta \not\in \mathbf{Q}$ then $\log\alpha/\log\beta \not\in \bar{\
mathbf{Q}}$. Baker's generalization asserts that for any $\alpha_1,\ldots,\alpha_n \in \bar{\mathbf{Q}}$, linear independence of $\log\alpha_1,\ldots,\log\alpha_n$ over $\mathbf{Q}$ implies linear
independence over $\bar{\mathbf{Q}}$. Moreover, one can give effective lower bounds for such linear forms in logarithms. This has profound consequences for the theory of Diophantine equations (see
[10]). Gel'fond's and Schneider's method has been further generalized to include $\bar{\mathbf{Q}}$-linear independence of periods and quasi-periods of elliptic curves (see [b1]) and finally, through
the work of G. Wüstholz, P. Philippon and M. Waldschmidt, this has resulted into very general statements of $\mathbf{Q}$-linear independence on commutative algebraic groups defined over $\mathbf{Q}$.
[a1] K. Mahler, "Lectures on transcendental numbers" , Lect. notes in math. , 546 , Springer (1976) MR0491533 Zbl 0332.10019
[a2] A.O. Gel'fond, "Transcendental and algebraic numbers" , Dover, reprint (1960) (Translated from Russian)
[a3] D., et al. Bertrand, "Les nombres transcendants" Mem. Soc. Math. France , 13 (1984) MR0763958 Zbl 0548.10021
[a4] A.B. Shidlovskii, "Transcendental numbers" , de Gruyter (1989) (Translated from Russian) MR1033015 Zbl 0689.10043
[a5] Y. André, "$G$-functions and geometry" , Vieweg (1988) MR0990016 Zbl 0688.10032
[b1] David Masser, , "Elliptic functions and transcendence", Lecture Notes in Mathematics 437 Springer (1975) ISBN 978-3-540-37410-7 Zbl 0312.10023
How to Cite This Entry:
Transcendental number. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Transcendental_number&oldid=54421
This article was adapted from an original article by V.G. Sprindzhuk (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098.
See original article | {"url":"https://encyclopediaofmath.org/index.php?title=Transcendental_number&oldid=54421","timestamp":"2024-11-06T17:55:22Z","content_type":"text/html","content_length":"25510","record_id":"<urn:uuid:f837333d-c269-4bde-91d1-35dbd07085a3>","cc-path":"CC-MAIN-2024-46/segments/1730477027933.5/warc/CC-MAIN-20241106163535-20241106193535-00239.warc.gz"} |
Our users:
I do like the layout of the software, and the user friendliness I have loaded it on my kids computer for them to use for homework.
Owen Patton, UT.
I just finished using Algebrator for the first time. I just had to let you know how satisfied I am with how easy and powerful it is. Excellent product. Keep up the good work.
K.W., Maine
Your new release is so much more intuitive! You team was quick to respond. Great job! I will recommend the new version to other students.
D.B., Washington
We bought it for our daughter and it seems to be helping her a whole bunch. It was a life saver.
T.G., Florida
Keep up the good work Algebrator staff! Thanks!
Trish Cooper, CO
Students struggling with all kinds of algebra problems find out that our software is a life-saver. Here are the search phrases that today's searchers used to find our site. Can you find yours among
Search phrases used on 2011-04-20:
• polynomial calculator code
• free downloadable past sats papers
• Square root worksheet
• basic formulas for expanding expressions
• ratio and proportion free worksheets
• quadratic equation factorer
• add and subtract rational expressions calculator
• McDougal Littell/-Geometry/answers with explanation
• "free probability worksheets"
• chart to simplify radicals
• maths problem solver GCSE
• Accountant and math problems?
• math "base 5" conversion chart "base 10" teaching lesson
• test preparation 6th online
• Math Poems
• factorization expressions calculator
• trigonomic integrals
• online graphing calculator from an equation
• algebra 2 homework solver free
• download saxon math calculator
• rational exponents vs. radical signs
• elementary algrebra
• McDougal Littell Algebra 1 Teacher Edition Free Online Answer Key
• lcm cheat sheet
• statistics combination
• permutation and combination 6th grade
• "9th grade algebra problems"
• differential equations + square roots
• compound interest formula math activities
• completing the square practice
• games and math probloms
• pre-algebra definitions
• properties of the roots of quadratic equations
• how do i divide exponets
• definition of mixture algebra
• what are the highest common factors of 36 and 52
• number factor program
• square root in Matlab
• cost accounting definition powerpoint presentations
• Index of Coincidence in java
• trigonomic identities chart for the unit circle
• vb6 solve equations examples
• free algebra homework solver
• solving trinomials
• 5th grade problem solving worksheets
• graphing linear equationwith 3 variable
• finding a variable exponent
• Algebra 2 poems
• second grade math expanded form worksheets
• activity for simplifying radicals
• Graphing Linear Equations Worksheet, Algebra
• solving nonhomogeneous differential equations in MATLAB
• programming the distance formual into the TI-83 graphing calculator
• dilation worksheet
• algebra homework help
• "free worksheets" geometric plane solid printable
• adding and subtracting integers property
• symmetry worksheets
• teach me algebra
• which is better ti-89 or ti-84
• poem of math algebra
• trigonometry worksheets
• Laplace transformations on ti 89 titanium
• trivia in linear equation
• Greatest common factors, lessons, glencoe
• free problem solver
• Online Homogeneous Equations Solver
• Ti calculators emulators
• free answers to Algebra 2 problems
• formula for converting fractions to decimals
• 4th grade decimels
• trigonometry exercis+ppt
• maths practices papers 8-9 to do free online
• Combining like terms
• mathematical applications for the management, life, and social sciences eighth edition "even answers"
• equation involving rational expression
• algebra 1 in steps
• how "do you" divide an exponent when the dominator is greater than the numerator
• examples of puzzle,trigonometry
• scott foresman algebra answers
• solving linear equation in three variable using determinant
• algerbra 1
• math factoring calculator
• algebra problem solver with work shown
• Online Adding Calculator
• solution manual abstract algebra john fraleigh
• balancing trig equations
• graphing TI -84 "step functions"
• easy permutation and combination problems | {"url":"http://algebra-help.com/algebra-help-factor/angle-complements/binomial-factoring.html","timestamp":"2024-11-03T16:14:47Z","content_type":"application/xhtml+xml","content_length":"13018","record_id":"<urn:uuid:22e2fe6f-479a-456a-818b-031addd5b943>","cc-path":"CC-MAIN-2024-46/segments/1730477027779.22/warc/CC-MAIN-20241103145859-20241103175859-00650.warc.gz"} |