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Network Repair, Hardware, Printers, Laptop Repair

Address 609 Bryden Ave Ste B, Lewiston, ID 83501 (208) 791-0484 http://priceright.tech

# forecast error measurements Pomeroy, Washington

Since the forecast error is derived from the same scale of data, comparisons between the forecast errors of different series can only be made when the series are on the same Compute the forecast accuracy measures based on the errors obtained. The SMAPE (Symmetric Mean Absolute Percentage Error) is a variation on the MAPE that is calculated using the average of the absolute value of the actual and the absolute value of While forecasts are never perfect, they are necessary to prepare for actual demand.

This give you Mean Absolute Deviation (MAD). Less Common Error Measurement Statistics The MAPE and the MAD are by far the most commonly used error measurement statistics. Kluwer Academic Publishers. ^ J. MAPE delivers the same benefits as MPE (easy to calculate, easy to understand) plus you get a better representation of the true forecast error.

best regards, Mark Author Posts Viewing 5 posts - 1 through 5 (of 5 total) The forum ‘General' is closed to new topics and replies. Hyndman and Koehler (2006) recommend that the sMAPE not be used. Forecast Error = | A – F |

Forecast Error as Percentage = | A – F | / A Where: A = Actual demand F = Forecast demand Forecast Accuracy Consider the following table:   Sun Mon Tue Wed Thu Fri Sat Total Forecast 81 54 61

When choosing models, it is common to use a portion of the available data for fitting, and use the rest of the data for testing the model, as was done in Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. Sometimes, different accuracy measures will lead to different results as to which forecast method is best. There are a slew of alternative statistics in the forecasting literature, many of which are variations on the MAPE and the MAD.

Unsourced material may be challenged and removed. (June 2016) (Learn how and when to remove this template message) In statistics, a forecast error is the difference between the actual or real One solution is to first segregate the items into different groups based upon volume (e.g., ABC categorization) and then calculate separate statistics for each grouping. Another interesting option is the weighted M A P E = ∑ ( w ⋅ | A − F | ) ∑ ( w ⋅ A ) {\displaystyle MAPE={\frac {\sum (w\cdot Measuring the extent of deviation helps determine the need to improve forecasting or rely on safety stock to meet customer service objectives.

Home Activity Members Most Recent Articles Submit an Article How Reputation Works Forum Most Recent Topics Start a Discussion General Forums Industries Operations Regional Views Forum Etiquette Dictionary View All Terms The multiplier is called a safety factor. By convention, the error is defined using the value of the outcome minus the value of the forecast. All error measurement statistics can be problematic when aggregated over multiple items and as a forecaster you need to carefully think through your approach when doing so.

More » Login Form Stay signed in Forgot your password? If Supply Chain is held responsible for inventories alone, then it will create a new bias to underforecast the true sales. Privacy policy About Wikipedia Disclaimers Contact Wikipedia Developers Cookie statement Mobile view Forecasting 101: A Guide to Forecast Error Measurement Statistics and How to Use It’s easy to look at this forecast and spot the problems.  However, it’s hard to do this more more than a few stores for more than a few weeks.

The size of the number reflects the relative amount of bias that it present. This scale sensitivity renders the MAPE close to worthless as an error measure for low-volume data. Mean Absolute Deviation (MAD) A common way of tracking the extent of forecast error is to add the absolute period errors for a series of periods and divide by the number If the error is denoted as e ( t ) {\displaystyle e(t)} then the forecast error can be written as; e ( t ) = y ( t ) − y

In my next post in this series, I’ll give you three rules for measuring forecast accuracy.  Then, we’ll start talking at how to improve forecast accuracy. So sMAPE is also used to correct this, it is known as symmetric Mean Absolute Percentage Error. Many professionals recommend the use of MAPE as standard measure of forecast error, and we do not take exception to that. Statistically speaking, the RMSE is just the standard error of the mean (forecast).

R code dj2 <- window(dj, end=250) plot(dj2, main="Dow Jones Index (daily ending 15 Jul 94)", ylab="", xlab="Day", xlim=c(2,290)) lines(meanf(dj2,h=42)$mean, col=4) lines(rwf(dj2,h=42)$mean, col=2) lines(rwf(dj2,drift=TRUE,h=42)$mean, col=3) legend("topleft", lty=1, col=c(4,2,3), legend=c("Mean method","Naive Suppose$k$observations are required to produce a reliable forecast. We recommend the use of the Square Root of MSE (or Root Mean Squared Error – RMSE) as the preferred measure of forecast error (Demand Std .Dev. ≈ SQRT(MSE). Hoover, Jim (2009) "How to Track Forecast Accuracy to Guide Process Improvement", Foresight: The International Journal of Applied Forecasting. Some argue that by eliminating the negative value from the daily forecast, we lose sight of whether we’re over or under forecasting. The question is: does it really matter? When Select the observation at time$k+i$for the test set, and use the observations at times$1,2,\dots,k+i-1$to estimate the forecasting model. This installment of Forecasting 101 surveys common error measurement statistics, examines the pros and cons of each and discusses their suitability under a variety of circumstances. About the author: Eric Stellwagen is Vice President and Co-founder of Business Forecast Systems, Inc. (BFS) and co-author of the Forecast Pro software product line. The problem is that when you start to summarize MPE for multiple forecasts, the aggregate value doesn’t represent the error rate of the individual MPEs. Most practitioners, however, define and use the MAPE as the Mean Absolute Deviation divided by Average Sales, which is just a volume weighted MAPE, also referred to as the MAD/Mean ratio. Calculating demand forecast accuracy From Wikipedia, the free encyclopedia Jump to: navigation, search It has been suggested that this article be merged into Demand forecasting. (Discuss) Proposed since April 2016. Repeat the above step for$i=1,2,\dots,T-k$where$T\$ is the total number of observations.

See also Consensus forecasts Demand forecasting Optimism bias Reference class forecasting References Hyndman, R.J., Koehler, A.B (2005) " Another look at measures of forecast accuracy", Monash University.


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# 2PI-effective action and functional derivatives

I'm trying to work out the 2PI-effective action for complex scalar fields.

Introducing a multi field index $$(a,b,c...)$$ the complex conjugation and all other degrees of freedoms are suppressed, and field vectors are used $$\phi=(\phi_a,\phi_b,...)^T=(\phi_1,\phi_1^*,....)^T .$$

The generating functional $$Z[J,R]$$ and $$W[J,R]$$ is then given by;

$$Z[J,R]= \int \mathcal{D} \phi \, \exp (i \left[ S[\phi] + J_a \phi_a + \frac{1}{2} \phi_a R_{a,b} \phi_b \right] ) = \exp(i W[J,R]).$$

We can now define the connected two points function $$G_{a,b}$$ and the macroscopic field $$\Phi_a$$ and find for the derivative of $$W$$:

$$\qquad \Phi_a = \frac{\delta W}{\delta J_a} \qquad G_{a,b} = \frac{\delta^2 W}{\delta J_a \delta J_b} \qquad \Rightarrow \frac{\delta W}{\delta R_{a,b}} = \frac{1}{2} (\Phi_a \Phi_b + i G_{a,b}).$$

We can now look for the Legendre transformation of W w.r.t. to the two fields.

$$\Gamma[\Phi,G] = W[J,R] - \Phi_a J_a - \frac{1}{2} (\Phi_a \Phi_b + i G_{a,b}) R_{b,a}.$$

From this we find for the sources;

$$\frac{\delta \Gamma}{\delta \Phi_a} = - J_a - \frac{1}{2} \Phi_a (R_{a,b}+R_{b,a})= - J_a - \Phi_a R_{a,b}\qquad \frac{\delta \Gamma}{\delta G_{a,b}} =- \frac{i}{2} R_{b,a} = - \frac{i}{2} R_{a,b}.$$

And here is my first question. I can see that $$R$$ must be symmetric by definition, therefore the expression does not depend on taking the derivative with $$G_{a,b}$$ or $$G_{b,a}$$. But how to take the derivative in general?

$$\qquad \qquad \frac{\delta G_{d,c}}{\delta G_{a,b}} = \delta_{a,d} \delta_{c,b} \qquad or \qquad \frac{\delta G_{d,c} }{\delta G_{a,b}} =\frac{1}{2} ( \delta_{a,d} \delta_{c,b} +\delta_{c,d} \delta_{a,b} ).$$

The second question is if that statement also implies that $$G_{a,b}$$ must by symmetric?

Following further the development the effective action is then found as;

$$\Gamma[\Phi,G]= S[\Phi] +\frac{i}{2} \text{tr} \log G^{-1} + \frac{i}{2} \text{tr} G_{0}^{-1}G + \Gamma^2$$

Where $$\Gamma^2$$ contains all 2-PI diagrams and will contribute the self energy. The effective action has boundary conditions at $$J=0, R=0$$, from where the Greens function can be found. Therefore we just have to take the functional derivative w.r.t. to $$G$$ of the upper equation.

$$\frac{\delta \Gamma}{\delta G_{a,b}}=0 = \frac{-i}{2} G^{-1}_{b,a} + \frac{i}{2} (G_{b,a}^0)^{-1} + \frac{\delta \Gamma}{\delta G_{a,b}}$$

Does this also implies that the self-energy $$\Sigma_{b,a} = 2i \frac{\delta \Gamma}{\delta G_{a,b}}$$ is symmetric in $$a,b$$?

1. The connected two-point function $$G_{ab}$$ and the self-energy $$\Sigma_{ab}$$ are in the 2PI formalism defined as manifestly symmetric tensors wrt. the indices $$a\leftrightarrow b$$.
2. So, Yes, the functional derivatives wrt. $$G_{ab}$$ needs to be symmetrized, cf. e.g. this and this Phys.SE posts.

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# What is the empirical chemical formula of a compound that is 69.9% of iron and 30.0% oxygen?

Apr 24, 2016

$F {e}_{2} {O}_{3}$

#### Explanation:

We assume there are $100 \cdot g$ of compound, and thus there are:

$\left(i\right)$ $\frac{69.9 \cdot g}{55.85 \cdot g \cdot m o {l}^{-} 1}$ $=$ $1.25 \cdot m o l \cdot F e$, and

$\left(i i\right)$ $\frac{30.0 \cdot g}{15.999 \cdot g \cdot m o {l}^{-} 1}$ $=$ $1.88 \cdot m o l \cdot O$.

If we divide thru by the lowest molar quantity we get a formula of $F e {O}_{1.5}$. Because, by definition the empirical formula is the simplest WHOLE number ratio, we double this result to give $F {e}_{2} {O}_{3}$.


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# Risk Management

Jump to navigation Jump to search
Basic Risk and Response Cycle
Application: Risk and Response Cycle with intergration of Satellite technology and smartphone (see Learning Task)
SDG11: Sustainable Cities and Communities - Learning Resource supports the SDGs - UN-Guidelines[1]

Risk management has two main tasks:

• determine and calculate the risk and
• organize the response to the identified risk:
• Improve the prepardness to an event,
• Reduce the probability of an event by risk mitigation activities,
• Reduce the impact of an event

## Response Time

When someone has a heart attack or a stroke the medical response is urgent in comparison to a broken leg that has in general a long time span in which medical response will not have a serious impact on the health condition of the patient. For the link between risk and response to the available time span is crucial for the assessment of the impact on an hazardous event. Going back to example of a patient with a heart attack, the main question is

```   "How long does it take until an ambulance with medical support is available?"
```

People living close to the health care facility have a better response time in an case of emergency than people living in rural ares. This leads to that fact that risk depends on spatial allocation of resources and distance of an event to the resource that can be used for risk mitigation (see Spatial risk management).

## Learning Task

Artificial lights can be detected from satellites. Light emission during night is a proxy variable for the availability of electricity after disasters.
• (Risk & Response Cycle) On this page on right you find an example of an extended risk and response cycle, with a focus on satellite technology and smartphones. Take your personal expertise as starting point and create your own cycle for a domain of your choice.
• (Planetary Boundaries) Approach risk management from the angle of planetary boundaries[8] and comsumption of planetary resources. Create a first risk mitigations concept that you think it will work in your family, school, university, town or region.
• (Sustainable Development Goals) Consider people in developing countries that battle to survive the next day, week, month. Describe the challenges for long-term goals in the context of climate change and the planetary boundaries (see Sustainable Development Goals SDG of United Nations[9]). Explain how Risk Management could contribute to sustainable communities and sustainable development in general!
• (Systems Thinking) If we apply systems thinking in risk management, we will now look on a basic case, where someone living in a semi-arid region will cut down trees for fire wood or for a campfire. Systems analysis will tell us, that cutting down trees will increase erosion of soil and it will cause long-term food problem of agricultural production.
• Analyze what you would do with the last trees, if you are risk literate and you know about this dependencies, but it gets ${\displaystyle 2^{o}C}$ during night?
• What are you implication for short-term and long-term risk management?
• (Risk Management for Electricity as Resource): Light emission during night is a proxy variable for the availability of electricity after disasters. Describe the procedure of assessment from the analysis of satellite images (before/after the event), to assessment of the impact of missing electricity for health service delivery, communication or provision of services in general. How would you assess the vulnerability in your hometown in comparision to other areas in the world?

## Resources

• Risk Management - Content Matrix
• Risk Literacy describes the individual skill/expertise to manage the risk
• Spatial risk management, risk vary in different geolocation, spatial risk management takes the spatio-temporal variations of risk into account
• Agricultural Water Pollution Management
• Systems Thinking and Risk Economy, environment, public health, social and cultural conditions for risk are connected and risk mitigation activities in Systemic Risk)
• Disaster Management considers risk management for disasters. Disaster Risk Reduction aims to reduce the damage caused by natural hazards like earthquakes, floods, droughts and cyclones, that cause a serious disruption of the functioning of a community or a society[10]. Disasters involve widespread human, material, economic or environmental impacts, which exceed the ability of the affected community or society to cope using its own resources. The systemic risk is managed in different phases from immediate response after an event and long-term prepardness measures and capacity building to reduce the vulverability.

## References

1. UN-Guidelines for Use of SDG logo and the 17 SDG icons (2016/10) - http://www.un.org/sustainabledevelopment/wp-content/uploads/2016/10/UN-Guidelines-for-Use-of-SDG-logo-and-17-icons.October-2016.pdf
2. Stulz, R. M. (1996). Rethinking risk management. Journal of applied corporate finance, 9(3), 8-25.
3. Power, M., & McCarty, L. S. (1998). Peer reviewed: a comparative analysis of environmental risk assessment/risk management frameworks. Environmental science & technology, 32(9), 224A-231A.
4. Cagliano, Anna Corinna, Sabrina Grimaldi, and Carlo Rafele. "A systemic methodology for risk management in healthcare sector." Safety Science 49.5 (2011): 695-708.
5. Rockström, J., Steffen, W., Noone, K., Persson, Å., Chapin III, F. S., Lambin, E., ... & Nykvist, B. (2009). Planetary boundaries: exploring the safe operating space for humanity. Ecology and society, 14(2).
6. McMichael, A. J., Woodruff, R. E., & Hales, S. (2006). Climate change and human health: present and future risks. The Lancet, 367(9513), 859-869.
7. O'connor, R. E., Bard, R. J., & Fisher, A. (1999). Risk perceptions, general environmental beliefs, and willingness to address climate change. Risk analysis, 19(3), 461-471.
8. Steffen, W., Richardson, K., Rockström, J., Cornell, S. E., Fetzer, I., Bennett, E. M., ... & Folke, C. (2015). Planetary boundaries: Guiding human development on a changing planet. Science, 347(6223), 1259855.
9. Griggs, D., Stafford-Smith, M., Gaffney, O., Rockström, J., Öhman, M. C., Shyamsundar, P., ... & Noble, I. (2013). Policy: Sustainable development goals for people and planet. Nature, 495(7441), 305-307.
10. United Nations Office for Disaster Risk Reduction (UNSDR) (2017) http://www.unisdr.org/we/inform/terminology


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+0

# gcf and lcm problem

+1
251
1
+549

When the greatest common divisor and least common multiple of two integers are multiplied, the product is 180. How many different values could be the greatest common divisor of the two integers?

Aug 5, 2019

#1
+109518
0

When the greatest common divisor and least common multiple of two integers are multiplied, the product is 180. How many different values could be the greatest common divisor of the two integers?

Let the numbers be ax and ay   where  x and y are relatively prime and a, x, and y are all positive integers.

So the GCD is    $$a$$

and the lowest commone multiple is     axy

The product of these is      $$a^2xy$$

So we have

$$a^2xy=180\\ a^2 \;\;must \;\;be\;\;1,4,9, or \; 36 \;\text{no other square integerwill make this true}\\ \text{So a = 1, -1, 2, -2, 3,- 3, 6 or - 6}\\$$

So there seems to be 8 possible values for the greatest common divisor.

Aug 5, 2019


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# What is the fifteenth term of the sequence 5,-10,20,-40,80?

${a}_{15} = 81920$

#### Explanation:

from the given set of numbers 5,-10,20,-40,80...it appears like Geometric Sequence and with first term ${a}_{1} = 5$ and the common ratio $r = \frac{80}{- 40} = \frac{- 40}{20} = \frac{20}{- 10} = \frac{- 10}{5} = - 2$

$r = - 2$

the formula to find the $n t h$ term in Geometric Progression is

${a}_{n} = {a}_{1} \cdot {r}^{n - 1}$

Use now ${a}_{1} = 5$ and $r = - 2$ and $n = 15$ in the formula

${a}_{n} = {a}_{1} \cdot {r}^{n - 1}$

${a}_{15} = 5 \cdot {\left(- 2\right)}^{15 - 1}$

${a}_{15} = 5 \cdot {\left(- 2\right)}^{14}$

${a}_{15} = 5 \cdot 16384$

${a}_{15} = 81920 \text{ " }$the 15th term

A long check helps after all there are only 15 numbers

5, -10, 20, -40, 80, -160, 320, -640, 1280, -2560, 5120, -10240, 20480, -40960, 81920

God bless....I hope the explanation is useful...


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# The number of retracts of $\mathbb{R}^2 \setminus \{(0,0)\}$ up to homeomorphic

We know that $\mathbb{S}^1$ is a (deformation) retract of $\mathbb{R}^2 - \{ (0,0)\}$. Obviously, the number of retracts of $\mathbb{R}^2\setminus \{ (0,0)\}$ equals to 1 up to homotopy equivalence. My question is that:

How many retracts are there up to homeomorphic for $\mathbb{R}^2 \setminus \{ (0,0)\}$?

This is more a comment than a answer. Clearly there are no more that $2^{\Bbb R}$ retracts. Here is a way to build $2^{\Bbb N}$ different retracts. I don't know if there are $2^{\Bbb R}$ retracts or not.

Consider $$R = S^1 \cup \{(0,y) : y \geq 1\} \cup \{(x,y) : x \in (-1,1) , y \in \Bbb N_{>1} \}$$

If you make a picture it is clear that $\Bbb R^2 \backslash \{(0,0)\}$ retracts on $R$. Now, $R$ is concretely a circle with a line and an infinity of crossing. If $(x_1,x_2, \dots, x_n, \dots ) \in 2^{\Bbb N}$, we can modify $R$ by thickening the $n$-th segment if $x_n = 1$ and do nothing else. We call this space $R_x$, concretly $R \cap \{ n < y < n+1 \} = \{(x,y) : x \in [-1/2,1/2], n < y < n+1\}$ if $x_n=1$ and $R_x \cap \{ n < y < n+1 \} = R \cap \{n<y<n+1\}$ else. In particular $R_0 = R$. Again a picture shows that $\Bbb R^2 \backslash \{(0,0)\}$ retracts on $R_x$.

Now, clearly if $f : R_{x} \to R_{x'}$ is an homeomorphism, $f(0,n) = (0,n)$ for all $n \geq 1$. In particular, $f$ restricts to an homeomorphism between every "strip" of $R_x$ and $R_{x'}$. Since $[0,1]$ is not homeomorphic to $[0,1] \times [-1/2,1/2]$ it follows that any sequence $x = \{x_1, \dots, x_n, \dots \}$ defines a retract of $\Bbb R^2 \backslash \{0\}$, with all a different topological type.

• Thank you so much for your nice comments and excellent answer. – M.Ramana Apr 22 '18 at 14:12
• @M.Ramana : you're very welcome ! – Nicolas Hemelsoet Apr 22 '18 at 15:18

There are infinitely many. For instance, given any natural number $n>2$, take $n$ unit discs and glue them together (so that each disc touches two other discs, each at a single point) into a ring around the origin. None of these rings are homeomorphic.

• In fact, there are uncountably many. So I guess the question is more if there is $|2^{\Bbb R}|$ such retracts or not. – Nicolas Hemelsoet Apr 22 '18 at 12:13
• @NicolasHemelsoet Sure, but to illustrate the difference between homotopy equivalence and homomorphism, my answer serves its purpose well in its simplicity. – Arthur Apr 22 '18 at 12:15
• I guess the OP is aware of this, but anyway it's indeed simple and might be useful to know for future readers. – Nicolas Hemelsoet Apr 22 '18 at 12:18
• @Arthur Thank you very much for your nice answer. – M.Ramana Apr 22 '18 at 14:32


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# Decimal as Fraction

We will discuss how to express decimal as fraction.

Let us consider some of the following examples on expressing a decimal as a fraction.

1. Convert 2.12 into a fraction.

Solution:

 2.12 = 2 + 1 tenth + 2 hundredths        = 2 + $$\frac{1}{10}$$ + $$\frac{2}{100}$$        = 2 + $$\frac{1 × 10}{10 × 10}$$ + $$\frac{2}{100}$$        = 2 + $$\frac{10}{100}$$ + $$\frac{2}{100}$$        = 2 + $$\frac{10 + 2}{100}$$        = 2 + $$\frac{12}{100}$$        = 2 + $$\frac{3}{25}$$        = 2$$\frac{3}{25}$$ We write the place value of digits of decimal and then add as usual.

2. Convert 5.125 into a fraction.

Solution:

 5.125 = 5 + 1 tenth + 2 hundredths + 5 thousandths         = 5 + $$\frac{1}{10}$$ + $$\frac{2}{100}$$ + $$\frac{5}{1000}$$         = 5 + $$\frac{1 × 100}{10 × 100}$$ + $$\frac{2 × 10}{100 × 10}$$ + $$\frac{5}{1000}$$         = 5 + $$\frac{1 × 100}{10 × 100}$$ + $$\frac{2 × 10}{100 × 10}$$ + $$\frac{5}{1000}$$         = 5 + $$\frac{100}{1000}$$ + $$\frac{20}{1000}$$ + $$\frac{5}{1000}$$         = 5 + $$\frac{100 + 20 + 5}{1000}$$         = 5 + $$\frac{125}{1000}$$         = 5 + $$\frac{1}{8}$$         = 5$$\frac{1}{8}$$ We write the place value of digits of decimal and then add as usual.

Note: We always reduce the fraction converted from a decimal to its lowest form.


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# DAVIDSTUTZ

Check out our latest research on weakly-supervised 3D shape completion.
27thSEPTEMBER2017

Xavier Glorot, Antoine Bordes, Yoshua Bengio. Deep Sparse Rectifier Neural Networks. AISTATS 2011: 315-323

Glorot et al. propose the use of rectified linear units for feed-forward networks. They present a motivation based on the following two facts relating models used in deep learning and neuroscience:

• Studies show that neurons encode information in a highly distributed and sparse way.
• A frequently used model for neurons looks as follows:

$f(I) = \begin{cases}\left[\tau \log\left(\frac{E + RI - V_r}{E + RI - V_{th}}\right) + t_{ref}\right]^{-1} & \text{ if }E + RI > V_{th}\\0 & \text{ else}\end{cases}$

where the individual parameters are unimportant in the context of artificial neural networks as long as the structure is understood.

Sparsity is further motivating by the following desirable properties:

• Information disentangling (i.e. disentangling of "neighboring" features).
• Variable-size representations as needed.
• High likelihood for linear separability.

The rectified linear unit, i.e. $\max(0, x)$ is introduced by discussing its advantages and potential problems. Advantages, briefly summarized, are sparsity, cheaper computation compared to the hyperbolic tangent and sigmoid, and better gradient flow due to the linear, non-saturating part. A potential problem is blocking gradient flow by the hard threshold at $0$. To alleviate this, they propose the softplus function:

$\text{softplus}(x) = \log(1 + e^x)$

However, experiments show, that this does not hinder optimization.

What is your opinion on the summarized work? Or do you know related work that is of interest? Let me know your thoughts in the comments below or get in touch with me:


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# Difference between volatility measures of a basket of assets

I am trying to understand intuitively the difference between two different measures of realized variance of a basket of assets.

The first measure I am aware of is when you take the realized variance to be the sum of squared log returns of the basket. I.e.

$$\sigma_B^2 = \sum_{i=1}^T{r_i}^2$$

where $$\sigma_B^2$$ is the realized variance of the basket and $$r_i$$ is the log returns of the basket ($$r_i = \sum_{j=1}^n\omega_jr_j$$ for weights $$\omega_j$$ and single stock returns $$r_j$$)

The second measure is obtained via consideration of basket components standard deviations and correlations:

$$\sigma_B^2 = \sum_{i=1}^n \omega^2_i\sigma^2_i + 2\sum_{i=1}^n\sum_{j=i+1}^n\omega_i\omega_j\sigma_i\sigma_j\rho_{ij}$$

where $$\sigma_B^2$$ is the basket variance, $$\omega_i, \sigma_i$$ is the weight and volatility corresponding to the $$i^{th}$$ basket component respectively and $$\rho_{ij}$$ is the pairwise correlation between the $$i^{th}$$ and $$j^{th}$$ components.

I know the former of these two measures assumes that the expected return of the basket is $$0$$, but this is potentially assumed in the second as well if each $$\sigma_i$$ is found by summing the $$i^{th}$$ components squared log returns and taking the answers square root. Is there a fundamental intuitive difference between these two measures of realized variance?

Thanks.

If the correlation estimate $$\rho_{ij}$$ is calculated using the same period $$[1,T]$$ then 2 expressions are identical. They just differ in the order in which you are performing the 2 summations (one in time direction and the other in the cross-sectional direction).


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# mirpyidl public interface¶

This shows the documentaiton for the mirpyidl public interface.

## mirpyidl¶

### author¶

Novimir Antoniuk Pablant - npablant@pppl.gov - novimir.pablant@amicitas.com

### purpose¶

Allows for integration of IDL routines into Python.

### warning¶

I have not been careful with generalizing the data types. At this point this will only work on 64 bit systems.

### descripton¶

A library to call IDL (Interactive Data Language) from python. Allows trasparent wrapping of IDL routines and objects as well as arbitrary execution of IDL code.

mirpyidl is hosted at:
https://bitbucket.org/amicitas/mirpyidl
Documentation can be found at:
http://amicitas.bitbucket.io/mirpyidl
To build use the command:
python setup.py build_ext
Known Issues:

As written, this will only work if the idlrpc server is using the default ServerId.

This module includes routines to start an idlrpc server if one is not already running. This currently has some problems:

• I don’t know a good way to check wheather the server is ready for connections. Currently I wait for the licence server to start, then wait an addition 0.5 seconds.
• The idlrpc server is left running regardless of whether it was an existing process or started by this module. This is not really the best way to handle things.

### IDL side variables¶

mirpyidl creates a number of variables within the IDL session to track pyidl instances and objects. These variables are then used to provide unique name spaces for different pyidl objects.

Here is a list of the persistent IDL side variables:
• _mirpyidl_instance_counter
• _mirpyidl_object_counter
mirpyidl.execute()
mirpyidl.ex()
mirpyidl.setVariable()
mirpyidl.set()
mirpyidl.getVariable()
mirpyidl.get()
mirpyidl.callFunction()
mirpyidl.callPro()
class mirpyidl.PyIDL

Bases: mirpyidl.PyIDLCore

Contains additional shortcut methods based on Python code.

In particular this attempts to simplify wapping of IDL routines. It also provides a workaround for structure, list and hash passing.

callFunction()

A shortcut routine to call IDL functions.

This just calls callMethod() with the options appropriate for an IDL function.

callMethod()

Call an idl subroutine or method.

result_name (string)

default = None

The name of the temporary result variable to use in the IDL function call. If None, a temporary name will be automatically generated.

return_result (bool)

default = True

If true, and function=True, then retrieve and return the result from IDL. If false, then do not return the result.

This option is used internally for object creation.

cleanup (bool)

default = True

If true the result from a function call will be deleted in the IDL session.

This object is used internally for object creation

callPro()

A shortcut routine to call IDL procedure.

This just calls callMethod() with the options appropriate for an IDL procedure.

deleteVariable()

Delete a variable from the idlrpc server.

destroyObject()

Destroy the given IDL object.

ex()

A shortcut to the execute method.

execute()

Execute a command in the IDLRPC session.

Programming Notes:

There are two issues that I need to work around:

Issue # 1

The call to IDL_ExecuteStr or IDL_RPCExecute Str does not always give me the status code that I want, which is the error number for any unrecovered error in the execute command. What is actually returned for the status code is whatever is in !ERROR_STATE.CODE at the end of the call. If an error handler is written in the way that is shown in the IDL manual, the !ERROR_STATE.CODE will in general still have the last error stored even if an error handler successfuly dealt with the error.

To get around this I add on a ” & MEASSAGE, /RESET” to the end of every call. If there is an unrecoverd error, this will not get called and the status code will be returned correctly. If the command completes, even with recoverd errors, then the status will be success.

Issue # 2

This issue is a bit more subtle. IDL has a mechanism for checking for floating point errors. The exact behavior is controled by the !EXCEPT system variable. The default setting is that IDL will check for math errors every time it returns to the main scope. If any math errors are found these will be reported in the returned status code from the execute command. This is generally the desired behavior and fine control can be implemented on either the IDL or python side.

The issue is when there are math errors on the processor floating point status register that have not otherwise been handled before the IDL execute command has been called. In this situaton IDL can pickup the math error after the command has been executed and return an error code that is actually from somewhere else.

This is probably not a common problem as I ran into it when calling both FORTRAN and IDL code from Python where an unhandled floating point error was happening in the FORTRAN code.

The expected behavior would be that IDL would only report math errors that occured within the IDL call. To ensure this I clear any accumulated math errors before calling the IDL command.

I can’t think of any time that this would not be reasonable behavior, however it does add more overhead.

get()

A shortcut to the getVariable method.

getHash()

I do not have a way to actually pass hash objects from IDL to python. In fact, without rebuilding the idl_rpc client/server I can’t even see that I am requesting an object.

This is a work around. Not particularly efficent.

warning:
This will only work if all of the hash tags are strings.
warning:
This will probably fail if the hash that is being retrieved is empty.
getIdlType()
getStructure()

I do not have a way to actually pass structures from IDL to python. In fact, without rebuilding the idl_rpc client/server I can’t even see that I am requesting a structure.

This is a work around. Not particularly efficent.

getTypeIdlFromNumpy()
getTypeNumpyFromIdl()
getVariable()

Get a varible from the idlrpc server. Check for complex types.

idlrpc
isHash()
isStructure()
newObject()

Create a new object and return a string identifier.

function
A string containing the object creation function. For example: “OBJ_NEW”
set()

A shortcut to the setVariable method.

setStructure()

Create a structure in IDL from dictionary in Python.

I cannot directly pass structures to IDL at this point since the structure definition is proprietary. The tools that IDL provides requireds that the IDL interpreter is running, which is not an option.

setVariable()
class mirpyidl.PyIDLObject

Bases: object

This is base class to use when wrapping IDL object. All python wrapper object should inherit from this class.

This class mostly just takes care of handling the mirpyidl object id so that it does not need to be delt with explicitly when wrapping.

callMethod()

Call a method of this object.

This is simply a wrapper of PyIDL, except that the object name is automaically provided.

callMethodFunction()

Call a function method of the object.

This is simply a wrapper of callMethod() but with the appropriate options for a function.

callMethodPro()

Call a procedure method of the object.

This is simply a wrapper of callMethod() but with the appropriate options for a procedure.


text:
# table layout inside a newcommand

I wonder if I can define something similar to the \newcommand that places the values inside a pre-defined table (tabular) template.

If you see the table above, imagine you would duplicate that many times (for instance by using a newly defined command \workpackage). The input arguments for that command would be:

\workpackage {2}{
\begin{itemize}......
}{none}

The layout itself is a table. Is it a good idea to put such a complex layout into a new command as kind of a template?

This example does not work :(

\newcommand{\wp}[3]{
\begin{tabular}{ l l }
Effort & #1 \\
Content & #2 \\
Pre-Requisites & #3 \\
\end{tabular}
}

Here's my final solution, which is inspired by the answers given below:

\usepackage{tabularx}
\usepackage{xkeyval}

% define the key (arguments)
\makeatletter
\define@key{wpkeys}{title}{%
\def\wptitle{#1}
}
\define@key{wpkeys}{number}{%
\def\wpnumber{#1}
}
\define@key{wpkeys}{weeks}{%
\def\wpweeks{#1 person weeks}
}
\define@key{wpkeys}{results}{%
\def\wpresults{#1}
}
\makeatother
% end of key definition

% new command for a work package
\newcommand{\workpackage}[2][]{%
\setkeys{wpkeys}{#1}%

\subsection*{WP\wpnumber: \wptitle}
\begin{tabularx}{\linewidth}{|p{3cm}|X|}
\hline
Effort & \wpweeks \tabularnewline
\hline
Content & #2 \tabularnewline
\hline
Expected results & \wpresults \tabularnewline
\hline
\end{tabularx}
}
% end of command definition

Used like this:

\workpackage[number=1, title={Project Management \& Reporting}, weeks=3,results={MS1}]{
\begin{itemize}
\item foo
\item baa
\end{itemize}
}

• Remember that a \newcommand only takes up to 9 arguments. If your table requires more entries than that, something more clever is required. – Steven B. Segletes Mar 23 '16 at 12:28
• There will be less than 9 parameters. But just curious what something else more clever would be? – Matthias Mar 23 '16 at 12:33
• Well for things with more than nine arguments, you could pass the data in a single argument as a space or comma separated list, and then have the macro parse the data accordingly. See tex.stackexchange.com/questions/2132/… – Steven B. Segletes Mar 23 '16 at 12:37
• I have done this for my worksheet headers and using a keyvalue-syntax to make it easier. A comma separated list is easier, but requires to remember which position stands for which entry in the table then – user31729 Mar 23 '16 at 12:39
• Hmm, a list is a good idea though. But nevertheless, I haven't found an easily understandable example how to iterate through arguments. – Matthias Mar 23 '16 at 12:43

Here's a keyvalue interface approach.

Define 'arbitrary' keys for a key family, say wpkeys with \define@key and assign the key-value to a macro that has a similar name like the key (easier to remember). Those keys can be given as an optional argument to \workpackage then.

The real content is given as the first mandatory argument, for example.

With

\setkeys{wpkeys}{prerequisites=none,leftheader={Effort},#1}%

it is possible to preset some keys that should some values if they are not explicitly given.

Please note that due to the shortness of my example this will leave the content of \leftheader etc. defined even for the next usage of the \workpackage macro.

\documentclass{article}

\usepackage{tabularx}
\usepackage{xkeyval}

\makeatletter

}

}

\define@key{wpkeys}{prerequisites}{%
\def\prerequisites{#1}
}

\makeatother

\newcommand{\workpackage}[2][]{%
\begin{tabularx}{\linewidth}{|p{3cm}|X|}
\hline
\hline
Content & #2 \tabularnewline
\hline
Pre-requisites & \prerequisites \tabularnewline
\hline
\end{tabularx}
}

\begin{document}

\workpackage[rightheader={2 person weeks}]{\begin{itemize} \item foo \item foobar \end{itemize}}

\workpackage[rightheader={5 person weeks},prerequisites={a lot}]{\begin{itemize} \item foo \item foobar \end{itemize}}

\end{document}

I leave the table design to the O.P.

Update A little bit nicer/easier to use:

\documentclass{article}
\usepackage[x11names]{xcolor}
\usepackage{tabularx}
\usepackage{xkeyval}

\makeatletter

}

}

\define@key{wpkeys}{prerequisites}{%
\def\prerequisites{#1}
}

\define@key{wpkeys}{contentname}{%
}

\define@key{wpkeys}{prerequisitesname}{%
}

}

}

}

}

% Tabular lengths etc.

\newlength\wp@leftcolumnwidth
\setlength{\wp@leftcolumnwidth}{3cm} % A default value

\define@key{wpkeys}{leftcolumnwidth}{%
\setlength{\wp@leftcolumnwidth}{#1}%
}

\define@key{wpkeys}{arraystretch}{%
\renewcommand{\arraystretch}{#1}%
}

\presetkeys{wpkeys}{%
arraystretch=1.5,
}{}

\newcommand{\workpackage}[2][]{%
\begingroup
\begin{tabularx}{\linewidth}{|p{\wp@leftcolumnwidth}|X|}
\hline
\hline
\hline
\hline
\end{tabularx}
\endgroup
}

\makeatother

\begin{document}

\workpackage[rightheader={2 person weeks}]{\begin{itemize} \item foo \item foobar \end{itemize}}

\workpackage[rightheader={5 person weeks},prerequisites={\begin{itemize} \item A nice list \item that ends \item after three items\end{itemize}}]{\begin{itemize} \item foo \item foobar \end{itemize}}

\end{document}

• cool example. but I don't understand two points. First: the double brackets in the newcommand line [2][] and the #1 in the end of the setkeys line. Why would you then invoke the command giving some arguments in the brackets and some in braces? – Matthias Mar 23 '16 at 13:07
• Ok, understood most of it. There is just no clear rule when to use keys (in brackets) and just the arguments (in curly braces) otherwise. If the pre-requisites are also a list of bullets points, then you would rather use them as an argument and not as keys. – Matthias Mar 23 '16 at 13:39
• @Matthias: The [...] is the optional argument. You can just omit it and then default settings for the key values come into action. (those ones you can set with \setkeys{...}{...,#1}. You see, that #1 occurs there -- i.e. the keys specified in [...] come last, overriding the default ones. – user31729 Mar 23 '16 at 13:46
• Ah, thanks for clarifying. Anyway, the itemize doesn't work for me. It says that maybe an \item is missing although it's there. – Matthias Mar 23 '16 at 13:51
• @Matthias: You can use prerequisites={\begin{itemize} \item ...\end{itemize}} as well. Just use {....} around the whole key value to be on the safe side! Und schönen Gruß nach Österreich! – user31729 Mar 23 '16 at 13:53


text:
14 questions linked to/from Footnote in tabular environment
115 views

### placing a footnote in a table [duplicate]

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33 views

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55k views

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20k views

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11k views

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813 views

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164 views

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27 views

### How can I get footnotes in awesomebox?

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text:
Ratio of money distributed among friends [closed]

Some money (dollars) is divided among friends A,B and C in the ratio of 5:6:9

After A gives fifty dollars to his mother, the ratio becomes 3:4:6

Find the amount of money A has after giving fifty dollars to his mother.

closed as off-topic by Saad, José Carlos Santos, Cesareo, Vidyanshu Mishra, jgonDec 4 '18 at 14:33

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Saad, José Carlos Santos, Cesareo, Vidyanshu Mishra, jgon
If this question can be reworded to fit the rules in the help center, please edit the question.

• What have you tried? – Tito Eliatron Nov 29 '18 at 18:37
• I couldn't find a logic to solve itt. – Wardah Nov 29 '18 at 18:38

The trick here is to observe that ratios are invariant to multiplication, i.e. 5:6:9 expresses the same proportions as 10:12:18 (Just by multiplying every number by 2).

So, given that we have the ratios 5:6:9 and 3:4:6, these can be rewritten as 10:12:18 and 9:12:18 respectively:

\begin{align} \text{Before} \quad 5:6:9 &\iff 10:12:18 \\ \text{After} \quad 3:4:6 &\iff 9:12:18 \end{align}

Now, the problem states that A has given $$\50$$ to his mother, and from the above ratios, we see that this has decreased the ratio from 10 to 9 for A (the ratio between the other two has not changed since they did not receive/give away any money).

This indicates that one unit of the ratio corresponds to $$\50$$.

Since now he has 9 units, he has $$9 \times \50 = \450$$.

• Is there any technique to solve it with simple algebra? – Wardah Nov 29 '18 at 18:57
• Yes, I believe the other answer solves it in an algebraic way. – Sean Lee Nov 29 '18 at 18:59
• I am just a beginer. Found it very hard to understand. As it is not solved completly. – Wardah Nov 29 '18 at 19:02

Hint: Let $$x$$ be the amount $$A$$ has to begin with. Then: $$\dfrac{x}{5} = \dfrac{b}{6}, \dfrac{x-50}{3} = \dfrac{b}{4}$$. Can you solve this system for $$x$$ ? $$b =$$ amount $$B$$ has. To be more specific, isolate $$b$$, and get $$\dfrac{6x}{5} = \dfrac{4(x-50)}{3}$$. Can you take it from here ?.

• I am just a beginer. I tried it but failed to understand. I will be grateful if you could explain it in some depth. – Wardah Nov 29 '18 at 19:03


text:
# Start a new discussion

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## Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMay 3rd 2016

I have added some minimum content to Stiefel manifold, also a little bit to Grassmannian

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeMay 3rd 2016
• (edited May 3rd 2016)

What’s a good account of the CW-structure on Stiefel manifolds compatible with the CW-structure on the Grassmannians? Hatcher’s book discusses really just the latter. On Math.SE here somebody claims that I. M. James’ “The topology of Stiefel manifolds” is a “good reference for this sort of thing”. But there I only see some remarks on pages 5 and 21 of which I am not sure whether they really constitute a good reference for this sort of thing.

• CommentRowNumber3.
• CommentAuthorDavidRoberts
• CommentTimeMay 3rd 2016

Schubert cells in flag manifolds are what I would look up. Don’t know a reference, sadly.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeMay 3rd 2016
• (edited May 3rd 2016)

The cleanest account which I find is in this presentation, on the last slides

• Zbigniew Błaszczyk, On cell decompositions of $SO(n)$ (pdf)
• CommentRowNumber5.
• CommentAuthorDavidRoberts
• CommentTimeMay 4th 2016
• (edited May 4th 2016)

There’s a nice argument in the example on page 58 in these notes that the inclusion $V_n(\mathbb{C}^N) \to V_n(\mathbb{C}^{2N})$ is null-homotopic, for what it’s worth.

• CommentRowNumber6.
• CommentAuthorDavidRoberts
• CommentTimeMay 4th 2016
• (edited May 4th 2016)

Also, Theorem 3.3 in this paper says that the inclusion of unitary groups $i\colon SU(k) \to SU(n)$, $k\lt n$, is cellular, and then 3.3.1 says that the action of $SU(n-m)$ on $SU(n)$ is cellular. I would be then happy to say that $i$ is equivariant relative to the cellular map of groups $SU(k-m) \to SU(n-m)$, and so we have a chance for the inclusion of Stiefel manifolds to be cellular. I guess if we knew that the quotient map itself, $SU(n) \to SU(n)/SU(n-m)$ were cellular, we would probably be done.

EDIT: Ah, I see page 301-302 of Hatcher’s Algebraic Topology that the quotient map $SO(n) \to SO(n)/SO(n-k)$ is cellular, for the cell structure on the Stiefel manifold inherited from the one on $SO(n)$. I would guess this works for both complex and real, and ditto for my first paragraph.

EDIT2: The following is probably not useful.

Page 13-15 in The Topology of CW complexes looks like it gives a cellular structure for the Stiefel manifold (there called $FQ(n,m)$) that would be compatible with inclusions.

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeMay 5th 2016

Thanks!!

I have recorded that here.

(No time for more at the moment.)


text:
## Temporal Abstractions-Augmented Temporally Contrastive Learning: An Alternative to the Laplacian in RL

28 Feb 2022, 19:45 (modified: 18 Jun 2022, 06:11)UAI 2022 PosterReaders: Everyone
Keywords: Graph Laplacian, Unsupervised RL, Task-Agnostic Representation, skill discovery
TL;DR: An alternative to the Laplacian representation without the uniform prior privilege.
Abstract: In reinforcement learning, the graph Laplacian has proved to be a valuable tool in the task-agnostic setting, with applications ranging from skill discovery to reward shaping. Recently, learning the Laplacian representation has been framed as the optimization of a temporally-contrastive objective to overcome its computational limitations in large (or continuous) state spaces. However, this approach requires uniform access to all states in the state space, overlooking the exploration problem that emerges during the representation learning process. In this work, we propose an alternative method that is able to recover, in a non-uniform-prior setting, the expressiveness and the desired properties of the Laplacian representation. We do so by combining the representation learning with a skill-based covering policy, which provides a better training distribution to extend and refine the representation. We also show that a simple augmentation of the representation objective with the learned temporal abstractions improves dynamics-awareness and helps exploration. We find that our method succeeds as an alternative to the Laplacian in the non-uniform setting and scales to challenging continuous control environments. Finally, even if our method is not optimized for skill discovery, the learned skills can successfully solve difficult continuous navigation tasks with sparse rewards, where standard skill discovery approaches are no so effective.
Supplementary Material: zip
4 Replies


text:
# Two sides $\mathrm{AB}$ and $\mathrm{BC}$ and median $\mathrm{AM}$ of one triangle $\mathrm{ABC}$ are respectively equal to sides $\mathrm{PQ}$ and $\mathrm{QR}$ and median $\mathrm{PN}$ of $\triangle \mathrm{PQR}$ (see Fig. 7.40). Show that:(i) $\triangle \mathrm{ABM} \equiv \triangle \mathrm{PQN}$(ii) $\triangle \mathrm{ABC} \cong \triangle \mathrm{PQR}$"

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Given:

Two sides $AB$ and $BC$ and median $AM$ of one triangle $ABC$ are respectively equal to sides $PQ$ and $QR$ and median $PN$ of $\triangle PQR$.

To do:

We have to show that:

(i) $\triangle ABM \cong \triangle PQN$
(ii) $\triangle ABC \cong \triangle PQR$.

Solution:

(i) Given,
$AM$ is the median of  $\triangle ABC$ and $PN$ is the median of $\triangle PQR$

This implies,

$\frac{1}{2}BC=BM$ and $\frac{1}{2}QR=QN$

and also, $BC=QN$

This implies,

$\frac{1}{2}BC=\frac{1}{2}QR$

Therefore,

$BM=QN$

We know that,

According to the Rule of Side-Angle-Side Congruence:

Triangles are said to be congruent if any pair of corresponding sides and their included angles are equal in both triangles.

In $\triangle ABM$ and $PQN$,

We have, $AM=PN$ and $AB=PQ$

We also proved $BM=QN$

Therefore,

$\triangle ABM \cong \triangle PQN$.

(ii) We know that,

According to the Rule of Side-Angle-Side Congruence:

Triangles are said to be congruent if any pair of corresponding sides and their included angles are equal in both triangles.

In $\triangle ABC$ and $PQR$,

We have, $AB=PQ$ and $BC=QR$

By CPCT we know that,

The corresponding parts of congruent triangles: If two triangles are congruent, all of their corresponding angles and sides must be equal.

Therefore,

$\triangle ABC=\triangle PQR$.

Hence, $\triangle ABC \cong \triangle PQR$.

Updated on 10-Oct-2022 13:41:17


text:
# What makes a circuit digital?

I've been trying to understand how a circuit becomes digital. I understand the different between an analog signal and a digital signal, but I don't see where digital circuits come from if all the components are analog.

For instance, this quote from one article:

Most of the fundamental electronic components – resistors, capacitors, inductors, diodes, transistors, and operational amplifiers – are all inherently analog.

Followed by this quote from the same article:

Digital circuits operate using digital, discrete signals. These circuits are usually made of a combination of transistors and logic gates and, at higher levels, microcontrollers or other computing chips.

But logic gates and microcontrollers are made from combinations of the components named above-- analog components.

Do you see my confusion?

• I know that it is common to speak about "digital circuits" and "digital parts". However, a closer look (perhaps a bit pedantic?) could lead to another view: There are no digital circuits or parts. It is more accurat to say: We have a digital application if parts/circuits are operated between two extreme conditions (states). As an example - what is the CMOS-Inverter? Analog or digital? We know, it can be used also as an analog (linear) amplifier – LvW Jul 27 '15 at 8:21
• A circuit is digital if it has fingers. – Nick Johnson Jul 27 '15 at 9:25
• More seriously, the really short answer is: A circuit is digital if its signals operate in exactly two states. – Nick Johnson Jul 27 '15 at 9:26
• Digital means "two states" . These can be considered high/low 1/0 on off true/false. A circuit that depends for its operation on circuits which make and use digital states is a digital circuit. It may use components which use analog technology to generate the digital states but if so they do so atr a lower level which is invisible to the digital abstration. eg a row of doors can each be able to be considred to be either open or shut. We know that there is a continuouslyt linear variable 'analog' path between open and shut but we ignore that when considering them as a digital system. – Russell McMahon Jul 27 '15 at 11:32
• I wouldn't say digital implies "two states." Binary, yes, but I'd consider any system with multiple discrete levels a digital system. – Shamtam Jul 28 '15 at 18:26

First of all, I like the title of the question, "What makes a circuit Digital" ;).

The world around us is analog so the electronics started with exploring the analog components like the ones mentioned by you resistors, capacitors etc. The need for digital circuits was realized when we started building devices like computers, started storing information digitally and many other things.

If you look closely, digital world is based on voltages similar to the analog world. The only difference and the most advantageous feature of digital is that we have reduced the number of variable to just 0 and 1.

Consider a voltage range 0V to 5V.Lets assume that 0V-2.5V is X and 2.5V to 5V is Y. Here we have grouped the voltages in two blocks but the bottom it remains the same. Sam we did with 0 and 1. To make it convenient for ourselves we thought (just for fun!) let X be 0 and Y be 1 and it all started from there. Whether you get a voltage of 1.1V or 2.4V we will interpret is as a 0. Similarly,you get 3.5V or 4.9V it is a 1 for us. This is biggest advantage of digital circuits called Noise Margin.

Since your question was about how a circuit becomes digital, i don't want to get into the technicality much. but if really want to blame someone for this. get hold of this man Claude Shannon. It is believed that it was his article that led to birth of Digital Revolution.

• I understand what you're saying and this helps and makes sense, but I am not completely clear yet. Given the information above, how do you take an analog circuit and make it digital? How do you get it stop treating a signal as analog and start treating it as digital, interpreting the values as either below 2.5V or above 2.5V ? – temporary_user_name Jul 28 '15 at 16:07
• @Aerovistae It's a chicken and egg situation. You define certain things as having to be certain ways, manufacture things so they meet the rules, make decisions based on the rules and the outcomes conform to the rules. Example: A simple two input AND gate which needs inputs 1 & 1 to produce output = 1. Inputs 00 01 10 produce output = 0. If we define 0 = < 20% of Vcc (=supply voltage) and 1 as > 80% of Vcc AND THEN make an ANALOG circuit that will treat an input of up to 30% of Vcc as a 0 and will treat a Vin of > 70% of Vcc as a high then a Vin source that meets the 20%/80% rule will .... – Russell McMahon Jul 29 '15 at 8:19
• ... always drive a cct that accepts up to 30%/70%. So, so far we have a signal which is basically analog BUT limited to certain analog ranges (<20% or > 80%) driving an input that will ALWAYS accept the input as having only two states. ||Now we make the output always make say <= 10% of Vcc if it should be low and > 90% of Vcc if it should be high. This will always drive a 20%/80% nominal cct as if it is either high or low. | Once we have electronic ccts tat obey these constraints we can use them without having tyo know the actual values. ... – Russell McMahon Jul 29 '15 at 8:30
• If we want an output to be low it will in fact be in the range 0-10% of Vcc, we would accept 0-20% of Vcc (so we have some "margin" in the spec relative to the Vinactual - and we drive a cct that will actually work with 0-30% as low so we have a margin between spec and actual Vin acceptance . xxx Once we know that supplied voltageds will ALWAYS fit inside specified Vhi or Vlo levels we can just say Vhi/Vlow, or 1/0 or true /false. Similarly once we have input ccts that will always see inputs as high or low they too can just been seen as 0 or 1 . .... – Russell McMahon Jul 29 '15 at 8:31
• ... NOW build logic circuits built o this 0/1 premise. You can extend this idea to the doors mentioned. Call them always open or shut. Ensure the actual door position is well inside the boundaries for open or shut and you have a digital situation and can make open & shut decisions :-) – Russell McMahon Jul 29 '15 at 8:31

Digital means having or using discrete or discontinuous states.

Modern digital electronic systems are usually binary (employing logic with two states) but ternary (3 state) systems have been built (as have a few systems with even more digital levels per digit.

In a binary 2-state system the two levels can be considered to be:

• high/low 1/0
on off
true/false
etc

A circuit that depends for its operation on circuits which make and use digital states is a digital circuit. It may use components which use analog technology to generate the digital states but if so they do so at a lower conceptual level which is invisible to the digital abstraction.

eg a row of doors can each be able to be considered to be either open or shut.
We know that there is a continuously linear variable 'analog' path between open and shut but we ignore that when considering them as a digital system . We may decide that up to 20 % open = shut.
And that 80%+ open = open.
And that from 20% to 80% open is undefined
And that doors must always be swung rapidly between open and shut
And that transient states from 20% to 80% ignored.

This is EXACTLY what is done with 'analog device' which are used in digital systems. States are low or high and eg <20% high low. > 80% high = high. 20-80% levels are illegal and system always switches rapidly between them.

Digital systems of any complexity tend to be "clocked" with the system changing state when the clock changes state and then being read 1/2 a cycle later.
like "musical chairs" where people change seats when the music plays and must be in a seat when the music stops.

In the case of the doors - one door can have two states ( 0 or 1, open or closed)
Two doors can have 4 states 00 01 10 11
(open open, open closed, closed open, closed closed)
3 doors can have 8 states
8 doors can have 256 states
16 doors can have 65656 8 states
All represented with 1/0 closed/open digital state analog doors.

• @ThePhoton Agh. Yes. Thanks. Brain fade/ corrected. I knew that :-) (of course) but fingers were thinking about levels per bit and brain was elsewhere :-) – Russell McMahon Jul 28 '15 at 14:33
• I understand what you're saying and this helps and makes sense, but I am not completely clear yet. Given the information above, how do you take an analog circuit and make it digital? How do you get it stop treating a signal as analog and start treating it as digital, interpreting the voltage values as either below a threshold or above a threshold, a.k.a. 0 or 1 ? – temporary_user_name Jul 28 '15 at 16:09

"Digital" and "analogue" are sets of design techniques and circuit interpretations. Both are simplifications of the real world focused on particular sets of properties.

You've asked as a clarification comment:

How do you take an analog circuit and make it digital? How do you get it stop treating a signal as analog and start treating it as digital, interpreting the voltage values as either below a threshold or above a threshold, a.k.a. 0 or 1?

There are two parts to this. The first is to recognise that transistors have three operating regions: cutoff, linear, and saturation ("fully on"). Analog designers arrange transistors so they are operating in the linear region. Digital designers arrange them so that the cutoff and saturation modes are used as much as possible.

The second is to consider the way feedback is used. In an amplifier, feedback will generally be negative. This results in an output voltage that's a linear multiple of the input voltage. A fluctuation in the output will be compensated for and the output reduced. In logic gate structures such as the flip-flop, positive feedback is used: being on will drive it more on, and being off will drive it more off. Being in an ambiguous state will drive it to one or the other.

The third is to realise that these are simplifications ("lies told to children"), and that sometimes the analogue properties matter after all. Flip-flops do not like inputs in the middle of their voltage range, and can become oscillators ("metastable"). CMOS inputs consisting of two transistors do not like ambiguous inputs either, and try to be both on and off, resulting in wasted current and possibly damage. Signals described as "on" or "off" do not have a clean edge transition between the two, they have a slope. If you drive it fast enough, they can become a sine wave. Seen in an eye diagram. Digital signals may "ring" like tiny bells.

I'm a Electrical Engineer and this question doesn't make sense to me. Let me start with the basics. Analog circuits use discrete components like Resistors, Capacitors, Inductors, Transistors, Diodes, etc. First of all, all through out school I heard, "Analog is going away, analog is dead". Anyone who says that is a complete idiot. Transistors are inherently analog devices which operate on a convenient digital abstraction to give us the digital functionality we need.

All the traditional RCL (resistor, capacitor, inductor) circuits that are governed by differential equations are analog. ALL real world circuits must use both analog and digital components. The two domains co-exist and you cannot have digital without some analog components.

Your question specifically must be answered in different contexts. (Sorry if you already know some of this!)

From a signal processing context, a signal is in the digital domain once an analog signal has been sampled (such as voice) into the digital domain through an Analog to Digital converter. Look up a typical DSP (digital signal processing) system flow chart. The signal starts analog, gets sampled into the digital domain, gets processed there and finally gets transformed back to analog so humans can understand it. An excellent example of this is your phone.

From a pure logic and computational point of view: Say you wanted to design a vending machine that gives you your drink and dispenses change. Such a semi-thinking machine can be handled entirely in the digital domain using the concept of state machines, which is simply a mapping of all possible events to states that can be coded and stored in memory. For example a nickel is put in, now the machine waits till a dime is put in... and then when the total money that has been put in equals the cost of the drink, the machine dispenses the beverage. However, even to realize such a circuit on a production circuit board you will still have analog components to provide power or capacitors to clean up the power or perhaps resistors to setup (bias) specific voltages for transistors.

Bottom line is when ANY circuit is actually realized into a circuit board you will have some analog components even if the majority of the circuit is 'deemed' digital. I would actually say all circuits are actually entirely analog but some of the components perform analog functions while others provide digital functionality. The digital domain is simply a convenient binary computational abstraction realized over analog components such as transistors and integrated circuits. Remember, our world is entirely analog: we only see, hear and process in analog not digital. There will always be a need to sample and process analog signals from the real world and ultimately present it back to us in analog.

Signals, the way I see it, are digital when you interpret them as different discrete values.

If you see signals in a circuit above 2.5v to be high, and below that as low - then you are interpreting the circuit as digital.

We can't have "true" digital circuits since, like you say, the components and signals are all analog. It's our interpretation that makes it digital.

-

An attempt at an analogy: If you draw a triangle on a piece of paper and someone looks at it, they will surely think it's a triangle. In reality it is just graphite on paper. It's your common interpretation that lets you see something abstract (like shapes or digital circuits) in a non-ideal medium (paper, analog voltages).

• @Mehrdad I never noticed that those were spelt differently. Corrected, thanks. – tehwalris Jul 27 '15 at 10:05

Digital circuits are made of many analog components(like transistors) but are called digital because they behave so,using the 1 and 0 concept.You can't call a microcontroller "analog" just because it's made of analog components.The same thing can be said about ICs who contain logic gates.On the other hand,a single transistor IS analog because it has a wider range of signal manipulation.Beside cut-off and saturation,it can work in active mode(between the two states) and in reverse active mode.In conclusion,you call a component analog or digital analyzing the way it behaves,not by looking at what it's made of.

All circuits are fundamentally analog. Digital is just an approximation of the underlying analog behavior, similar to the small signal model.

With digital circuits, it is common to run components open loop with high gain so they will saturate at the power rail voltage, something that you only really do in analog with comparators.

When you consider a circuit in the digital domain, all of the analog behavior gets boxed up in the propagation delay, rise time, fall time, input and output logic levels, etc. The propagation delay depends on voltage, for example. You can analyze the circuit as an analog circuit and figure out what the relationship is exactly if you want to. Generally it is just measured under different conditions to get as best case and worst case value.

This makes it possible to analyze complex systems to figure out, say, the worst case propagation delay between all of the inputs and outputs. It would be possible to do so with a full analog simulation, but that could take many hours while the digital approximation can be done almost instantly by adding up the worst case delays adding each path. These techniques are used in the software for integrated circuit design to make sure the design will run correctly at a given clock frequency.


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## Intermediate Algebra (12th Edition)

We are given the equation $4x+1=49$. In order to solve, first subtract 1 from both sides. $4x=48$ Divide both sides by 4. $x=12$


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# The central idea of this poem is that a man and his son happily bond while on a fishing trip. Write a paragraph that describes how the

###### Question:

The central idea of this poem is that a man and his son happily bond while on a fishing trip. Write a paragraph that describes how the structure of the poem helps to express this central idea. Use at least three details from the text to support your response.

$The central idea of this poem is that a man and his son happily bond while on a fishing trip. Write$

### I wandered lonely as a cloud That floats on high o'er vales and hills, When all at once I saw a crowd,

I wandered lonely as a cloud That floats on high o'er vales and hills, When all at once I saw a crowd, A host, of golden daffodils; Beside the lake, beneath the trees, Fluttering and dancing in the breeze. Continuous as the stars that shine And twinkle on the milky way, They stretched in never-endin...

I got this wrong (WRITE ANSWER AS SIMPLIFIED FRACTION) please list correct answers thanks $I got this wrong (WRITE ANSWER AS SIMPLIFIED FRACTION) please list correct answers thanks$$I got this wrong (WRITE ANSWER AS SIMPLIFIED FRACTION) please list correct answers thanks$...

### Problem and Solution Whatproblem is the biologist trying tosolve? How is he hoping toaccomplish

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### 5. A total of 64 athletes enter a competition, and of the athletesare gymnasts. Some of the gymnasts perform a vault, and the restperform a floor

5. A total of 64 athletes enter a competition, and of the athletes are gymnasts. Some of the gymnasts perform a vault, and the rest perform a floor routine. The ratio of the number of gymnasts performing a vault to the total number of gymnasts in the competition is 1 : 4. How many gymnasts perform...

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Use the image above to identify and explain the relationship between the segments and circles a and b. in your explanation, be sure to include specific vocabulary and definitions for the relationships. cd...

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# XIII International Workshop on Hadron Physics - XIII Hadron Physics

22-27 March 2015
Hotel do Bosque
Brazil/East timezone

## Electromagnetic form factor for the K meson with a symmetric light-front model

Not scheduled
3h 30m
Hotel do Bosque

#### Hotel do Bosque

Rodovia Mário Covas (Rio-Santos) BR - 101 Sul, Km 533, Angra dos Reis, RJ, Brazil
Poster Field theoretical approaches to QCD

### Speaker

Mr George Yabusaki (UNICSUL)

### Description

The study of the lightest pseudoscalar mesons plays an important role in order to understand the low energy QCD,being the lightest strongly bound quark-antiquark states as well as the Goldstone bosons associated with chiral symmetry breaking. Their static and dynamical properties have also been investigated theoretically and experimentally. With respect to the description of bound states on the light cone, a detailed review of hadronic wave functions in QCD models can be found. Additional important knowledge about the meson's internal structure can be inferred from their valence-quark parton distribution functions. The theoretical framework we adopt is the light-front field theory formalism, more specifically, we here ameliorate the light-front approach, where two classes of quark-antiquark bound-state models for the Bethe-Salpeter amplitude of the K meson must be distinguished: the nonsymmetric and the symmetric vertex model. The light-front component $J^+$ of the electromagnetic current has been successfully used to calculate elastic form factors. For the symmetric vertex model, the components of the current are conveniently obtained in the Drell-Yan frame, where that on the light-cone the bound state wavefunctions are defined on the hypersurface $x^0+x^3 = 0$ and are covariant under kinematical boosts due to the stability of Fock-state decomposition. In this work, we consider the symmetrical quark-antoquark bound-state vertex function with the intention to optimize and unify the parameter set which simultaneously reproduces the K meson decay constants, charge radii and their electromagnetic form factors, for the latter, our numerical results are compared with experimental data up to $10~GeV^2$ in order to explore the validity of the model at large $q^2$ transfer.

### Primary author

Mr George Yabusaki (UNICSUL)

### Co-authors

Dr Ali Paracha (National University of Science and Technology) Prof. Bruno El-Bennich (UNICSUL) Dr Ishtiaq Ahmed (Quaid-I-Azam University) Prof. Joao Pacheco Bicudo Cabral de Melo (UNICSUL)

### Presentation Materials

There are no materials yet.


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Unlimited Plugins, WordPress themes, videos & courses! Unlimited asset downloads! From \$16.50/m

# Introduction to Popmotion: Pointers and Physics

Difficulty:IntermediateLength:ShortLanguages:

Welcome back to the Introduction to Popmotion tutorial series. In part 1, we discovered how to use tweens and keyframes to make precise, time-scheduled animations.

In Part 2, we're going to look at pointer tracking and velocity-based animations.

Pointer tracking allows us to create scrollable product shelves, custom value sliders, or drag-and-drop interfaces.

Velocity-based animations are different to a time-based animation like tween in that the primary property that affects how the animation behaves is velocity. The animation itself might take any amount of time.

We'll look at the three velocity-based animations in Popmotion, springdecay, and physics. We'll use the velocity of the pointer tracking animation to start these animations, and that'll demonstrate how velocity-based animations can create engaging and playful UIs in a way that time-based animations simply can't.

First, open this CodePen to play along.

## Pointer Tracking

Popmotion provides the pointer function to track and output the coordinates of either a mouse or single touch pointer.

Let's import this along with styler, which will allow us to set the position of the ball.

For this example, we want to drag the ball. Let's add an event that will output the pointer's position to the ball:

We'll also want some code to stop tracking when we release the ball:

If you try and drag the ball now, there's an obvious problem. The ball jumps away when we touch it! Not a great user experience.

This is because, by default, pointer outputs the pointer's position relative to the page.

To output the pointer's position relative to another point, in this case the ball's x/y transform, we can simply pass that position to pointer like this:

Now you've made the ball, in very few lines of code, draggable! However, when the user releases the ball, it stops dead.

This isn't satisfying: Imagine a scrollable carousel of products that a user can drag to scroll. If it just stopped dead instead of momentum scrolling, it'd be less pleasurable to use.

It'd be harder, too, because the overall physical effort needed to scroll the carousel would be higher.

To enable animations like this, we first need to know the velocity of the object being thrown.

## Track Velocity

Popmotion provides a function that can help us track velocity. It's called value. Let's import that:

To speak technically for a moment, all of Popmotion's animations are known as actions. Actions are reactive streams of values that can be started and stopped.

A value is, conversely, a reaction. It can't be stopped or started. It just passively responds when its update method is called. It can keep track of values and can be used to query their velocity.

So, after we define ballStyler, let's define a new value for ballXY:

Whenever ballXY updates, we want to update ballStyler. We can pass a second argument to value, a function that will run whenever ballXY updates:

Now we can rewrite our pointer to update ballXY instead of ballStyler.set:

Now, at any pointer, we can call ballXY.getVelocity() and we'll receive the velocities of both x and y, ready to plug into our velocity-based animations.

## Velocity-Based Animations

### spring

The first velocity-based animation to introduce is spring. It's based on the same equations that govern Apple's CASpringAnimation, the spring animation behind all that iOS springy playfulness.

Import:

Now, amend stopTracking so that instead of stopping the pointerTracker animation, it starts a spring animation like this:

We provide it with the ball's current position, its velocity, and a target, and the simulation is run. It changes depending on how the user has thrown the ball.

The cool thing about springs is they're expressive. By adjusting the massstiffness and damping properties, you can end up with radically different spring-feels.

For instance, if you only change the stiffness above to 1000, you can create a motion that feels like high-energy snapping. Then, by changing mass to 20, you create motion that looks almost like gravity.

There's a combination that will feel right and satisfying for your users, and appropriate to your brand, under almost any circumstance. By playing with different spring-feels, you can communicate different feelings, like a strict out-of-bounds snap or a softer affirmative bounce.

### decay

The decay animation, as the name suggests, decays the provided velocity so that the animation gradually slows to a complete stop.

This can be used to create the momentum scrolling effect found on smartphones, like this:

Import the decay function:

And replace the stopTracking function with the following:

decay automatically calculates a new target based on the provided from and velocity props.

It's possible to adjust the feel of the deceleration by messing with the props outlined in the docs linked above but, unlike spring and physicsdecay is designed to work out of the box.

### physics

Finally, we have the physics animation. This is Popmotion's Swiss Army knife of velocity-based animations. With it, you can simulate:

• constant velocity
• acceleration
• springs
• friction

spring and decay offer super-precise motion and a wider variety of "feels". Soon, they'll both also be scrubbable.

But both are immutable. Once you've started either, their properties are set in stone. Perfect for when we want to start an animation based on the initial from/velocity state, but not so good if we want ongoing interaction.

physics, instead, is an integrated simulation closer to that of a video game. It works by, once per frame, taking the current state and then modifying it based on the current properties at that point in time.

This allows it to be mutable, which means we can change those properties, which then changes the outcome of the simulation.

To demonstrate this, let's make a twist on classic pointer smoothing, with elastic smoothing.

Import physics:

This time, we're going to change the startTracking function. Instead of changing ballXY with pointer, we'll use physics:

Here, we're setting from and velocity as normal. friction and springStrength both adjust the properties of the spring.

restSpeed: false overrides the default behaviour of the animation stopping when motion stops. We want to stop it manually in stopTracking.

On its own, this animation won't do anything because we set to, the spring's target, to the same as from. So let's reimplement the pointer tracking this time to change the spring target of physics. On the last line of startTracking, add:

Here, we're using a similar pointer animation as before. Except this time, we're using it to change the target of another animation. In doing so, we create this elasticated pointer tracking:

## Conclusion

Velocity-based animations paired with pointer tracking can create engaging and playful interfaces.

spring can be used to create a wide-variety of spring-feels, while decay is specifically tailored for momentum scroll animations. physics is more limited than either in terms of configurability, but also provides the opportunity to change the simulation in progress, opening new interaction possibilities.

In the next and final part of this introductory series on Popmotion, we're going to take everything we've learned in the first two parts and use them along with some light functional composition to create a scrubbable animation, along with a scrubber to do the scrubbing with!


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# Multinomial distribution

polynomial distribution

2010 Mathematics Subject Classification: Primary: 60E99 [MSN][ZBL]

The joint distribution of random variables $X _ {1} \dots X _ {k}$ that is defined for any set of non-negative integers $n _ {1} \dots n _ {k}$ satisfying the condition $n _ {1} + \dots + n _ {k} = n$, $n _ {j} = 0 \dots n$, $j = 1 \dots k$, by the formula

$$\tag{* } {\mathsf P} \{ X _ {1} = n _ {1} \dots X _ {k} = n _ {k} \} = \ \frac{n!}{n _ {1} ! \dots n _ {k} ! } p _ {1} ^ {n _ {1} } \dots p _ {k} ^ {n _ {k} } ,$$

where $n, p _ {1} \dots p _ {k}$( $p _ {j} \geq 0$, $\sum p _ {j} = 1$) are the parameters of the distribution. A multinomial distribution is a multivariate discrete distribution, namely the distribution for the random vector $( X _ {1} \dots X _ {k} )$ with $X _ {1} + \dots + X _ {k} = n$( this distribution is in essence $( k- 1)$- dimensional, since it is degenerate in the Euclidean space of $k$ dimensions). A multinomial distribution is a natural generalization of a binomial distribution and coincides with the latter for $k = 2$. The name of the distribution is given because the probability (*) is the general term in the expansion of the multinomial $( p _ {1} + \dots + p _ {k} ) ^ {n}$. The multinomial distribution appears in the following probability scheme. Each of the random variables $X _ {i}$ is the number of occurrences of one of the mutually exclusive events $A _ {j}$, $j = 1 \dots k$, in repeated independent trials. If in each trial the probability of event $A _ {j}$ is $p _ {j}$, $j = 1 \dots k$, then the probability (*) is equal to the probability that in $n$ trials the events $A _ {1} \dots A _ {k}$ will appear $n _ {1} \dots n _ {k}$ times, respectively. Each of the random variables $X _ {j}$ has a binomial distribution with mathematical expectation $np _ {j}$ and variance $np _ {j} ( 1- p _ {j} )$.

The random vector $( X _ {1} \dots X _ {k} )$ has mathematical expectation $( np _ {1} \dots np _ {k} )$ and covariance matrix $B = \| b _ {ij} \|$, where

$$b _ {ij} = \left \{ \begin{array}{ll} np _ {i} ( 1- p _ {i} ), & i = j, \\ - np _ {i} p _ {j} , & i \neq j, \\ \end{array} \ \ i, j = 1 \dots k \right .$$

(the rank of the matrix $B$ is $k- 1$ because $\sum _ {i=} 1 ^ {k} n _ {i} = n$). The characteristic function of a multinomial distribution is

$$f( t _ {1} \dots t _ {k} ) = \left ( p _ {1} e ^ {it _ {1} } + \dots + p _ {k} e ^ {it _ {k} } \right ) ^ {n} .$$

For $n \rightarrow \infty$, the distribution of the vector $( Y _ {1} \dots Y _ {k} )$ with normalized components

$$Y _ {i} = \ \frac{X _ {i} - np _ {i} }{\sqrt {np _ {i} ( 1- p _ {i} ) } }$$

tends to a certain multivariate normal distribution, while the distribution of the sum

$$\sum _ { i= } 1 ^ { k } ( 1 - p _ {i} ) Y _ {i} ^ {2}$$

(which is used in mathematical statistics to construct the "chi-squared" test) tends to the "chi-squared" distribution with $k- 1$ degrees of freedom.

#### References

 [C] H. Cramér, "Mathematical methods of statistics" , Princeton Univ. Press (1946) MR0016588 Zbl 0063.01014


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# Elliptic functions

1. Jul 16, 2012

### Nilupa

∫(1/sqrt(1-(2/x)-((x^2)/3)))dx

2. Jul 16, 2012

### chiro

Hey Nilupa and welcome to the forums.

Try multiplying the integral by x/x and factor out the denominators with x in it (i.e. get rid of the 2/x term and make all terms in the square root positive powers of x).

3. Jul 17, 2012

### Nilupa

Thank you,, I did that. but,it is still impossible...


text:
## Found 86,942 Documents (Results 1–100)

100
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MSC:  30D35 39A05 39A10
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### Inclusion results on subclasses of harmonic univalent functions associated with Pascal distribution series. (English)Zbl 07589566

MSC:  30C45 30C50 30C80
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MSC:  30C45
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### Faber polynomial coefficient estimates for certain subclass of bi-univalent functions associated with $$(p,q)$$-Ruscheweyh derivative. (English)Zbl 07589554

MSC:  30C45 30C50
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### On the growth measures of entire functions focusing their generalized relative order $$(\alpha, \beta)$$ and generalized relative type $$(\alpha, \beta)$$. (English)Zbl 07589548

MSC:  30D35 30D30 30D20
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MSC:  30C45
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### Complex symmetry of linear combinations of composition operators on the Fock space. (English)Zbl 07589463

MSC:  47B33 30H20 47B15
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### Coronizations and big pieces in metric spaces. (Construction en couronnes et grands morceaux dans des espaces métriques.) (English. French summary)Zbl 07589436

MSC:  28A75 30L99 43A85
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### Fekete-Szegő inequality for classes of analytic functions connected with the $$(p,q)$$-derivative. (English)Zbl 07589101

MSC:  30C45 30C50
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### Path connectedness of Volterra type integral operators on Bergman and Dirichlet type spaces. (English)Zbl 07589100

MSC:  30B40 30D10
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### Coefficient problems of a class of $$q$$-starlike functions associated with $$q$$-analogue of Al-Oboudi-Al-Qahtani integral operator and nephroid domain. (English)Zbl 07589099

MSC:  30C45 30C50
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MSC:  30D35
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MSC:  30D35
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### Exact essential norm of generalized Hilbert matrix operators on classical analytic function spaces. (English)Zbl 07588413

MSC:  47B38 30H20
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### The over-determined boundary value problems and convolution type integral transformations. (English)Zbl 07588345

MSC:  30-XX 44Axx 35Nxx
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### Basic applications of the $$q$$-derivative for a general subfamily of analytic functions subordinate to $$k$$-Jacobsthal numbers. (English)Zbl 07588237

MSC:  11B39 30C45 33D15
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### On strongly starlike functions related to the Bernoulli lemniscate. (English)Zbl 07588045

MSC:  30C45 30C80
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### Infinite order of growth of solutions of second order linear differential equations. (English)Zbl 07588038

MSC:  34M10 30D35
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### On the dimension of Bergman spaces on $$\mathbb{P}^1$$. (English)Zbl 07587851

MSC:  32A36 32L05 30F99
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### Uniformization of Riemann surfaces revisited. (English)Zbl 07587843

MSC:  30F10 53Bxx
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### Preorders on subharmonic functions and measures with applications to the distribution of zeros of holomorphic functions. (English)Zbl 07587455

MSC:  32Axx 30Dxx 31Bxx
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### On indicator and type of an entire function with roots lying on a ray. (English)Zbl 07587450

MSC:  30Dxx 30Cxx 30Bxx
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MSC:  30C45
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### Linear differential polynomials sharing a set $$IM$$. (English)Zbl 07587204

MSC:  30D35 30D30
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MSC:  30C45
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### Hankel determinant for a subclass of analytic functions associated with generalized struve function of order $$p$$ bounded by conical regions. (English)Zbl 07587185

MSC:  30C45 30C45 33E99
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### Coefficient estimates of bi-Bazilevič functions defined by $$q$$-Ruscheweyh differential operator associated with Horadam polynomials. (English)Zbl 07587180

MSC:  30C45 30C50
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### Multipliers on class of Dirichlet series having vector valued frequencies. (English)Zbl 07587170

MSC:  30B50 30D15
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### Certain subclasses of multivalent functions associated with $$q$$-analogue of Mittag Leffler functions. (English)Zbl 07587164

MSC:  30C45 30C50
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MSC:  30D35
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### Corrigendum to: “Some properties of meromorphically uniformly convex functions defined by Hurwitz-Lerch zeta function”. (English)Zbl 07587145

MSC:  30C45 30C80
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MSC:  30D35
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### $$\phi$$-relative order and $$\phi$$-relative type of meromorphic functions in $$\mathbb{C}$$. (English)Zbl 07586609

MSC:  30D30 30D35
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### Some remarks on primeness and dynamics of some classes of entire functions. (English)Zbl 07586607

MSC:  30D15 37F10
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### Inequalities of Erdős-Lax-type for a complex polynomial. (English)Zbl 07586599

MSC:  30A10 30C10 30C15
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### Quasiconformal harmonic mappings between the unit ball and a spatial domain with $$C^{1, \alpha}$$ boundary. (English)Zbl 07585802

MSC:  30C65 31B05
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### Linear combination of composition operators on Bergman and Korenblum spaces. (English)Zbl 07585800

MSC:  47B33 30H20
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### Harmonic spirallike functions and harmonic strongly starlike functions. (English)Zbl 07585785

MSC:  30C55 30C45 31A05
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### Slice conformality and Riemann manifolds on quaternions and octonions. (English)Zbl 07585684

MSC:  30G35 30C35 30F99
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### Rigidity estimates for isometric and conformal maps from $$\mathbb{S}^{n-1}$$ to $$\mathbb{R}^n$$. (English)Zbl 07585649

MSC:  26D10 30C70 49Q20
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### A note on Hadamard-Bergman convolution operators. (English)Zbl 07585486

MSC:  30H99 47G40 47B35
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### Coefficient functionals for alpha-convex functions associated with the exponential function. (English)Zbl 07585483

MSC:  30C45 30C50 30C55
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### Affine transformations of hyperbolic number plane. (English)Zbl 07585482

MSC:  15A04 28A80 30D05
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### Rigidity of Newton dynamics. (English)Zbl 07585353

MSC:  30D05 37F10 37F20
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### On the generalized growth and approximation of entire solutions of certain elliptic partial differential equation. (English)Zbl 07585336

MSC:  41A15 30B10
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MSC:  30H10
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### Fekete-Szegö problem for univalent mappings in one and higher dimensions. (English)Zbl 07584829

MSC:  30Cxx 32Hxx 32Axx
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### Joint approximation by non-linear shifts of Dirichlet $$L$$-functions. (English)Zbl 07584827

MSC:  11Mxx 11-XX 30Exx
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### Meromorphic solutions of autonomous ordinary differential equations without the finiteness property. (English)Zbl 07584819

MSC:  34Mxx 34Axx 30Dxx
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### Multiplicative property of the series used in the Nevanlinna-Pick problem. (English. Russian original)Zbl 07584670

Vestn. St. Petersbg. Univ., Math. 55, No. 1, 27-33 (2022); translation from Vestn. St-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 9(67), No. 1, 37-45 (2022).
MSC:  47-XX 30-XX 30Exx
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### Properties of sine series in weighted spaces. (English. Russian original)Zbl 07584502

Mosc. Univ. Math. Bull. 77, No. 2, 49-66 (2022); translation from Vestn. Mosk. Univ., Ser. I 77, No. 2, 3-17 (2022).
MSC:  30-XX 42Axx 42Bxx
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### Carleman’s formula for solutions of generalized Cauchy-Riemann systems in multidimensional spatial domains. (English. Russian original)Zbl 07584488

J. Math. Sci., New York 265, No. 1, 90-102 (2022); translation from Sovrem. Mat., Fundam. Napravl. 65, No. 1, 95-108 (2019).
MSC:  35Jxx 35Axx 30Gxx
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### Starlike functions associated with a petal shaped domain. (English)Zbl 07584458

MSC:  30C80 30C45
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### Uniqueness of meromorphic solutions of a certain type of difference equations. (English)Zbl 07584446

MSC:  39A45 30D35
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MSC:  30C45
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MSC:  30C45
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### On the asymptotics of counting functions for Ahlfors regular sets. (English)Zbl 07584114

MSC:  30L99 28A80
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### Generic power series on subsets of the unit disk. (English)Zbl 07584092

MSC:  30B30 28A05 54H05
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### $$L_{p}$$ inequalities for the growth of polynomials with restricted zeros. (English)Zbl 07584087

MSC:  26D10 41A17 30C15
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### Studies on fuzzy PID control method based on improved variational threshold. (English)Zbl 07584059

MSC:  30B60 93C62
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### Counting hyperbolic multigeodesics with respect to the lengths of individual components and asymptotics of Weil-Petersson volumes. (English)Zbl 07584044

MSC:  30F60 32G15
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### Effective bilipschitz bounds on drilling and filling. (English)Zbl 07584041

MSC:  30F40 57K10 57K32
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