text:
• ### The 72-Hour WEBT Microvariability Observation of Blazar S5 0716+714 in 2009(1310.4670)

Oct. 17, 2013 astro-ph.HE
Context. The international whole earth blazar telescope (WEBT) consortium planned and carried out three days of intensive micro-variability observations of S5 0716+714 from February 22, 2009 to February 25, 2009. This object was chosen due to its bright apparent magnitude range, its high declination, and its very large duty cycle for micro-variations. Aims. We report here on the long continuous optical micro-variability light curve of 0716+714 obtained during the multi-site observing campaign during which the Blazar showed almost constant variability over a 0.5 magnitude range. The resulting light curve is presented here for the first time. Observations from participating observatories were corrected for instrumental differences and combined to construct the overall smoothed light curve. Methods. Thirty-six observatories in sixteen countries participated in this continuous monitoring program and twenty of them submitted data for compilation into a continuous light curve. The light curve was analyzed using several techniques including Fourier transform, Wavelet and noise analysis techniques. Those results led us to model the light curve by attributing the variations to a series of synchrotron pulses. Results. We have interpreted the observed microvariations in this extended light curve in terms of a new model consisting of individual stochastic pulses due to cells in a turbulent jet which are energized by a passing shock and cool by means of synchrotron emission. We obtained an excellent fit to the 72-hour light curve with the synchrotron pulse model.
• ### Asteroids' physical models from combined dense and sparse photometry and scaling of the YORP effect by the observed obliquity distribution(1301.6943)

Jan. 29, 2013 astro-ph.EP
The larger number of models of asteroid shapes and their rotational states derived by the lightcurve inversion give us better insight into both the nature of individual objects and the whole asteroid population. With a larger statistical sample we can study the physical properties of asteroid populations, such as main-belt asteroids or individual asteroid families, in more detail. Shape models can also be used in combination with other types of observational data (IR, adaptive optics images, stellar occultations), e.g., to determine sizes and thermal properties. We use all available photometric data of asteroids to derive their physical models by the lightcurve inversion method and compare the observed pole latitude distributions of all asteroids with known convex shape models with the simulated pole latitude distributions. We used classical dense photometric lightcurves from several sources and sparse-in-time photometry from the U.S. Naval Observatory in Flagstaff, Catalina Sky Survey, and La Palma surveys (IAU codes 689, 703, 950) in the lightcurve inversion method to determine asteroid convex models and their rotational states. We also extended a simple dynamical model for the spin evolution of asteroids used in our previous paper. We present 119 new asteroid models derived from combined dense and sparse-in-time photometry. We discuss the reliability of asteroid shape models derived only from Catalina Sky Survey data (IAU code 703) and present 20 such models. By using different values for a scaling parameter cYORP (corresponds to the magnitude of the YORP momentum) in the dynamical model for the spin evolution and by comparing synthetics and observed pole-latitude distributions, we were able to constrain the typical values of the cYORP parameter as between 0.05 and 0.6.
• ### The Recently-Discovered Dwarf Nova System ASAS J002511+1217.2: A New WZ Sagittae Star(astro-ph/0510078)

Jan. 15, 2006 astro-ph
The cataclysmic variable ASAS J002511+1217.2 was discovered in outburst by the All-Sky Automated Survey in September 2004, and intensively monitored by AAVSO observers through the following two months. Both photometry and spectroscopy indicate that this is a very short-period system. Clearly defined superhumps with a period of 0.05687 +/- 0.00001 days (1-sigma) are present during the superoutburst, 5 to 18 days following the ASAS detection. We observe a change in superhump profile similar to the transition to late superhumps'' observed in other short-period systems; the superhump period appears to increase slightly for a time before returning to the original value, with the resulting superhump phase offset by approximately half a period. We detect variations with a period of 0.05666 +/- 0.00003 days (1-sigma) during the four-day quiescent phase between the end of the main outburst and the single echo outburst. Weak variations having the original superhump period reappear during the echo and its rapid decline. Time-resolved spectroscopy conducted nearly 30 days after detection and well into the decline yields an orbital period measurement of 82 +/- 5 minutes. Both narrow and broad components are present in the emission line spectra, indicating the presence of multiple emission regions. The weight of the observational evidence suggests that ASAS J002511+1217.2 is a WZ Sge-type dwarf nova, and we discuss how this system fits into the WZ classification scheme.


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# prioritylasso Vignette

## Introduction

prioritylasso was developed for situations in which different types of high dimensional omics-data in combination with clinical data are available. We want to include these so called blocks of data together in a prediction model. prioritylasso thereby tries to find a good compromise between prediction accuracy and practical aspects. This is done by letting the practitioner include prior knowledge in the form of priorities, which define the importance of every block. The priorities can be chosen in several different ways.
The model is successively calculated as LASSO-based, while the Linear Predictor after each fit is taken as an Offset in the LASSO Regression of the block with the next lowest priority. The Penalized Regression models are computed via the R package glmnet. Moreover, the R package survival is used when the outcome consists of survival data. In addition to the main function, the package prioritylasso contains an extension of the standard function named cvm_prioritylasso. It is also explained under practical aspects in the following examples.

## Getting started with prioritylasso

The data we will use for the examples was simulated and shall represent AML data with 4 blocks of variables. We first have to load the package which contains this data set.

library(prioritylasso)

To take a deeper look at the data, open the description through ?pl_data. The different types of data are all stored together. To get and define the block structure which implies the priorities, we look at the names of the variables and the matrix dimension.

dim(pl_data)
## [1]  400 1029
colnames(pl_data)[1:30]
##  [1] "b1.1"  "b1.2"  "b1.3"  "b1.4"  "b2.1"  "b2.2"  "b2.3"  "b2.4"  "b2.5"
## [10] "b3.1"  "b3.2"  "b3.3"  "b3.4"  "b3.5"  "b3.6"  "b3.7"  "b3.8"  "b3.9"
## [19] "b3.10" "b3.11" "b3.12" "b3.13" "b3.14" "b3.15" "b3.16" "b3.17" "b3.18"
## [28] "b3.19" "b4.1"  "b4.2"
colnames(pl_data)[1025:1029]
## [1] "b4.997"  "b4.998"  "b4.999"  "b4.1000" "pl_out"

We see that the last column contains the outcome. We will re-save the outcome and the matrix of predictors separately and define the argument blocks afterwards. We will need that for the application of prioritylasso where the indices have to correspond with the variables in the predictor matrix.

pl_out <- pl_data[,1029]
pl_pred <- pl_data[,1:1028]
blocks <- list(bp1=1:4, bp2=5:9, bp3=10:28, bp4=29:1028)

For an easier interpretation, we can consider the first block as clinical variables of most importance, the second block as other clinical data, and the third block as mutations. These blocks are all low-dimensional. That will later be an advantage regarding computation time. Another type of data is high dimensional gene expression data. Moreover, pl_out consists of a binary outcome for 400 subjects. Before we go further we want to split the data into training and validation set. The training set should be used to build the model with prioritylasso while the validation data should later be used to assess the prediction accuracy in an independent data set. Here we just do a random split such that 2/3 of the data belongs to the training set and 1/3 to the validation set.

set.seed(1234)
label <- sample(dim(pl_pred)[1],round(dim(pl_pred)[1]*(2/3)))
pl_train <- pl_pred[label,]
pl_val <- pl_pred[-label,]
pl_out_train <- pl_out[label]
pl_out_val <- pl_out[-label]

We can now run prioritylasso for the first time.

set.seed(1234)
pl1 <- prioritylasso(X = pl_train, Y = pl_out_train, family = "binomial", type.measure = "auc",
blocks = blocks, standardize = FALSE)

Because we have a binary outcome, we specified family = "binomial" and type.measure = "auc". The priority structure was given through the block definition in the data set. An extended use of the block definition and the general functionality of prioritylasso will be given in the following sections.

## prioritylasso - extended application

#### Specifying the priorities

If we want to specify another block order, we have to redefine the argument blocks. Let us assume that we do not want to include the variables b1 first in the model, but b3 first, b1 second and b2 third. That would be done by blocks = list(bp1 = 10:28, bp2 = 1:4, bp3 = 5:9, bp4 = 29:1028). So the position on the list indicates when the variables are considered in the model or in other words, the priority. It is not necessary to name the entries of the list, but it may help in avoiding confusion. We chose the names such that “bp1”" means “block of priority 1”.

set.seed(1234)
pl2 <- prioritylasso(X = pl_train, Y = pl_out_train, family = "binomial", type.measure = "auc",
block1.penalization = TRUE, blocks = list(10:28, 1:4, 5:9,  29:1028),
standardize = FALSE)
pl2$nzero ## [[1]] ## [1] 15 ## ## [[2]] ## [1] 4 ## ## [[3]] ## [1] 0 ## ## [[4]] ## [1] 25 The output lists are to be interpreted according to the definition in blocks. Therefore, the first entry corresponds to the variables of columns 10:28 in the data set. #### Set a maximal number of nonzero coefficients. As we can see in pl2, we have a lot of nonzero coefficients of bp4, although it is the block with lowest priority. In general, there should be a reason why the glmnet procedure chooses these coefficients. On the other hand, it is sometimes not appropriate from a practical point of view that the number exceeds a particular value. Therefore we made it possible to set a maximal number of nonzero coefficients. Because we just want to set a limit for bp4, we set the other entries to Inf. set.seed(1234) pl3 <- prioritylasso(X = pl_train, Y = pl_out_train, family = "binomial", type.measure = "auc", block1.penalization = TRUE, blocks = list(10:28, 1:4, 5:9, 29:1028), max.coef = c(Inf, Inf, Inf, 10), standardize = FALSE) pl3$nzero
## [[1]]
## [1] 15
##
## [[2]]
## [1] 4
##
## [[3]]
## [1] 0
##
## [[4]]
## [1] 10

#### Include the block with the highest priority without a penalty

We can further diversify the option of whether or not bp1 is included without a penalty in the model. In a not penalized version, the block has to be low-dimensional and the model includes all of its variables. In this case, the model fit is stored in block1unpen. Otherwise, the block is treated like the other blocks and a LASSO model is fitted.

set.seed(1234)
pl4 <- prioritylasso(X = pl_train, Y = pl_out_train, family = "binomial", type.measure = "auc",
block1.penalization = FALSE, blocks = list(1:4, 5:9, 10:28, 29:1028),
max.coef = c(Inf, Inf, Inf, 10), standardize = FALSE)
pl4$block1unpen ## ## Call: glm(formula = Y ~ X[, blocks[[1]]], family = family, weights = weights) ## ## Coefficients: ## b1.1 b1.2 b1.3 b1.4 ## 0.1683 1.0135 0.9081 1.0682 0.3760 ## ## Degrees of Freedom: 266 Total (i.e. Null); 262 Residual ## Null Deviance: 351 ## Residual Deviance: 336.8 AIC: 346.8 pl4$lambda.ind
## [[1]]
## NULL
##
## [[2]]
## [1] 5
##
## [[3]]
## [1] 10
##
## [[4]]
## [1] 14

The first entries of the values which correspond to the blocks list remain empty as you can see for the example of lambda.ind.

#### Options for the cross validation procedure

nfolds and lambda.type are options which refer to the cross-validation procedure in cv.glmnet. nfolds specifies the number of folds in the procedure while lambda.type handles the amount of cross-validation error. It can be set to either lambda.min, which is also the default, or lambda.1se. lambda.min gives the result with minimum mean cross-validation error, whereas lambda.1se gives the result such that the cross-validation error is within 1 standard error of the minimum, and thus leads to more sparse results. Note that the latter can only be chosen in combination with no restrictions in max.coef.

set.seed(1234)
pl5_min <- prioritylasso(X = pl_train, Y = pl_out_train, family = "binomial",
type.measure = "auc", block1.penalization = TRUE,
blocks = list(1:4, 5:9, 10:28, 29:1028),
lambda.type = "lambda.min", standardize = FALSE)

set.seed(1234)
pl5_1se <- prioritylasso(X = pl_train, Y = pl_out_train, family = "binomial",
type.measure = "auc", block1.penalization = TRUE,
blocks = list(1:4, 5:9, 10:28, 29:1028),
lambda.type = "lambda.1se", standardize = FALSE)

pl5_min$nzero ## [[1]] ## [1] 4 ## ## [[2]] ## [1] 1 ## ## [[3]] ## [1] 5 ## ## [[4]] ## [1] 57 pl5_1se$nzero
## [[1]]
## [1] 4
##
## [[2]]
## [1] 0
##
## [[3]]
## [1] 1
##
## [[4]]
## [1] 15

In addition, other options for prioritylasso can be specified. For example, we can change the type of cross validation measurement for binary outcome to the misclassification error. Examples for other outcome variables are shown in the function documentation. Further arguments can be passed to prioritylasso which are used in cv.glmnet, e.g. the elasticnet mixing parameter. Here, we are only using the default value 1 which corresponds to the standard LASSO method, but a parameter alpha between 0 and 1 can be chosen as well.

#### Some notes on the output

The function used for every LASSO fit is glmnet which creates a sequence of lambda values. The lambda which is chosen according to lambda.type is the lambda on position lambda.ind of the sequence and its value is stored in lambda.min. In general, the lower the value of lambda.ind, the higher the lambda.min and thus the penalization. This leads to more sparse models. The number of lambda values can be chosen with an optional argument. We give the output of pl1 as an example.

pl1$lambda.ind ## [[1]] ## [1] 34 ## ## [[2]] ## [1] 5 ## ## [[3]] ## [1] 8 ## ## [[4]] ## [1] 50 pl1$lambda.min
## [[1]]
## [1] 0.001150484
##
## [[2]]
## [1] 0.05165214
##
## [[3]]
## [1] 0.01300162
##
## [[4]]
## [1] 0.02032733

The values of lambda are generated in every call of glmnet and hence cannot be compared. The corresponding mean cross validated error is stored in the list min.cvm. The interpretation of its values depend on the argument type.measure. In our examples with a binary outcome it is usually the area under the ROC curve (AUC).

pl1$min.cvm ## [[1]] ## [1] 0.6610836 ## ## [[2]] ## [1] 0.6396907 ## ## [[3]] ## [1] 0.674019 ## ## [[4]] ## [1] 0.8356987 We see that for the example of pl1 it grows with the number of considered modalities. That is what we expected because the more coefficients we have in our model, the better the prediction should be. ## Use of the function cvm_prioritylasso prioritylasso was generally implemented with the idea, that practitioners have prior knowledge about the data that allows them to specify the priorities. However, it might be, especially in the presence of several blocks, that it is not clear which order of blocks is the best. That is why we implemented cvm_prioritylasso that allows us to define more than one possible list of blocks. The function chooses the best block order according to the mean cross-validated error. Analogously, several vectors with maximal coefficients can be specified in max.coef.list. In the next example we do not know if it is better to include variables b4 before those of b3. set.seed(1234) cvm_pl1 <- cvm_prioritylasso(X = pl_train, Y = pl_out_train, family = "binomial", type.measure = "auc", standardize = FALSE, block1.penalization = FALSE, blocks.list = list(list(1:4, 5:9, 10:28, 29:1028), list(1:4, 5:9, 29:1028, 10:28)), max.coef.list = list(c(Inf, Inf, Inf, 10), c(Inf, Inf, 10, Inf))) cvm_pl1$best.blocks
## [1] "bp1 = 1:4"     "bp2 = 5:9"     "bp3 = 29:1028" "bp4 = 10:28"

We see that the order of blocks which leads to the best result is specified first in blocks.list. It might be inconvenient to define a lot of lists in the block argument. Note that it is not the general idea of prioritylasso to be applied to any order of blocks and fish for the best.

## Validation

Now we give a detailed example with a validation.

set.seed(1234)
pl_fit1 <- prioritylasso(X = pl_train, Y = pl_out_train, family = "binomial",
type.measure = "auc", blocks = list(1:4, 5:9, 10:28, 29:1028),
block1.penalization = FALSE, max.coef = c(Inf, Inf, Inf, 10),
standardize = FALSE)

The idea before simulating the data was to include it in the order as it was defined in the data matrix. The first block, a block with only 4 variables should not be penalized. Because of prior knowledge (we have it because we generated the data, normally a practitioner could have it, too) we know that all of its variables are relevant. The maximal number of coefficients for the last block is restricted to 10. We can easily extract the coefficients and print those which are nonzero.

coeff1 <- pl_fit1$coefficients coeff1 <- coeff1[coeff1 != 0] print(round(coeff1, 4)) ## b1.1 b1.2 b1.3 b1.4 b2.3 b3.2 b3.3 b3.4 b3.7 ## 0.1683 1.0135 0.9081 1.0682 0.3760 0.1123 0.3115 -0.4062 0.8406 -0.2676 ## b3.11 b4.1 b4.8 b4.106 b4.269 b4.549 b4.623 b4.748 b4.831 b4.977 ## 0.1103 0.0056 0.0615 0.0407 0.0516 0.0056 0.0863 0.0211 0.0012 0.2553 We see that every variable from block 1 is nonzero, but we also have variables from every other block in our model. library(pROC) The R package pROC gives a lot possibilities to evaluate and visualize the results. First we can calculate the score and the ROC curve in the training set and get an AUC value. pl1_score <- pl_train[ , names(coeff1)[-1], drop=F] %*% coeff1[-1] pl1_roc <- roc(factor(pl_out_train), pl1_score[,1]) ## Setting levels: control = 0, case = 1 ## Setting direction: controls < cases auc(pl1_roc) ## Area under the curve: 0.8318 Of course we can’t use this as a performance measure because it is estimated based on the data that was already used for training the model and is thus biased. A more appropriate value can be obtained with the test set. val1_score <- pl_val[ , names(coeff1)[-1], drop=F] %*% coeff1[-1] val1_roc <- roc(factor(pl_out_val), c(val1_score)) ## Setting levels: control = 0, case = 1 ## Setting direction: controls < cases auc(val1_roc) ## Area under the curve: 0.6471 To investigate the influence of the priorities on the prediction accuracy, we can calculate the model again with another order of blocks and get the ROC curve in the same way. set.seed(1234) pl_fit2 <- prioritylasso(X = pl_train, Y = pl_out_train, family = "binomial", type.measure = "auc", blocks = list(1:4, 10:28, 5:9, 29:1028), block1.penalization = FALSE, max.coef = c(Inf, Inf, Inf, 10), standardize = FALSE) coeff2 <- pl_fit2$coefficients
coeff2 <- coeff2[coeff2 != 0]

val2_score <- pl_val[ , names(coeff2)[-1], drop=F] %*% coeff2[-1]
val2_roc <- roc(factor(pl_out_val), c(val2_score))
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
auc(val2_roc)
## Area under the curve: 0.6394

We can plot the ROC curves and perform a paired test if the two AUC values are equal.

roc.test(val1_roc, val2_roc, paired=TRUE)
##
##  DeLong's test for two correlated ROC curves
##
## data:  val1_roc and val2_roc
## Z = 0.90554, p-value = 0.3652
## alternative hypothesis: true difference in AUC is not equal to 0
## sample estimates:
## AUC of roc1 AUC of roc2
##   0.6470588   0.6394070

The test result shows that we cannot reject the hypotheses that the AUC values are equal.

plot.roc(val1_roc, grid=0.1)
col=c("black", "red"), lwd=2)

format: plain


text:
Lemma 37.62.6. Let $X \to Y$ and $Y' \to Y$ be morphisms of schemes and let $X' = Y' \times _ Y X$ be the base change of $X$.

1. If $X \to X \times _ Y X$ is flat, then $X' \to X' \times _{Y'} X'$ is flat.

2. If $X \to Y$ is weakly étale, then $X' \to Y'$ is weakly étale.

Proof. Assume $X \to X \times _ Y X$ is flat. The morphism $X' \to X' \times _{Y'} X'$ is the base change of $X \to X \times _ Y X$ by $Y' \to Y$. Hence it is flat by Morphisms, Lemmas 29.25.8. This proves (1). Part (2) follows from (1) and the fact (just used) that the base change of a flat morphism is flat. $\square$

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# How to end the game after the player has defeated all the enemies in Game Maker?

I'm making a simple version of the game asteroids as I'm learning how to develop with Game Maker Studio. Currently, mostly everything works properly except that when the player destroys all of the asteroids, I need the game to exit.

I've tried add the following line of script to the step event for the asteroid, but it resulted in a runtime error:

if (!instance_exists(obj))
game_end();

This is a pretty simple problem but I haven't been able to find the answer on Google. What code should I add to check for any instances of asteroids and then to end the game when there are none?

One idea is to keep an array that tracks all of your asteroids. Every time you create an asteroid, add it to the array, and every time an asteroid is destroyed, remove it from the array. You can then use this function to check how many asteroids currently exist. If the answer is 0, end the game.

Someone who knows the GML API better might have a better solution, but this should certainly work. This method has the added benefit that you can check the number of asteroids in existence at any time; you could have a counter on the corner of your screen that tells the user how they're doing.

• Thanks for the response! Do you know where I could store this file (i.e. which event to add the script)? If it would be in the create event, would I just have code in the script to basically add the current instance to the array? I'm assuming then that the check for the array length would go in the step event for the asteroid? – loremIpsum1771 Feb 10 '16 at 22:36
• It depends how you're creating the asteroids. If you have a "Controller" object that has a line of code to create an asteroid, I would add the asteroid to the array at that same spot. If the asteroids aren't created, but instead start off in the room, then I think your only option is to use the create event in the asteroid object. As for the check, I wouldn't put it in the asteroid's step event, because then you'd have every asteroid checking the same thing (inefficiency). I would put the check in the step event of an object that there's only one of, such as the player. – Peter Feb 10 '16 at 22:42
• This should not be the accepted answer. instance_count() does this in one line of code. – The Great Duck Dec 28 '18 at 7:18

You could simply do:

if instance_number(obj) == 0 {
game_end()
}

This code should be put in a step event.

instance_number(obj) gets the amount of the defined objects in the room.


text:
# Position And Velocity Vs. Time

Classical Mechanics Level 1

Consider a particle which starts from rest and has position $$x(t) = t^2$$. What is the color of the curve which represents its velocity as a function of time?

Different possible graphs of velocity vs time.

×


text:
# 0.2 National foundation phase maths olympiad - grade three - final

 Page 1 / 1

## Grade three – final round paper: 2007 question booklet

DURATION: 1 HOUR 15 MINUTES

MARKS: 20

NAME OF LEARNER:___________________________________

NAME OF SCHOOL:____________________________________

## Instructions to learners:

1. You are expected to answer 15 questions.

3. Use the space provided for your working.

4. You are not allowed to use the calculator.

7. First 10 questions – 1 mark each.

8. Questions 11-20: 2 marks each.

## Exercise 1

What is the 15 th number of this sequence ?

7 ; 12; 17 ; 22 ; . . .

## Exercise 2

Virginia counted in 4’s as follows:

4; 8; 12; 16; . . .

She stopped at the 64th number. What number did she count last?

## Exercise 3

Find the value of $\Delta$ :

$\Delta +\Delta +\Delta +O=42+\Delta +O$

## Exercise 4

Each letter in the following subtraction problem represents a digit. What is the value of A?

## Exercise 5

Sally said that $\frac{3}{4}$ of the health biscuits is 27. What is half the number of health biscuits ?

## Exercise 6

Matchsticks were used to make the following blocks:

How many blocks are there in the 10 th figure?

## Exercise 7

How many blocks are there in this stack?

## Exercise 8

5 different counting numbers (starting from 4) were added to give 70. What is the largest possible number that could have been added?

## Exercise 9

Liz makes 4 cones in 9 minutes. Taz makes 5 cones in 12 minutes. If both work together and at the same rate then how many cones could be made in 72 minutes.

## Exercise 10

Guess the number I stand for:

* I am a 3 digit number.

* My unit’s digit is 1 more than my ten’s digit.

* My hundred’s digit is 1 less than twice the ten’s digit.

* The sum of my digits is 12.

## Exercise 11

Try to work out what * is doing to the 2 numbers.

5 * 4 = 7

1 * 1 = 2

2 * 3 = 2

5 # 5= 6

10 * 5

## Exercise 12

In the following game the rule is double the number in the left block and subtract the number in the right block to give the number in the block above it.

Find the number in block A.

## Exercise 13

Prince collected R20 more than Fred.

Bessy collected R20 less than Jenny.

Fred collected R10 less than Jenny.

Who collected the most money for charity?

## Exercise 14

Calculate:

10+11+12+13+14+………+48+49+50.

## Exercise 15

Guess the mystery number in box 3, using the information given:

* The number in box 3 is twice the number in box 1.

* The number in box 2 is 6 more than box 3.

* The number in box 4 is 3 less than half the number in box 3.

* The sum of the numbers in all 4 boxes is 75.

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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text:
## Sum of Two Positive Integers

$N$ and $Y$ are positive integers, $N\neq Y$. If $N\times Y\div 2=N+Y$, what is the sum $N+Y$?
Source: NCTM Mathematics Teacher 2008

SOLUTION
$N\times Y\div 2=N+Y$
$NY=2(N+Y)$
$NY-2Y=2N$
$Y(N-2)=2N$
$Y=\dfrac{2N}{N-2}$
Table of $N$ and $Y$ values
$N\qquad Y$
$1\qquad -2$
$2\qquad\text{undefined}$
$3\qquad 6$
$4\qquad 4$
$5\qquad 3.33$
$6\qquad 3$
$7\qquad 2.8$
$8\qquad 2.67$
$9\qquad 2.57$
$10\qquad 2.5$
$\cdots$
The graph of $Y$ as a function of $N$ shows a horizontal asymptote at $Y=2$. For $N>6,\: 2.

Two possible values of $(N,Y):(3,6)$ or $(6,3)$.
$N+Y=3+6=9$

Answer: $9$


text:
# The froth stabilizers, generally used during froth-floatation

$(a)\;\text {Cresol and amine.} \\(b)\;\text{Amine and phenol} \\(c)\;\text{Alcohol and Amide} \\ (d)\;\text{Cresol and Aniline}$

Cresol and aniline stabilize the froth before it is taken out for further treatment.
Hence d is the correct answer.


text:
1

# How do you solve 8x = 2( x + 15)?

## Question

###### How do you solve 8x = 2( x + 15)?
How do you solve 8x = 2( x + 15)?

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text:
# Recentering data or creating an index based on another variable

#### cruzeconomics

##### New Member
hello all. I am trying to recenter some data that I have to run some regression discontinuity analysis. I have a data set that has variables on the make, model, model year, and percent of production with airbags and I am trying to create an index based on when airbags became standard (i.e. 100% of production had airbags). I have the following but I am running into some errors:

Code:
function(){

for (i in 1:length(levels(cleanData$Model)){ y <- cleanData[cleanData$Model %in% levels(cleanData$Model)[i],] z <- subset(y, Airbag.Driver. == 100) w <- min(z$ModelYear)

#if (cleanData$Model == get(x[i])){ # cleanData$center <- cleanData$ModelYear - w # } } } Just running through the first section (before the commented out if statement), I am running into some warnings that: >In min(z$ModelYear) : no non-missing arguments to min; returning Inf

I'm guessing that means that there are some models which don't ever have 100% airbag implementation but I'm not sure how to make the program just ignore those (or leave them coded as 99 or something).

After that, I want to make a new variable (already in the cleanData dataset as cleanData$center) that makes the year that airbags became standard for that model 0 and the year before -1, the year after 1, etc. (e.g. ford taurus airbags became standard in 1990, so 1988 => -2, 1989 => -1, 1990=> 0, 1991 => 1, etc). Any help with this would be greatly appreciated. Thanks! #### bryangoodrich ##### Probably A Mammal For centering, you might want to check out the scale function. Code: c(scale(1988:1994, center = 1990, FALSE)) # [1] -2 -1 0 1 2 3 4 I use c(...) because it returns it as a vector instead of a matrix. As for min returning Inf, I assume there's something weird about the data. Run Code: str(cleanData) The ModelYear must be numeric for min to be meaningful. Also, your code, to me, would look better this way Code: for (i in seq(levels(cleanData$Model)) {
y <- cleanData[cleanData$Model == levels(cleanData$Model)[i], ]
There's no reason to use %in% when you can only have 1 level you're referencing with that 'i' integer. Therefore, do an equality comparison. If you're doing sequences from 1 to something, just use seq. I'd also probably just store levels(cleanData$Model) in its own object because you're making references to it so much. #### cruzeconomics ##### New Member Thanks for the help! I will check out the scale function but as for the other problems, cleanData$ModelYear is an integer variable, so it should still work for min() (I think the problem is arising from the fact that some car models do not ever reach Airbag.Driver. == 100, so not every model is included). Not sure though. I still think min should work because it works if I use it on individual models (like the taurus).

Thanks for the help cleaning up the for statement though!

Last edited:

#### bryangoodrich

##### Probably A Mammal
I'm still unclear about the warning and why it would come out. If you have values which should be empty, set them to NA.

Code:
cleanData[someBooleanToReferenceNARecords, 'ModelYear'] <- NA

#### cruzeconomics

There are no empty cells in the whole data set (I've already cleaned it) but there are some car models (cleanData$Model) which never fully implement airbags, so that the subset line: Code: z <- subset(y, Airbag.Driver. == 100) returns an empty data set. I was thinking that this may be the source of the problem. (e.g. the ford *** never has an airbag in my data set, but there are several years of observation, so this would return an empty subset with the above code) #### bryangoodrich ##### Probably A Mammal Okay, I get it. So when you go through the loop you'll come to an empty subset you're trying to run min on. I replicated your result. Code: > df <- data.frame(A = rnorm(10), B = gl(5,2)) > df A B 1 1.50612055 1 2 -0.25453457 1 3 -0.01874759 2 4 -2.50998664 2 5 0.31753606 3 6 0.65032532 3 7 -1.13789731 4 8 0.17341094 4 9 2.33955179 5 10 -0.58415921 5 > df[df$B == '6', ]
[1] A B
<0 rows> (or 0-length row.names)
> min(df[df$B == '6', 1]) [1] Inf Warning message: In min(df[df$B == "6", 1]) : no non-missing arguments to min; returning Inf

#### cruzeconomics

##### New Member
That's my problem exactly. Any ideas on how to fix it?

#### bryangoodrich

##### Probably A Mammal
There is no "fix" because you're trying to run an operation on something that doesn't exist! Instead, avoid the operation.

Code:
if (length(y[[1]]) == 0)  {  # Does not contain any records
w <- NA
} else
w <- min(...)

#### cruzeconomics

##### New Member
I'm still running into the same warning message. (Sorry for being a bit inept). This is what I've got now:

Code:
function(){

indexedData <- matrix(0, 1, dim(cleanData)[2])

colnames(indexedData) <- c("ModelYear", "Make", "Model", "Production", "Airbag.Driver.", "center")

for (i in seq(levels(cleanData$Model))) { y <- cleanData[cleanData$Model == levels(cleanData$Model)[i], ] z <- subset(y, Airbag.Driver. == 100) #w <- min(z$ModelYear)

if (length(z) == 0)  {  # Does not contain any records

w <- NA

} else {

w <- min(z$ModelYear) } y$center <- c(scale(y$ModelYear, center = w, FALSE)) indexedData <- rbind(indexedData, y) #if (cleanData$Model == get(x[i])){

#	cleanData$center <- cleanData$ModelYear - w

#	}

}

indexedData <<- indexedData

}
Still returning the same

>In min(z$ModelYear) : no non-missing arguments to min; returning Inf warning message. #### bryangoodrich ##### Probably A Mammal What type of object is z? How can you determine the number of observations it contains? #### Dason ##### Ambassador to the humans My guess is if it's a data frame you'll just want to replace length with nrow or dim(whatever)[1] or something similar. #### cruzeconomics ##### New Member I think I may have gotten it to work. Here's what I've got: Code: function(){ indexedData <- matrix(0, 1, dim(cleanData)[2]) colnames(indexedData) <- c("ModelYear", "Make", "Model", "Production", "Airbag.Driver.", "center") for (i in seq(levels(cleanData$Model))) {
y <- cleanData[cleanData$Model == levels(cleanData$Model)[i], ]

z <- subset(y, Airbag.Driver. == 100)

if (dim(z)[1] == 0)  {  # Does not contain any records

w <- 0

} else {

w <- min(z$ModelYear) } if (w >= 1984 && w <= 1994){ y$center <- c(scale(y$ModelYear, center = w, FALSE)) } else { y$center <- matrix(99, dim(y)[1], 1)

}

indexedData <- rbind(indexedData, y)

}

indexedData <<- indexedData

}
Thank you for all of your help!

#### Dason

if(!is.finite(suppressWarnings(w <- min(z$ModelYear)))){w <- 0} #or w <- ifelse(is.finite(suppressWarnings(w <- min())), w, 0) Then again the if/else is probably more clear as to what is going on and probably runs faster too. But I had fun making it. But really I'm wondering why you need to do this in the first place? You're just getting a warning (it's not actually an error) and it returns Inf so w will contain Inf and it looks like that isn't going to mess up any of your other checks later. So if it's just the warning that is bugging you you could just do: Code: w <- suppressWarnings(min(z$ModelYear))


text:
## Introduction

Development of intelligent materials1,2 have drawn continuous attentions for their potential applications in sensors3,4,5, displays6, and memories7,8. As one promising candidate, stimulus-responsive materials are highly desirable9,10,11,12,13. Of particular interest are those mechanoresponsive luminescent (MRL) materials14,15,16, as force is a facile and easily handled external stimulus. From universe to earth, from machine to human body, from cell to organelle, force exists and plays vital roles17,18,19. Moreover, luminescence is a sensitive and visible responsive signal20, making MRL materials attractive in responding the mechanical properties of local environment and human body21. MRL materials provide valuable insights into the artificial intelligent systems and human health status, offering potential applications in data recording and storage, security and counterfeiting, optoelectronic devices and haptic sensors, etc.22. As a result, much effort has been placed to develop the MRL family23,24,25,26. However, the performance of the reported system is still far-reaching from the real applications in terms of sensitivity and reversibility. Examples exhibiting ultra-sensitivity, high contrast, fast and response to low force are even rare22.

High contrast MRL materials normally show obvious two-color switching or dramatic luminescence intensity change, such as luminescence turn-on and turn-off (On–Off)27,28,30. However, few examples of On–Off MRL materials with high contrast are available in the literature and their overall performance is unsatisfactory. Few limited representatives of On–Off MRL materials utilize the processes of photodimerizaiton31, photoinduced electron transfer32,33, intramolecular charge transfer34,35, and strong π–π interactions modulation36,37 to control the solid-state luminescence. These traditional strategies employ the strong intermolecular interactions to control the photophysical process of excited state in the solid phase and require strong force to induce the obvious morphology or conformation switching. The reversibility and reproducibility are thus generally low. To realize sensitively on–off luminescence switching, the related photophysical process requires to alter dramatically in the presence of small mechanical stimulus, which is really difficult for traditional MRL materials23,38,39. Hence, new design strategies for controlling the related photophysical process in the solid-state of highly sensitive MRL materials are needed but challenging.

Intersystem crossing (ISC) is a nonradiative relaxation process from excited singlet state to highly sensitive triplet state, which weakens or quenches the fluorescence40,41,42. If we can effectively control the ISC process and the triplet state is nonemissive, such an approach can be utilized as a novel strategy to obtain On–Off MRL materials (Fig. 1a). According to the perturbation theory, the rate of ISC, kISC, is influenced by the spin–orbit coupling constant (ξST) and the energy gap (∆EST) between the involved singlet and triplet states, and is expressed by Eq. (1):

$$k_{{\mathrm{ISC}}} \propto \frac{{\xi _{{\mathrm{ST}}}^2}}{{e^{\Delta E_{{\mathrm{ST}}}^2}}}$$
(1)

Nitrophenyl group with abundant lone pair electrons can boost the efficient ISC pathway with the aid of a great ξST and a negligible ∆EST, where the spin–orbit interaction mixes two states differing in both spin and electronic configurations (Fig. 1b, Supplementary Fig. 18)43,44,45,46. It is well known that ξST and ∆EST are closely related to molecular conformations and electronic configurations, and thus are highly sensitive to the surrounding environments such as the solid-state morphology. Therefore, it is promising to design new On–Off MRL materials by controlling the ISC process of nitrophenyl-substituted luminophores.

On the other hand, the morphology of organic molecules with twisted conformations can be easily modulated by mechanical stimulus47,48. Aggregation-induced emission (AIE) refers to a class of luminogens (AIEgen) which are nonemissive in solutions but become highly emissive when cluster into aggregates49. AIEgens often have twisted molecular conformation, such as twisted intramolecular charge transfer conformation50, cistrans isomerized configuration51, herringbone conformation52, etc. Among them, triphenylamine (TPA) and tetraphenyethylene (TPE) are widely used as AIE cores with propeller-like conformation (Fig. 1c). Therefore, AIEgens enjoy intrinsic advantages as excellent sensitive MRL candidates.

In this article, we combine nitrophenyl groups with AIEgens to create sensitive On–Off MRL materials. Six nitro-substituted AIEgens were synthesized and their properties were systemically investigated. The manipulation of ISC is unprecedentedly employed as an on–off methodology and a rational design strategy is introduced to provide a series of high performance On–Off MRL candidates with versatile applications. These results provide a big step in expanding the scope of MRL family.

## Results

### Photophysical property

To validate our proposal, six luminogens (Fig. 1d) were designed and synthesized through controlling nitration of TPA and TPE. All the molecules were purified by twice recrystallization in a yield of higher than 80% (Supplementary Fig. 1)53. As expected, all the six luminogens inherit the AIE property of TPA and TPE core54. They are nonemissive in acetonitrile solutions while their aggregates emit bright green or yellow fluorescence (Fig. 2b), which fulfills the basic prerequisite as MRL materials23.

Morphology-dependent photophysical properties are then carefully investigated (Fig. 2a). In the crystalline state, TPA-1N, TPA-2N, TPE-3N, and TPE-4N are nearly nonemissive with ultralow quantum yields, which indicates that nitrophenyl groups successfully open the nonradiative ISC channel to quench the emission. The ISC becomes the dominant decay pathway as nitrophenyl groups are efficient triplet state promoters55 (Fig. 1b). In the amorphous state, all the six luminogens recover or enhance the luminescence. They exhibit bright green or yellow fluorescence as well as in thin films and in aggregates, suggesting the ISC is blocked due to morphology change (Supplementary Fig. 2 and Supplementary Table 1-2). The difference is also proved by detecting the morphology-dependent singlet oxygen generated by energy transfer from triplet states (Supplementary Fig. 3). TPA-1N, TPA-2N, TPE-3N, and TPE-4N exhibit the proposed ISC modulated On–Off MRL properties with a high luminescence contrast ratio of up to 103 (Supplementary Figs. 4-6). For comparison, TPE-1N and TPE-2N crystals show intense emission with high quantum yield of 20.24% and 24.35%, respectively, possibly because the number of nitrophenyl groups is still not enough to overwhelm the AIE effect. Such a factor is critical in constructing On–Off MRL materials, which will be discussed later.

TPE-4N, for example exhibits the On–Off MRL property with the highest contrast. We placed TPE-4N crystals on a piece of weighing paper and ground them into powders, through which a yellow emissive paper was obtained under the UV irradiation. The emission is firstly turned off when annealing at 150 °C or fuming with acetone for 10 s (Process I). The yellow emission can be easily recovered by grinding (Process II). Contrast patterns are obtained through process I and II using a designed mask (Fig. 2c). Monitored by the quantum yields, the processes can be repeated for several cycles without obvious fatigue, suggesting the good reversibility (Fig. 2d and Supplementary Fig. 7).

Organic crystals with twisted molecular structures can be easily amorphorized by applying mechanical stimulus. In addition to photophysical study, we performed powder X-ray diffraction (PXRD) and differential scanning calorimetry (DSC) analyses to investigate the morphology change. The PXRD patterns of ground powders show no visible diffraction peaks, indicating their amorphous characteristic caused by mechanical grinding (Supplementary Figs. 8-9). In contrast, the PXRD patterns of thermal annealed or solvent-fumed samples exhibit sharp diffraction peaks which coincide with single crystals, indicating that the amorphous powder transfers to crystalline state. Such transformation is verified by PXRD and DSC in Supplementary Fig. 10. The above results show that the solid-state luminescence of TPE-4N is strongly related to the morphology, which is easily switched by mechanical stimulus and thermo-annealing or solvent-fuming. Meanwhile, TPA-1N, TPA-2N, and TPE-3N show similar On–Off MRL properties as TPE-4N (Supplementary Figs. 10-12).

Single-crystal XRD analysis shows the presence of abundant weak intermolecular interactions between the nitro and phenyl groups in all the crystals (Supplementary Figs. 13-16). For example, one TPA-1N molecule is surrounded by seven neighboring molecules through multiple weak C–H···C and C–H···O interactions (Fig. 3a). Together with the twisted structure inheriting from TPA and TPE, those luminogens have quite loose crystal packing. Solvent molecules are encapsulated in the crystal cavities of TPE-3N and TPE-4N (Supplementary Figs. 12, 15, Table 4-6). After removing the solvent molecules, the crystals pack in a looser manner but still are nonemissive, which excludes the possibility of solvent-caused quenching effect (Supplementary Figs. 8-9). For those loose packed crystals, the mechanical force could easily break the weak interactions to release the molecular conformations to free states.

As proposed, AIEgens substituted with suitable nitro groups can realize unique On–Off MRL properties, verifying the validate of our design strategy. However, both crystals and amorphous powders are solid phase, why they exhibit distinctly different luminescence behaviors?

### Theoretical calculation

To gain deeper insight into the mechanism of On–Off MRL property, we performed investigations on single molecule in both gas and crystalline states by first-principle density functional theory (DFT) and time-dependent DFT (TD-DFT). The aggregation effect was considered by using the hybrid quantum mechanics and molecular mechanics approach. The computation models are built by digging a 5 × 5 × 5-unit supercell from the single-crystal structures. The calculated energy gaps (∆EST), nature transition orbitals, spin–orbit coupling constants (ξST) between S1 and involved triplet states are summarized in Fig. 3 and Supplementary Figs. 18-25. As well known, luminescence change is the outcome of variation of intermolecular interaction and molecular conformation during morphology transformation.

The effect of intermolecular interaction is first considered. The energy levels and ξST are carefully calculated under the same molecular conformation in the absence or presence of intermolecular interactions. The almost same calculation results suggest that the intermolecular interactions are not the main or direct factor for the MRL On–Off properties (Supplementary Figs. 20-25).

The effect of molecular conformation is then investigated. TPA-1N is chosen as the calculated model. As shown in Fig. 3c, d, a big difference in molecular conformation in crystalline and gas state is found, that molecule in crystal has much smaller torsion angles (α = 17.62°, β = 26.81°) than that in free gas state (α = β = 27.95o). The variation of molecular conformation is accompanied with a decreasing energy gap of S1–S0 from 3.37 eV in crystal state to 3.22 eV in gas state, which agrees with the notable redshift in absorption (Supplementary Fig. 17). Thus, the amorphous state can be considered as a state close to gas state with similar molecular conformation. In detail, TPA-1N molecule in crystal state possesses a typical 1(π,π*) S1 state and a low-lying transition-allowed 3(n,π*) T3 state with a large ξS1T3 = 4.85 cm−1 and a small ∆ES1T3 = 0.17 eV, which enables the efficient ISC and thus causes fluorescence quenching. For molecule in gas state, the low-lying triplet state changes to a transition-forbidden 3(π,π*) T2 state, accompanied by a reduced ξS1T2 = 0.91 cm−1 and a larger ∆ES1T2 = 0.35 eV, which blocks the efficient ISC process and turns on the fluorescence in amorphous state. Similar explanations are applicable for TPA-2N, TPE-3N, and TPE-4N, where transformation from crystal to amorphous state enlarges ∆EST and reduces ξST, simultaneously (Supplementary Figs. 20-25).

To further simulate how molecular conformation influences the ISC process, a rigid potential energy surface scan is performed by varying the torsion angle α from 10 to 40° in the ground state. The vertical excitation energies of low-lying excited states S1 and T1–4 and the involved ξST are also calculated. As shown in Fig. 3b, e, when α is smaller than 26°, T3 with a 3(n,π*) configuration is the closest low-lying triplet state to S1 with a high ξST (>4.5 cm−1). The different orbital character and the close proximity of the S1 state to the T3 state favors the occurrence of efficient ISC in the crystalline state (α = 17.62o). As α is larger than 26°, the energy of S1 decreases significantly which results in T3 higher than S1 in energy. T2 now becomes the closest low-lying triplet state to S1 instead. The ISC then becomes inefficient as S1 and T2 have the same orbital character and a large energy gap exists between them. This situation is similar in the amorphous state.

Last, the effect of substituent number is studied. From TPA-1N to TPA-2N, from TPE-1N to TPE-4N, more nitrophenyl groups gradually increase the number of involved triplet states with minimizing energy gaps and enhancing ξST (Supplementary Figs. 20-25). Therefore, the ISC process is boosted by multiple nitrophenyl group substitution to lead TPE-4N the highest On–Off contrast.

### Thin-film On–Off property

To demonstrate the practical applicability and to measure the sensitivity, TPE-4N in thin film was prepared by simple spin-coating of its chloroform solution on quartz plates. As shown in Fig. 4a and Supplementary Figs. 25-26, the freshly coated film is quite transparent and smooth. It emits bright green light peaked at 520 nm (Fig. 4b). The emission quenches quickly and the PL intensity remarkably decreases by a factor of 103 when the film is annealed at 150 °C by a handed heat gun for 3 s. The PXRD patterns demonstrate that the freshly coated film is amorphous in nature while the annealed one is crystallized (Supplementary Fig. 28). Interestingly, well-defined and bright green emissive words appear when writing on the annealed film by using a fine glass tube. After thermal treatment, the emissive words erase completely. The writing and erasing processes can be repeated for many times, suggesting the excellent reversibility of the fluorescence switching process.

In a further experiment, we demonstrate the On–Off sensitivity of thin-film fluorescence switching. The polarizing optical microscopic photo of the annealed film taken under room light show the presence of uniform spherulites (Fig. 4c). When a weak force is applied using a glass tube, scratch was not observed under room light but was clearly visualized under UV light irradiation with more than 100-fold contrast (Fig. 4d). Again, upon thermal treatment, the bright fluorescent scratch disappears. Because of such ultra-sensitivity, we are now conducting investigations on fluorescence mapping and visualization of stress distribution and fatigue crack propagation for industry use.

### Optical information storage and haptic sensor

The designed On–Off MRL materials have the advantages of high contrast and sensitivity, good reversibility, and fast response, which encourage us to further explore their practical applications in optical information storage and haptic sensor.

Figure 5a describes the rewriteable optical information storage system containing the procedures of film preparation, micro-embossing, and recovery. A nonemissive film was facilely prepared by thermal annealing of the spin-coated film. After applying a finger pressure using a designed mold to the annealed film, a high-resolution micro-embossing fluorescent patterns can be easily replicated with a width of 10 μm and a spacing of 10 μm. To the best of our knowledge, this is the first MRL patterns with micrometer resolution. The micro-embossing patterns are erased completely upon thermal treatment, and the film is rewriteable again.

Next, we utilized TPE-4N to construct haptic sensor. The TPE-4N films are deposited on aluminum, ceramic, and wooden substrates by simple brush coating process (Methods), which show bright fluorescence (Fig. 5b). The fluorescence signal of the freshly prepared films is turned off completely by thermal annealing. Upon pressing with thumb fingers, the fluorescence of the touched area was turned on immediately to generate well-defined fingerprint patterns observable by naked eyes (Supplementary Fig. 29). In detail, the pressure is gradually enhanced from 0 to 0.98 MPa (Fig. 5c and Supplementary Fig. 30). To allow visualize monitoring, the fluorescent signal is digitized using image grayscale processing. As shown in Fig. 5d, when the applied finger pressure reaches 0.15 MPa, the grayscale intensity increases by 3.5-fold. At 0.25 MPa, a 7.7-fold strong signal was detected. The intensity reaches its maximum (15-fold) at 0.55 MPa. After thermal treatment, the film recovers to its nonemissive state and is reusable (Supplementary Fig. 31). The results suggest a promising fast responsive and reversible haptic sensor.

## Discussion

Nitrophenyl group is a well-known electron and energy acceptor and can serve as an excited state or fluorescence quencher30,56,57. However, the use of nitro-substituted aromatics in constructing luminescent materials is seldom explored because it promotes ultrafast nonradiative relaxation ISC process to give nonemissive character of triplet state. Apparently, nitro substitution effect and AIE effect are conflict in terms of solid-state luminescence. Here, we unprecedentedly integrate them in constructing highly sensitive MRL materials. In the crystalline state, the nitrophenyl group effectively opens the nonradiative ISC channel to the highly sensitive and nonemissive triplet states to overwhelm the AIE effect to give fluorescence “Off” state. Mechanical stimulus manipulates the solid-state morphology and changes the molecular conformations. The AIE effect then dominates the photophysical process to recover the solid-state emission to give fluorescence “On” state.

Except ISC, nitrophenyl group imparts abundant weak intermolecular interactions to benefit easy crystallization and loose crystal packing. Coupled with the twisted and propeller-like molecular structure, the morphology transformation of the resulting molecules becomes facile and reversible. The pressure required for luminescence switching is then dramatically reduced to result in excellent sensitivity, fast response, and high contrast On–Off performance. The nitrophenyl group is also helpful for thin-film coating or printing on varied substrate to make the materials valuable for optical information recording and haptic sensing with facile preparation and low cost.

Controlling ISC is a general strategy to achieve novel On–Off MRL materials. Following this strategy, we choose the benzophenonyl group as another triplet promoter and two TPE derivatives, namely TPE-BP and 2TPE-BP, are synthesized as proof-of-concept examples (Supplementary Figs. 32-33). As expected, they are nonemssive in both solution and crystalline state but their amorphous powders emit bright green fluorescence. The benzophenonyl groups are considered to open the efficient nonradiative ISC channels to quench the light emission as they show even stronger triplet-state promotion effect than nitrophenyl group. One benzophenone moiety can turn off the emission two TPE groups in crystalline state. Efforts to expand On–Off MRL family by using this rational design strategy are still in progress.

In summary, we put forth a new design strategy for high performance On–Off MRL materials by controlling the ISC process. Nitro groups are incorporated into twisted AIEgens to facilitate the efficient ISC process. Theoretical calculations indicate that the torsion angle and the number of nitrophenyl group are key factors for tuning the ISC process. Mechanical stimulus modulates the molecular conformations to give varied solid-state morphology with luminescence On–Off switching. Experiments demonstrate the high contrast and sensitive On–Off MRL performance as well as reversibility and fast responding behaviors. Such properties enable them to find versatile applications such as the optical information storage and haptic sensor. Thus, the design strategy introduced in the present study is expected to provide a big step in expanding the scope of On–Off MRL family.

## Methods

### Crystal growth

All the crystals were cultivated through slow solvent evaporation at room temperature. Single crystals of TPA-1N, TPA-2N, TPE-2N, TPE-3N, and TPE-4N can been obtained easily, while TPE-1N crystal is not suitable for single-crystal analysis. Single crystals of TPA-1N, TPA-2N, and TPE-2N were cultivated from methylene chloride and hexane mixtures. Single crystal of TPE-3N was cultivated from chloroform and hexane mixtures. Single crystal of TPE-4N was cultivated from acetone.

### Solid samples preparation

The amorphous solids of AIEgens were prepared by heating the crystalline AIEgens to melts with a heating gun and quenching the melts with liquid nitrogen. The ground powers were prepared with a mortar and pestle for 3 min.

### Film preparation of TPE-4N

Spin-coating films of TPE-4N were prepared by simple spin-coating on quartz substrates (2 cm × 2 cm) from a chloroform solution (5 wt%). Spin-coating speed: slow spin speed (0.3 kR/min, 6 s) and fast spin speed (1 kR/min, 30 s). Brush coating samples were prepared by simply brushing on different substrates using a chloroform solution (10 wt%).

### Stamping mold

A stamping mold was prepared on a circular silicon substrate (2 inches in diameter): striping pattern with 0.5 mm in thickness, 10 μm in width, and 10 μm in fringe spacing. The etching depth is 20 μm.

### Data availability

The authors declare that the all data supporting the findings of this study are available within this article and Supplementary Information files, and also are available from the authors upon reasonable request. CCDC 1550422, 1550423, 1550424, and 1850508 contain the crystallographic data for this paper. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/getstructures.


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<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />

# Polynomials in Standard Form

## Understand polynomials as specific kinds of Algebraic expressions

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Polynomials in Standard Form

Suppose that two square plots of land both have a side length of x\begin{align*}x\end{align*} feet. For one of the plots of land, the length is increased by 2 feet, and the width is decreased by 3 feet. For the other plot of land, the length is increased by 3 feet, and the width is decreased by 4 feet. What is the difference in the resulting areas of the plots? Could you rewrite the expression representing the difference in standard form? In this Concept, you'll learn how to classify, simplify, and rewrite polynomials in standard form so that you can produce expressions such as the one asked for here.

### Guidance

So far we have discussed linear functions and exponential functions. This Concept introduces polynomial functions.

Definition: A polynomial is an expression made with constants, variables, and positive integer exponents of the variables.

An example of a polynomial is: 4x3+2x23x+1\begin{align*}4x^3 + 2x^2 - 3x + 1\end{align*}. There are four terms: 4x3, 2x2, 3x,\begin{align*}4x^3, \ 2x^2, \ {-3x},\end{align*} and 1. The numbers appearing in each term in front of the variable are called the coefficients. 4, 2, and -3 are coefficients because those numbers are in front of a variable. The number appearing all by itself without a variable is called a constant. 1 is the constant because it is by itself.

#### Example A

Identify the following expressions as polynomials or non-polynomials.

(a) 5x22x\begin{align*}5x^2 - 2x\end{align*}

(b) 3x22x2\begin{align*}3x^2 - 2x^{-2}\end{align*}

(c) xx1\begin{align*}x\sqrt{x} - 1\end{align*}

(d) 5x3+1\begin{align*}\frac{5}{x^3 + 1}\end{align*}

(e) 4x13\begin{align*}4x^{\frac{1}{3}}\end{align*}

(f) 4xy22x2y3+y33x3\begin{align*}4xy^2 - 2x^2y - 3 + y^3 - 3x^3\end{align*}

Solution:

(a) 5x22x\begin{align*}5x^2 - 2x\end{align*} This is a polynomial.

(b) 3x22x2\begin{align*}3x^2 - 2x^{-2}\end{align*} This is not a polynomial because it has a negative exponent.

(c) xx1\begin{align*}x\sqrt{x} - 1\end{align*} This is not a polynomial because is has a square root.

(d) 5x3+1\begin{align*}\frac{5}{x^3 + 1}\end{align*} This is not a polynomial because the power of x\begin{align*}x\end{align*} appears in the denominator.

(e) 4x13\begin{align*}4x^{\frac{1}{3}}\end{align*} This is not a polynomial because it has a fractional exponent.

(f) 4xy22xy3+y33x3\begin{align*}4xy^2 - 2x^y - 3 + y^3 - 3x^3\end{align*} This is a polynomial.

Classifying Polynomials by Degree

The degree of a polynomial is the largest exponent of a single term.

• 4x3\begin{align*}4x^3\end{align*} has a degree of 3 and is called a cubic term or 3rd\begin{align*}3^{rd}\end{align*} order term.
• 2x2\begin{align*}2x^2\end{align*} has a degree of 2 and is called a quadratic term or 2nd\begin{align*}2^{nd}\end{align*} order term.
• 3x\begin{align*}-3x\end{align*} has a degree of 1 and is called a linear term or 1st\begin{align*}1^{st}\end{align*} order term.
• 1 has a degree of 0 because there is no variable.

Polynomials can have more than one variable. Here is another example of a polynomial: t46s3t212st+4s45\begin{align*}t^4-6s^3t^2-12st+4s^4-5\end{align*}. This is a polynomial because all exponents on the variables are positive integers. This polynomial has five terms. Note: The degree of a term is the sum of the powers on each variable in the term.

t4\begin{align*}t^4\end{align*} has a degree of 4, so it’s a 4th\begin{align*}4^{th}\end{align*} order term.

6s3t2\begin{align*}-6s^3t^2\end{align*} has a degree of 5, so it’s a 5th\begin{align*}5^{th}\end{align*} order term.

12st\begin{align*}-12^{st}\end{align*} has a degree of 2, so it’s a 2nd\begin{align*}2^{nd}\end{align*} order term.

\begin{align*}4s^4\end{align*} has a degree of 4, so it’s a \begin{align*}4^{th}\end{align*} order term.

–5 is a constant, so its degree is 0.

Since the highest degree of a term in this polynomial is 5, this is a polynomial of degree 5 or a \begin{align*}5^{th}\end{align*} order polynomial.

#### Example B

Identify the coefficient on each term, the degree of each term, and the degree of the polynomial.

Solution: The coefficients of each term in order are 1, –3, and 8, and the constant is –12.

The degrees of each term are 4, 5, 1, and 0. Therefore, the degree of the polynomial is 5.

A monomial is a one-termed polynomial. It can be a constant, a variable, or a variable with a coefficient. Examples of monomials are the following: \begin{align*}b^2; \ 6; \ -2ab^2; \ \frac{1}{4} x^2\end{align*}

Rewriting Polynomials in Standard Form

Often, we arrange the terms in a polynomial in standard form in which the term with the highest degree is first and is followed by the other terms in order of decreasing powers. The first term of a polynomial in this form is called the leading term, and the coefficient in this term is called the leading coefficient.

#### Example C

Rearrange the terms in the following polynomials so that they are in standard form. Indicate the leading term and leading coefficient of each polynomial.

(a) \begin{align*}7-3x^3+4x\end{align*}

(b) \begin{align*}ab-a^3+2b\end{align*}

Solution:

(a) \begin{align*}7-3x^3+4x\end{align*} is rearranged as \begin{align*}-3x^3+4x+7\end{align*}. The leading term is \begin{align*}-3x^3\end{align*} and the leading coefficient is –3.

(b) \begin{align*}ab-a^3+2b\end{align*} is rearranged as \begin{align*}-a^3+ab+2b\end{align*}. The leading term is \begin{align*}-a^3\end{align*} and the leading coefficient is –1.

Simplifying Polynomials

A polynomial is simplified if it has no terms that are alike. Like terms are terms in the polynomial that have the same variable(s) with the same exponents, but they can have different coefficients.

\begin{align*}2x^2y\end{align*} and \begin{align*}5x^2y\end{align*} are like terms.

\begin{align*}6x^2y\end{align*} and \begin{align*}6xy^2\end{align*} are not like terms.

If we have a polynomial that has like terms, we simplify by combining them.

This polynomial is simplified by combining the like terms: \begin{align*}6xy-4xy=2xy\end{align*}. We write the simplified polynomial as \begin{align*}x^2+2xy+y^2\end{align*}.

#### Example D

Simplify by collecting and combining like terms.

Solution: Use the Commutative Property of Addition to reorganize like terms and then simplify.

### Guided Practice

Simplify and rewrite the following polynomial in standard form. State the degree of the polynomial.

Solution:

Start by simplifying by combining like terms:

In order to rewrite in standard form, we need to determine the degree of each term. The first term has a degree of \begin{align*}2+3=5\end{align*}, the second term has a degree of \begin{align*}1+5=6\end{align*}, and the last term has a degree of \begin{align*}1+1=2\end{align*}. We will rewrite the terms in order from largest degree to smallest degree:

\begin{align*}-3xy^5+9x^2y^3+2xy\end{align*}

The degree of a polynomial is the largest degree of all the terms. In this case that is 6.

### Explore More

Sample explanations for some of the practice exercises below are available by viewing the following video. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. However, the practice exercise is the same in both. CK-12 Basic Algebra: Addition and Subtraction of Polynomials (15:59)

Define the following key terms.

1. Polynomial
2. Monomial
3. Degree
4. Leading coefficient

For each of the following expressions, decide whether it is a polynomial. Explain your answer.

1. \begin{align*}x^2+3x^{\frac{1}{2}}\end{align*}
2. \begin{align*}\frac{1}{3}x^2y-9y^2\end{align*}
3. \begin{align*}3x^{-3}\end{align*}
4. \begin{align*}\frac{2}{3}t^2-\frac{1}{t^2}\end{align*}

Express each polynomial in standard form. Give the degree of each polynomial.

1. \begin{align*}3-2x\end{align*}
2. \begin{align*}8x^4-x+5x^2+11x^4-10\end{align*}
3. \begin{align*}8-4x+3x^3\end{align*}
4. \begin{align*}-16+5f^8-7f^3\end{align*}
5. \begin{align*}-5+2x-5x^2+8x^3\end{align*}
6. \begin{align*}x^2-9x^4+12\end{align*}

Mixed Review

1. Solve by graphing \begin{align*}\begin{cases} y=\frac{1}{3} x-4\\ y=-4x+10 \end{cases}\end{align*}.
2. Solve for \begin{align*}u\end{align*}: \begin{align*}12=- \frac{4}{u}\end{align*}.
3. Graph \begin{align*}y=|x-4|+3\end{align*}on a coordinate plane.
1. State its domain and range.
2. How has this graph been shifted from the parent function \begin{align*}f(x)=|x|\end{align*}?
1. Two dice are rolled. The sum of the values are recorded.
1. Define the sample space.
2. What is the probability the sum of the dice is nine?
1. Consider the equation \begin{align*}y=6500(0.8)^x\end{align*}.
1. Sketch the graph of this function.
2. Is this exponential growth or decay?
3. What is the initial value?
4. What is its domain and range?
5. What is the value when \begin{align*}x=9.5\end{align*}?
1. Write an equation for the line that is perpendicular to \begin{align*}y=-5\end{align*} and contains the ordered pair (6, –5).

### Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 9.1.

### Vocabulary Language: English Spanish

constant

constant

In a polynomial, the number appearing all by itself without a variable is called the constant.
degree

degree

The degree of a polynomial is the largest degree of the terms. The degree of a term is the power of the variable, or if the term has more than one variable, it is the sum of the powers on each variable.
monomial

monomial

A monomial is a one-termed polynomial. It can be a constant, a variable, or a variable with a coefficient.
Polynomial

Polynomial

A polynomial is an expression with at least one algebraic term, but which does not indicate division by a variable or contain variables with fractional exponents.
standard form of a polynomial

standard form of a polynomial

Arrangement of terms in a polynomial where the term with the highest degree is first and is followed by the other terms in order of decreasing powers.
Polynomial Function

Polynomial Function

A polynomial function is a function defined by an expression with at least one algebraic term.

### Explore More

Sign in to explore more, including practice questions and solutions for Polynomials in Standard Form.

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##### Overview

It is the process of taking pixels from one place in the image and locating them in another position in a new image.

To accomplish the mapping process, it might be necessary to do some interpolation for non-integer pixel locations, since there will not always be a one-to-one-pixel correspondence between source and destination images.

We can express the remap for every pixel location (x,y) as:
g(x,y) = f ( h(x,y) )
where g() is the remapped image, f() the source image and h(x,y) is the mapping function that operates on (x,y)

Remapping


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OpenStudy (anonymous):

does anyone understand this finding the real solution? the 3 and 2 are exponets ???x^3/^2 -27=0

7 years ago

Hm. What do you mean? The real solution of each is the appropriate root. e.g.: $$x^2 - 27 = 0$$ $$x^2 = 27$$ $$x = \pm \sqrt{27}$$

7 years ago

Ah, sorry, misunderstood. You have $$x^{\frac{3}{2}}$$ In that case the process is similar, but you have to remember that $$\sqrt{x}$$ is the same as $$x^2$$, so $$x^{\frac{3}{2}}$$ is really the same as $$\sqrt{x^3}$$. So, you end up with: $$\sqrt{x^3} = 27$$ You can reverse the square root by squaring and the cube by taking the cubed root.

7 years ago
I meant $$\sqrt{x}$$ is the same as $$x^{\frac{1}{2}}$$.


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dcemri: Pharmacokinetic Models for Dynamic Contrast-Enhanced MRI Data In dcemri: A Package for Medical Image Analysis

Description

Parameter estimation for single compartment models is performed using literature-based or user-specified arterial input functions. The Levenburg-Marquardt algorithm does the heavy lifting.

Usage

 1 2 dcemri.lm(conc, time, img.mask, model="extended", aif=NULL, nprint=0, user=NULL, verbose=FALSE, ...)

Arguments

 conc is a multidimensional (1D-4D) array of contrast agent concentrations. The last dimension is assumed to be temporal, while the previous dimensions are assued to be spatial. time is a vector of acquisition times (in minutes) relative to injection of the contrast agent. Negative values should be used prior to the injection. img.mask is a (logical) multidimensional array that identifies the voxels to be analyzed. Has to have same dimension as conc minus temporal dimension. model is a character string that identifies the type of compartmental model to be used. Acceptable models include: “weinmann”Tofts & Kermode AIF convolved with single compartment model “extended”Weinmann model extended with additional vascular compartment (default) “orton.exp”Extended model using Orton's exponential AIF “orton.cos”Extended model using Orton's raised cosine AIF aif is a character string that identifies the parameters of the type of arterial input function (AIF) used with the above model. Acceptable values are: tofts.kermode (default) or fritz.hansen for the weinmann and extended models; orton.exp (default) and user for the orton.exp model; orton.cos (default) and user for the orton.cos model. All AIF models set the parametric form and parameter values – except user where a set of user-defined parameter values are allowed. nprint is an integer, that enables controlled printing of iterates if it is positive. In this case, estimates of par are printed at the beginning of the first iteration and every nprint iterations thereafter and immediately prior to return. If nprint is not positive, no tracing information on the progress of the optimization is produced. user is a list with the following paramters required: D, AB, muB, AG, muG. verbose . ... Additional parameters to the function.

Details

Compartmental models are the solution to the modified general rate equation (Kety 1951). The specific parametric models considered here include the basic Kety model

C_t(t)=K^{trans}≤ft[C_p(t)\otimes\exp(-k_{ep}t)\right],

where \otimes is the convoluation operator, and the so-called extended Kety model

C_t(t)=v_pC_p(t)+K^{trans}≤ft[C_p(t)\otimes\exp(-k_{ep}t)\right].

The arterial input function must be either literature-based (with fixed parameters) or the exponential AIF from Orton et al. (2008) with user-defined parameters.

Value

Parameter estimates and their standard errors are provided for the masked region of the multidimensional array. They include

 ktrans Transfer rate from plasma to the extracellular, extravascular space (EES). kep Rate parameter for transport from the EES to plasma. ve Fractional occupancy by EES (the ratio between ktrans and kep). vp Fractional occupancy by plasma. ktranserror Standard error for ktrans. keperror Standard error for kep. vperror Standard error for vp.

The residual sum-of-squares is also provided, along with the original acquisition times (for plotting purposes).

Author(s)

Brandon Whitcher, Volker Schmid

References

Ahearn, T.S., Staff, R.T., Redpath, T.W. and Semple, S.I.K. (2005) The use of the Levenburg-Marquardt curve-fitting algorithm in pharmacokinetic modelling of DCE-MRI data, Physics in Medicine and Biology, 50, N85-N92.

Fritz-Hansen, T., Rostrup, E., Larsson, H.B.W, Sondergaard, L., Ring, P. and Henriksen, O. (1993) Measurement of the arterial concentration of Gd-DTPA using MRI: A step toward quantitative perfusion imaging, Magnetic Resonance in Medicine, 36, 225-231.

Orton, M.R., Collins, D.J., Walker-Samuel, S., d'Arcy, J.A., Hawkes, D.J., Atkinson, D. and Leach, M.O. (2007) Bayesian estimation of pharmacokinetic parameters for DCE-MRI with a robust treatment of enhancement onset time, Physics in Medicine and Biology 52, 2393-2408.

Orton, M.R., d'Arcy, J.A., Walker-Samuel, S., Hawkes, D.J., Atkinson, D., Collins, D.J. and Leach, M.O. (2008) Computationally efficient vascular input function models for quantitative kinetic modelling using DCE-MRI, Physics in Medicine and Biology 53, 1225-1239.

Tofts, P.S., Brix, G, Buckley, D.L., Evelhoch, J.L., Henderson, E., Knopp, M.V., Larsson, H.B.W., Lee, T.-Y., Mayr, N.A., Parker, G.J.M., Port, R.E., Taylor, J. and Weiskoff, R. (1999) Estimating kinetic parameters from dynamic contrast-enhanced T_1-weighted MRI of a diffusable tracer: Standardized quantities and symbols, Journal of Magnetic Resonance, 10, 223-232.

Tofts, P.S. and Kermode, A.G. (1984) Measurement of the blood-brain barrier permeability and leakage space using dynamic MR imaging. 1. Fundamental concepts, Magnetic Resonance in Medicine, 17, 357-367.

Weinmann, H.J., Laniado, M. and Mutzel, W. (1984) Pharmacokinetics of Gd-DTPA/dimeglumine after intraveneous injection into healthy volunteers, Physiological Chemistry and Physics and Medical NMR, 16, 167-172.

dcemri.bayes, dcemri.map, dcemri.spline, nls.lm
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 data("buckley") ## Set up breast data for dcemri xi <- seq(5, 300, by=5) img <- array(t(breast$data)[,xi], c(13,1,1,60)) time <- buckley$time.min[xi] aif <- buckley$input[xi] mask <- array(TRUE, dim(img)[1:3]) ## Generate AIF params using the orton.exp function from Buckley's AIF aifparams <- orton.exp.lm(time, aif) fit <- dcemri.lm(img, time, mask, model="orton.exp", aif="user", user=aifparams) ## Scatterplot comparing true and estimated Ktrans values plot(breast$ktrans, fit$ktrans, xlim=c(0,0.75), ylim=c(0,0.75), xlab=expression(paste("True ", K^{trans})), ylab=expression(paste("Estimated ", K^{trans}))) abline(0, 1, lwd=1.5, col="red") cbind(breast$ktrans, fit\$ktrans[,,1])