text:
Probabilités
Exponential inequalities for the supremum of some counting processes and their square martingales
Comptes Rendus. Mathématique, Tome 359 (2021) no. 8, pp. 969-982.

Nous établissons ici des inégalités exponentielles pour le supremum de martingales et de martingales carrées issues de processus de comptage, ainsi que pour le processus d’oscillation de ces processus. Ces inégalités, qui jouent un rôle essentiel dans le contrôle d’erreur de certaines procédures statistiques, s’appliquent à des processus de comptage non-explosifs généraux, comme les processus de Poisson, de Hawkes ou encore les processsus de Cox. Quelques applications aux $U$-statistiques sont aussi abordées dans cet article.

We establish exponential inequalities for the supremum of martingales and square martingales obtained from counting processes, as well as for the oscillation modulus of these processes. Our inequalities, that play a decisive role in the control of errors in statistical procedures, apply to general non-explosive counting processes including Poisson, Hawkes and Cox models. Some applications for $U$-statistics are discussed.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : https://doi.org/10.5802/crmath.206
Classification : 60G55
@article{CRMATH_2021__359_8_969_0,
author = {Ronan Le Gu\'evel},
title = {Exponential inequalities for the supremum of some counting processes and their square martingales},
journal = {Comptes Rendus. Math\'ematique},
pages = {969--982},
publisher = {Acad\'emie des sciences, Paris},
volume = {359},
number = {8},
year = {2021},
doi = {10.5802/crmath.206},
language = {en},
}
Ronan Le Guével. Exponential inequalities for the supremum of some counting processes and their square martingales. Comptes Rendus. Mathématique, Tome 359 (2021) no. 8, pp. 969-982. doi : 10.5802/crmath.206. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.206/

[1] Miguel A. Arcones; Evarist Giné Limit theorems for U-processes, Ann. Probab., Volume 21 (1993) no. 3, pp. 1494-1542 | MR 1235426 | Zbl 0789.60031

[2] Richard F. Bass The measurability of hitting times, Electron. Commun. Probab., Volume 15 (2010), pp. 99-105 | Article | MR 2606507 | Zbl 1202.60054

[3] Richard F. Bass Stochastic processes, Cambridge Series in Statistical and Probabilistic Mathematics, 33, Cambridge University Press, 2011 | Zbl 1247.60001

[4] Bernard Bercu; Bernard Delyon; Emmanuel Rio Concentration Inequalities for Sums and Martingales, SpringerBriefs in Mathematics, Springer, 2015 | Zbl 1337.60002

[5] Pierre Brémaud Point processes and queues: martingale dynamics, Springer Series in Statistics, Springer, 1981 | Zbl 0478.60004

[6] Pierre Brémaud; Laurent Massoulié Stability of nonlinear Hawkes processes, Ann. Probab., Volume 24 (1996) no. 3, pp. 1563-1588 | MR 1411506 | Zbl 0870.60043

[7] Jean Bretagnolle A new large deviation inequality for U-statistics of order 2, ESAIM, Probab. Stat., Volume 3 (1999), pp. 151-162 | Article | Numdam | MR 1742613 | Zbl 0957.60031

[8] Magalie Fromont; Béatrice Laurent Adaptive goodness-of-fit tests in a density model, Ann. Stat., Volume 34 (2006) no. 2, pp. 680-720 | MR 2281881 | Zbl 1096.62040

[9] Magalie Fromont; Béatrice Laurent; Patricia Reynaud-Bouret Adaptive test of homogeneity for a Poisson process, Ann. Inst. Henri Poincaré, Probab. Stat., Volume 47 (2011) no. 1, pp. 176-213 | Numdam | MR 2779402 | Zbl 1207.62161

[10] Evarist Giné; Rafał Latała; Joel Zinn Exponential and Moment Inequalities for U-Statistics, High Dimensional Probability II. 2nd international conference, Univ. of Washington, DC, USA, August 1-6, 1999 (Progress in Probability), Volume 47, Birkhäuser, 2000, pp. 13-88 | MR 1857312 | Zbl 0969.60024

[11] Evarist Giné; Joel Zinn On Hoffmann–Jorgensen’s Inequality for U-Processes, Probability in Banach Spaces, 8. Proceedings of the Eighth International Conference, held at Bowdoin College in summer of 1991 (Progress in Probability), Volume 30, Birkhäuser, 1992, pp. 80-91 | Zbl 0787.60020

[12] David L. Hanson; F. T. Wright A bound on tail probabilities for quadratic forms in independent random variables, Ann. Math. Stat., Volume 42 (1971) no. 3, pp. 1079-1083 | Article | MR 279864 | Zbl 0216.22203

[13] Wassily Hoeffding Probability Inequalities for Sums of Bounded Random Variables, J. Am. Stat. Assoc., Volume 58 (1963) no. 301, pp. 13-30 | Article | MR 144363 | Zbl 0127.10602

[14] Christian Houdré; Patricia Reynaud-Bouret Exponential Inequalities for U-Statistics of Order Two with Constants, Stochastic Inequalities and Applications. Selected papers presented at the Euroconference on “Stochastic inequalities and their applications”, Barcelona, June 18–22, 2002 (Evariste ad others Giné, ed.) (Progress in Probability), Volume 56, Birkhäuser, 2003, pp. 55-69 | Zbl 1036.60015

[15] Olav Kallenberg Foundations of Modern Probability, Probability and Its Applications, Springer, 1997 | Zbl 0892.60001

[16] Michael J. Klass; Krzysztof Nowicki Order of magnitude bounds for expectations of ${\Delta }_{2}$ functions of nonnegative random bilinear forms and generalized U-statistics, Ann. Probab., Volume 25 (1997), pp. 1471-1501 | MR 1457627 | Zbl 0895.60018

[17] Béatrice Laurent Adaptive estimation of a quadratic functional of a density by model selection, ESAIM, Probab. Stat., Volume 9 (2005), pp. 1-18 | Article | Numdam | MR 2148958 | Zbl 1136.62333

[18] Michel Ledoux On Talagrand’s deviation inequalities for product measures, ESAIM, Probab. Stat., Volume 1 (1997), pp. 63-87 | Article | Numdam | MR 1399224 | Zbl 0869.60013

[19] Pascal Massart About the constants in Talagrand’s concentration inequalities for empirical processes, Ann. Probab., Volume 28 (2000) no. 2, pp. 863-884 | MR 1782276 | Zbl 1140.60310

[20] Pascal Massart Concentration Inequalities and Model Selection: École d’Été de Probabilités de Saint-Flour XXXIII - 2003, Lecture Notes in Mathematics, 1896, Springer, 2007, pp. 147-181 | Zbl 1170.60006

[21] Philip E. Protter Stochastic differential equations, Stochastic integration and differential equations, Volume 21, Springer, 2005, pp. 243-355 | Article | MR 2273672

[22] Patricia Reynaud-Bouret Adaptive estimation of the intensity of inhomogeneous Poisson processes via concentration inequalities, Probab. Theory Relat. Fields, Volume 126 (2003) no. 1, pp. 103-153 | Article | MR 1981635 | Zbl 1019.62079

[23] Patricia Reynaud-Bouret Compensator and exponential inequalities for some suprema of counting processes, Stat. Probab. Lett., Volume 76 (2006) no. 14, pp. 1514-1521 | Article | MR 2245573 | Zbl 1101.60033

[24] Alexander Sokol; Niels Hansen Exponential Martingales and Changes of Measure for Counting Processes, Stochastic Anal. Appl., Volume 33 (2012) no. 5, pp. 823-843 | Article | MR 3378040 | Zbl 1325.60063

[25] Michel Talagrand New concentration inequalities in product spaces, Invent. Math., Volume 126 (1996) no. 3, pp. 505-563 | Article | MR 1419006 | Zbl 0893.60001

[26] Sara Van De Geer Exponential inequalities for martingales, with application to maximum likelihood estimation for counting processes, Ann. Stat., Volume 23 (1995) no. 5, pp. 1779-1801 | MR 1370307 | Zbl 0852.60019


text:
# CDF of correlated mixed random variables

1. Dec 30, 2013

### nikozm

Hello,

i m trying to evaluate the following:

r*x - r*y ≤ g, where r,x,y are nonnegative random variables of different distribution families and g is a constant nonnegative value.

Then, Pr[r*x - r*y ≤ g] = Pr[r*x ≤ g + r*y] = ∫ Fr x(g + r*y)*fr*y(y) dy, where F(.) and f(.) denote CDF and PDF, respectively.

The above formula works for independent variables. I m not sure if it works for correlated variables (the above are correlated due to the "r" variable in both "r*x" and "r*y").

Any help would be useful.

Thanks

2. Dec 30, 2013

### Staff: Mentor

I would express the inequality as $r(x-y) \leq g$ and find the distribution for x-y first, afterwards you just have two variables left.

3. Dec 30, 2013

### nikozm

However, the distribution of (x-y) is unreachable..Is there an other way to solve the problem ?

Thanks

4. Dec 30, 2013

### Stephen Tashi

I think you'll get a better answer if you explain completely what facts are known about the random variables.

5. Dec 30, 2013

### nikozm

Ok, assume that x and y are independent and identically distributed variables following a PDF as given bellow:
fz(z)=Exp[-1/z]/(z^2), where z ε {x,y}

(Thus, they follow an inverse exponential distribution..)

6. Dec 30, 2013

### Staff: Mentor

I don't understand what is unreachable about the difference of two of those distributions.
I guess it is not a nice expression, but it is still something you can write down.

7. Dec 30, 2013

### nikozm

The difference of (x-y) when both of them (x and y) follow the above distribution (i.e., see fz(z)) can not be obtained in closed-form. Moreover, both x and y are i.i.d. and real positive random numbers.

What else...?

8. Dec 31, 2013

### Stephen Tashi

What happens if x > y ?

9. Dec 31, 2013

### nikozm

Ok, assume that (x-y) ≥ 0, and thus r*(x-y) ≥ 0.

Thanks

10. Dec 31, 2013

### Stephen Tashi

If that is assumed then x and y are not independent.

format: plain


text:
# Determine whether each statement makes sense or does not make sense, and explain your reasoning. A system of linear equations in three variables, x, y

Determine whether each statement makes sense or does not make sense, and explain your reasoning. A system of linear equations in three variables, x, y, and z cannot contain an equation in the form $y=mx+b$.

You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

rogreenhoxa8

The general form of a system in three variables x,y,z has equation in the general form:
$akx+bky+ckz=dk$
If one of the coefficients ck of the variables z is zero, we can isolate y and bring that equation to the form $y=mx+b.$
$akx+bky=dk$
$bky=-akx+dk$
$y=-\left(ak/bk\right)x+dk/bk$


text:
# Introduction to impactr

impactr is an R package whose main goal is to process raw accelerometer data into mechanical loading-related variables. It contains functions to read the raw data, process the accelerometer signal and to predict some mechanical loading variables such as ground reaction force (GRF) and loading rate (LR). Currently it only works with raw accelerometer data from triaxial ActiGraph accelerometers stored as csv files, but with plans to expand the support for more accelerometer brands and file types.

This vignette provides a short introduction on how to use impactr, guiding you through each of the functions necessary to operate it. If anything is not clear in the package documentation, please let us know by creating an issue in GitHub following this link.

## Walkthrough

Before we begin, the package needs to be installed and then loaded into your R session.

If you don’t have much experience using R, we recommend you to install the latest impactr release from CRAN, by running:

install.packages("impactr")

After the package is installed, it should be loaded into your R session:

library(impactr)

The first step is to read the raw accelerometer data into R. We do it by using the read_acc() function specifying the path to the csv file containing the raw accelerometer data:

read_acc("path/to/file")

Remember that currently impactr only accepts raw data from triaxial ActiGraph accelerometers. In the raw data, acceleration values are stored as gravitational acceleration units (1g = 9.81m·s-2).

To show the package functionalities, impactr provides some short example files. The name of these files are shown when running:

impactr_example()
#> [1] "hip-raw.csv"

When entering one of these file names as an argument to the impactr_example() function, we obtain the path to the example data, and can pass it to read_acc():

acc_data <- read_acc(impactr_example("hip-raw.csv"))

The output of this function was assigned to the acc_data object with the R’s assignment operator (<-).

We can, then, inspect this object.

acc_data
#> # Start time:              2021-04-06 15:43:00
#> # Sampling frequency:      100Hz
#> # Accelerometer placement: Non-specified
#> # Subject body mass:       Non-specified
#> # Filter:                  No filter applied
#> # Data dimensions:         30,000 × 4
#>    timestamp           acc_X  acc_Y acc_Z
#>    <dttm>              <dbl>  <dbl> <dbl>
#>  1 2021-04-06 15:43:00 0.262 -0.688 0.063
#>  2 2021-04-06 15:43:00 0.25  -0.727 0.039
#>  3 2021-04-06 15:43:00 0.254 -0.816 0.191
#>  4 2021-04-06 15:43:00 0.258 -0.891 0.367
#>  5 2021-04-06 15:43:00 0.281 -0.914 0.344
#>  6 2021-04-06 15:43:00 0.316 -0.922 0.23
#>  7 2021-04-06 15:43:00 0.32  -0.891 0.203
#>  8 2021-04-06 15:43:00 0.332 -0.926 0.109
#>  9 2021-04-06 15:43:00 0.363 -1.02  0.168
#> 10 2021-04-06 15:43:00 0.418 -0.996 0.387
#> # … with 29,990 more rows

It shows the data with four columns – one for the timestamp and one for each of the accelerometer axes (X, Y and Z) – and a 6-line header with metadata. Among this metadata is the accelerometer data start time and sampling frequency, extracted from the csv file header, and also information about the accelerometer placement and the subject body mass, that are needed for applying the mechanical loading prediction models. It also shows information about the filter applied to the accelerometer signal and the data dimensions (30000 rows and 4 columns in this case).

Remember that, when using this function to read your own data, you need to specify the correct path to it. For example, if you have a file named id_001_raw_acceleration.csv inside the accelerometer_data folder in your Desktop, you need to write the path to it:

# For macOS or Linux
# For Windows
read_acc("C:/Users/username/Desktop/accelerometer_data/id_001_raw_acceleration.csv")

### define_region()

define_region() is an optional function to be used when you only want to analyse a specify portion of your data. To use it, you must specify the start and end time of your region of interest to the start_time and end_time arguments, along with the data read by the read_acc() function to the data argument:

acc_data <- define_region(
data = acc_data,
start_time = "2021-04-06 15:45:00",
end_time = "2021-04-06 15:46:00"
)
acc_data
#> # Start time:              2021-04-06 15:43:00
#> # Sampling frequency:      100Hz
#> # Accelerometer placement: Non-specified
#> # Subject body mass:       Non-specified
#> # Filter:                  No filter applied
#> # Data dimensions:         6,000 × 4
#>    timestamp            acc_X acc_Y acc_Z
#>    <dttm>               <dbl> <dbl> <dbl>
#>  1 2021-04-06 15:45:00 -0.148 -1.05 0.094
#>  2 2021-04-06 15:45:00 -0.098 -1.08 0.176
#>  3 2021-04-06 15:45:00 -0.055 -1.11 0.234
#>  4 2021-04-06 15:45:00 -0.035 -1.12 0.254
#>  5 2021-04-06 15:45:00 -0.02  -1.11 0.23
#>  6 2021-04-06 15:45:00 -0.004 -1.09 0.184
#>  7 2021-04-06 15:45:00  0.004 -1.06 0.152
#>  8 2021-04-06 15:45:00 -0.004 -1.08 0.152
#>  9 2021-04-06 15:45:00  0.008 -1.15 0.176
#> 10 2021-04-06 15:45:00  0.039 -1.20 0.195
#> # … with 5,990 more rows

### specify_parameters()

Apart from the raw accelerometer data, the mechanical loading prediction models need informations regarding the accelerometer body placement and the subject body mass. These informations are provided to impactr by the function specify_parameters():

acc_data <- specify_parameters(
data = acc_data, acc_placement = "hip", subj_body_mass = 78
)
acc_data
#> # Start time:              2021-04-06 15:43:00
#> # Sampling frequency:      100Hz
#> # Accelerometer placement: Hip
#> # Subject body mass:       78kg
#> # Filter:                  No filter applied
#> # Data dimensions:         6,000 × 4
#>    timestamp            acc_X acc_Y acc_Z
#>    <dttm>               <dbl> <dbl> <dbl>
#>  1 2021-04-06 15:45:00 -0.148 -1.05 0.094
#>  2 2021-04-06 15:45:00 -0.098 -1.08 0.176
#>  3 2021-04-06 15:45:00 -0.055 -1.11 0.234
#>  4 2021-04-06 15:45:00 -0.035 -1.12 0.254
#>  5 2021-04-06 15:45:00 -0.02  -1.11 0.23
#>  6 2021-04-06 15:45:00 -0.004 -1.09 0.184
#>  7 2021-04-06 15:45:00  0.004 -1.06 0.152
#>  8 2021-04-06 15:45:00 -0.004 -1.08 0.152
#>  9 2021-04-06 15:45:00  0.008 -1.15 0.176
#> 10 2021-04-06 15:45:00  0.039 -1.20 0.195
#> # … with 5,990 more rows

The supported accelerometer placements are “ankle”, “back” or “hip” and the body mass must be given as kilograms. Notice that these informations are added to the data header.

### filter_acc()

The raw accelerometer data can be digitally filtered to reduce noise. The filter_acc() function does it by getting the coefficients of a Butterworth digital filter and applying it twice (forwards and backwards) to the acceleration signal. The simplest way to use it is to call the filter_acc() function supplying only the accelerometer data:

acc_data <- filter_acc(data = acc_data)
acc_data
#> # Start time:              2021-04-06 15:43:00
#> # Sampling frequency:      100Hz
#> # Accelerometer placement: Hip
#> # Subject body mass:       78kg
#> # Filter:                  Butterworth (4th-ord, low-pass, 20Hz)
#> # Data dimensions:         6,000 × 4
#>    timestamp               acc_X  acc_Y  acc_Z
#>    <dttm>                  <dbl>  <dbl>  <dbl>
#>  1 2021-04-06 15:45:00 -0.0900   -0.742 0.0878
#>  2 2021-04-06 15:45:00 -0.102    -1.08  0.171
#>  3 2021-04-06 15:45:00 -0.0768   -1.20  0.235
#>  4 2021-04-06 15:45:00 -0.0375   -1.16  0.253
#>  5 2021-04-06 15:45:00 -0.00870  -1.09  0.229
#>  6 2021-04-06 15:45:00  0.000810 -1.06  0.188
#>  7 2021-04-06 15:45:00 -0.00329  -1.07  0.156
#>  8 2021-04-06 15:45:00 -0.00753  -1.10  0.148
#>  9 2021-04-06 15:45:00  0.00602  -1.14  0.166
#> 10 2021-04-06 15:45:00  0.0510   -1.19  0.206
#> # … with 5,990 more rows

This function lets you select the order, cut-off frequency and type of the Butterworth filter (more details in the function documentation help(filter_acc)). To better reproduce the conditions in which the models validation were performed, we suggest you not to change the default values of order, cutoff and type arguments, unless you have a strong reason to do so.

### use_resultant()

The mechanical loading prediction models included in impactr work with either the acceleration vertical vector or the resultant vector computed as the Euclidean norm of the three vectors $$(r = \sqrt{X^2 + Y^2 + Z^2})$$. To compute the resultant you can use the use_resultant() function:

acc_data <- use_resultant(data = acc_data)
acc_data
#> # Start time:              2021-04-06 15:43:00
#> # Sampling frequency:      100Hz
#> # Accelerometer placement: Hip
#> # Subject body mass:       78kg
#> # Filter:                  Butterworth (4th-ord, low-pass, 20Hz)
#> # Data dimensions:         6,000 × 5
#>    timestamp               acc_X  acc_Y  acc_Z acc_R
#>    <dttm>                  <dbl>  <dbl>  <dbl> <dbl>
#>  1 2021-04-06 15:45:00 -0.0900   -0.742 0.0878 0.753
#>  2 2021-04-06 15:45:00 -0.102    -1.08  0.171  1.10
#>  3 2021-04-06 15:45:00 -0.0768   -1.20  0.235  1.22
#>  4 2021-04-06 15:45:00 -0.0375   -1.16  0.253  1.18
#>  5 2021-04-06 15:45:00 -0.00870  -1.09  0.229  1.11
#>  6 2021-04-06 15:45:00  0.000810 -1.06  0.188  1.07
#>  7 2021-04-06 15:45:00 -0.00329  -1.07  0.156  1.08
#>  8 2021-04-06 15:45:00 -0.00753  -1.10  0.148  1.11
#>  9 2021-04-06 15:45:00  0.00602  -1.14  0.166  1.15
#> 10 2021-04-06 15:45:00  0.0510   -1.19  0.206  1.21
#> # … with 5,990 more rows

This function add a new column acc_R with the resultant acceleration values. We suggest to utilise this function after filter_acc(), otherwise the resultant vector computation will use the non-filtered acceleration signal.

### find_peaks()

To apply the prediction models, the peaks in the acceleration signal should be found. The find_peaks() function does it and returns the timestamp of the peak in a column and its magnitude in another. The vector argument controls in which vector the peaks should be found and can be set to either vertical, resultant or all.

acc_data <- find_peaks(data = acc_data, vector = "resultant")
acc_data
#> # Start time:              2021-04-06 15:43:00
#> # Sampling frequency:      100Hz
#> # Accelerometer placement: Hip
#> # Subject body mass:       78kg
#> # Filter:                  Butterworth (4th-ord, low-pass, 20Hz)
#> # Data dimensions:         32 × 2
#>    timestamp           resultant_peak_acc
#>    <dttm>                           <dbl>
#>  1 2021-04-06 15:45:00               1.32
#>  2 2021-04-06 15:45:01               1.36
#>  3 2021-04-06 15:45:04               1.30
#>  4 2021-04-06 15:45:04               2.32
#>  5 2021-04-06 15:45:05               1.50
#>  6 2021-04-06 15:45:06               1.68
#>  7 2021-04-06 15:45:06               1.51
#>  8 2021-04-06 15:45:07               1.96
#>  9 2021-04-06 15:45:08               1.37
#> 10 2021-04-06 15:45:08               1.86
#> # … with 22 more rows

As with filter_acc(), find_peaks() default values of the minimum height (min_height) and distance (min_dist) of the peaks are set to replicate the values used in the calibration study. You should only change them if you have a strong reason to.

Finally, the predict_loading() is used to predict the mechanical loading variables based on the acceleration signal. Currently, impactr provides models to predict ground reaction force (GRF) and loading rate (LR) of the resultant vector and its vertical component with a models validated in walking and running activities. The outcome, vector and model arguments are used to control this parameters. More details regarding the values accepted by these paremeters can be found in the function documentation (help(predict_loading)).

predict_loading(
data = acc_data,
outcome = "grf",
vector = "resultant",
model = "walking/running"
)
#> # Start time:              2021-04-06 15:43:00
#> # Sampling frequency:      100Hz
#> # Accelerometer placement: Hip
#> # Subject body mass:       78kg
#> # Filter:                  Butterworth (4th-ord, low-pass, 20Hz)
#> # Data dimensions:         32 × 3
#>    timestamp           resultant_peak_acc resultant_peak_grf
#>    <dttm>                           <dbl>              <dbl>
#>  1 2021-04-06 15:45:00               1.32              1387.
#>  2 2021-04-06 15:45:01               1.36              1392.
#>  3 2021-04-06 15:45:04               1.30              1384.
#>  4 2021-04-06 15:45:04               2.32              1521.
#>  5 2021-04-06 15:45:05               1.50              1412.
#>  6 2021-04-06 15:45:06               1.68              1435.
#>  7 2021-04-06 15:45:06               1.51              1412.
#>  8 2021-04-06 15:45:07               1.96              1473.
#>  9 2021-04-06 15:45:08               1.37              1393.
#> 10 2021-04-06 15:45:08               1.86              1459.
#> # … with 22 more rows

As can be seen above, predict_loading() adds columns to the supplied data corresponding to the outcome and vector specified in the arguments. Note that GRF are expressed as newton (N) and LR as newton per second (N·s-1)

## Wrap up

impactr helps you to move from the raw accelerometer data to discrete estimates of mechanical loading variables in an easy way. All the functions necessary to this analysis are described above in a step-by-step manner. These functions were also designed to be used with pipe operators (either of the magrittr package or the base R package for R version >= 4.1.0). By using the pipe, the output of a function call is passed directly to the next, avoiding nested function calls or the need to assign local variables. Below are examples the whole analysis assigning local variables in intermediate steps and using the base R pipe:

# Using intermediate steps
acc_data <- specify_parameters(
data = acc_data, acc_placement = "hip", subj_body_mass = 78
)
acc_data <- filter_acc(data = acc_data)
acc_data <- use_resultant(data = acc_data)
acc_data <- find_peaks(data = acc_data, vector = "resultant")
data = acc_data,
outcome = "grf",
vector = "resultant",
model = "walking/running"
)

# Using the base R pipe operator
)


text:
# Solving an equation?

solving an equation??

## Homework Statement

how to get from here
sin@-.3cos@=.3
to
@=33.40 degrees

## The Attempt at a Solution

I try every thing teacher said to put it in the calculator and find the where it intersects x-axis but I get @=30 degrees

this is pretty simple problem, I suggest you to study the sine and cosine functions well, and you will find that sin(pi) = 0 and cos(pi)=-1

Then sin(pi)-0.3*cos(pi)=0.3

0 + 0.3 = 0.3

tiny-tim


text:
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# A solar C/O and sub-solar metallicity in a hot Jupiter atmosphere

## Abstract

Measurements of the atmospheric carbon (C) and oxygen (O) relative to hydrogen (H) in hot Jupiters (relative to their host stars) provide insight into their formation location and subsequent orbital migration1,2. Hot Jupiters that form beyond the major volatile (H2O/CO/CO2) ice lines and subsequently migrate post disk-dissipation are predicted have atmospheric carbon-to-oxygen ratios (C/O) near 1 and subsolar metallicities2, whereas planets that migrate through the disk before dissipation are predicted to be heavily polluted by infalling O-rich icy planetesimals, resulting in C/O < 0.5 and super-solar metallicities1,2. Previous observations of hot Jupiters have been able to provide bounded constraints on either H2O (refs. 3,4,5) or CO (refs. 6,7), but not both for the same planet, leaving uncertain4 the true elemental C and O inventory and subsequent C/O and metallicity determinations. Here we report spectroscopic observations of a typical transiting hot Jupiter, WASP-77Ab. From these, we determine the atmospheric gas volume mixing ratio constraints on both H2O and CO (9.5 × 10−5–1.5 × 10−4 and 1.2 × 10−4–2.6 × 10−4, respectively). From these bounded constraints, we are able to derive the atmospheric C/H ($${0.35}_{-0.10}^{+0.17}$$ × solar) and O/H ($${0.32}_{-0.08}^{+0.12}$$ × solar) abundances and the corresponding atmospheric carbon-to-oxygen ratio (C/O = 0.59 ± 0.08; the solar value is 0.55). The sub-solar (C+O)/H ($${0.33}_{-0.09}^{+0.13}$$ × solar) is suggestive of a metal-depleted atmosphere relative to what is expected for Jovian-like planets1 while the near solar value of C/O rules out the disk-free migration/C-rich2 atmosphere scenario.

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## Data availability

The raw PLP extracted IGRINS data files and subsequent data products are available here: https://www.dropbox.com/sh/0cxfolfmrs8ip37/AABZYoHr8nuRlHJG84dArX4ea?dl=0.

## Code availability

The IGRINS PLP used to perform the initial reduction and extraction by the instrument team is available at https://github.com/igrins/plp. The barycenter correction and planetary phase calculations were made using the python astropy library found here https://www.astropy.org/. Python numpy specific tools are noted in the text (for example, the SVD for the PCA). The chemical abundance analysis/physical plausibility assessment made use of the VULCAN chemical kinetics tool. (https://github.com/exoclime/VULCAN). Absorption cross-sections were generated using the HELIOS-K tool (https://helios-k.readthedocs.io/en/latest/). Finally, we make available a an end-to-end python2/GPU HRCCS retrieval code example available here https://www.dropbox.com/sh/0cxfolfmrs8ip37/AABZYoHr8nuRlHJG84dArX4ea?dl=0, which makes use of the pymultinest nested-sampling package (https://johannesbuchner.github.io/PyMultiNest/), joblib loop parallelization package (https://joblib.readthedocs.io/en/latest/), and corner.py (https://corner.readthedocs.io/en/latest/).

## References

1. 1.

Mordasini, C., van Boekel, R., Molliere, P., Henning, T. & Benneke, B. The imprint of exoplanet formation history on observable present-day spectra of hot Jupiters. Astrophys. J. 832, 41 (2016).

2. 2.

Madhusudhan, N. Exoplanetary atmospheres: key insights, challenges, and prospects. Ann. Rev. Astron. Astrophys. 57, 617–663 (2019).

3. 3.

Tsiaras, A. et al. A population study of gaseous exoplanets. Astron. J. 155, 156 (2018).

4. 4.

Welbanks, L. et al. Mass-metallicity trends in transiting exoplanets from atmospheric abundances of H2O, Na, and K. Astrophys. J. Lett. 887, L20 (2019).

5. 5.

Gandhi, S., Madhusudhan, N., Hawker, G. & Piette, A. HyDRA-H: simultaneous hybrid retrieval of exoplanetary emission spectra. Astron. J. 158, 228 (2019).

6. 6.

Pelletier, S. et al. Where is the water? Jupiter-like C/H ratio but strong H2O depletion found on τ Boötis b using SPIRou. Astron. J. 162, 73 (2021).

7. 7.

Brogi, M. & Line, M. R. Retrieving temperatures and abundances of exoplanet atmospheres with high-resolution cross-correlation spectroscopy. Astron. J. 157, 114 (2019).

8. 8.

Maxted, P. F. L. et al. WASP-77 Ab: a transiting hot Jupiter planet in a wide binary system. Pub. Astron. Soc. Pac. 125, 48 (2013).

9. 9.

Park, C. et al. Design and early performance of IGRINS (immersion grating infrared spectrometer). In Ground-based and Airborne Instrumentation for Astronomy V, vol. 9147 of Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series (eds Ramsay, S. K., McLean, I. S. & Takami, H.) 91471D (2014).

10. 10.

Mace, G. et al. IGRINS at the Discovery Channel Telescope and Gemini South. In Ground-based and Airborne Instrumentation for Astronomy VII, vol. 10702 of Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series (eds. Evans, C. J., Simard, L. & Takami, H.) 107020Q (2018).

11. 11.

Lee, Jae-Joon & Gullikson, Kevin. PLP: v2.1 alpha 3 [Data set]. Zenodo https://doi.org/10.5281/zenodo.56067 (2016)

12. 12.

de Kok, R. J. et al. Detection of carbon monoxide in the high-resolution day-side spectrum of the exoplanet HD 189733b. Astron. J. 554, A82 (2013).

13. 13.

Brogi, M. et al. The signature of orbital motion from the dayside of the planet τ Boötis b. Nature 486, 502–504 (2012).

14. 14.

Birkby, J. L. et al. Detection of water absorption in the day side atmosphere of HD 189733 b using ground-based high-resolution spectroscopy at 3.2 µm. Mon. Not. R. Astron. Soc. 436, L35–L39 (2013).

15. 15.

Lockwood, A. et al. Near-IR direct detection of water vapor in Tau Boötis b. Astrophys. J. Lett. 783, L29 (2014).

16. 16.

Snellen, I. A. G., de Kok, R. J., de Mooij, E. J. W. & Albrecht, S. The orbital motion, absolute mass and high-altitude winds of exoplanet HD209458b. Nature 465, 1049–1051 (2010).

17. 17.

Moses, J. I. Chemical kinetics on extrasolar planets. Philos. Trans. R. Soc. A 372, 20130073 (2014).

18. 18.

Parmentier, V., Fortney, J. J., Showman, A. P., Morley, C. & Marley, M. S. Transitions in the cloud composition of hot Jupiters. Astrophys. J. 828, 22 (2016).

19. 19.

Asplund, M., Grevesse, N., Sauval, A. J. & Scott, P. The chemical composition of the Sun. Ann. Rev. Astron. Astrophys. 47, 481–522 (2009).

20. 20.

Öberg, K. I., Murray-Clay, R. & Bergin, E. A. The effects of snowlines on C/O in planetary atmospheres. Astrophys. J. Lett. 743, L16 (2011).

21. 21.

Madhusudhan, N., Amin, M. A. & Kennedy, G. M. Towards chemical constraints on hot Jupiter migration. Astrophys. J. Lett. 794, L12 (2014)

22. 22.

Madhusudhan, N., Bitsch, B., Johansen, A. & Eriksson, L. Atmospheric signatures of giant exoplanet formation by pebble accretion. Mon. Not. R. Astron. Soc. 469, 4102–4115 (2017).

23. 23.

Booth, R. A., Clarke, C. J., Madhusudhan, N. & Ilee, J. D. Chemical enrichment of giant planets and discs due to pebble drift. Mon. Not. R. Astron. Soc. 469, 3994–4011 (2017).

24. 24.

Kreidberg, L. et al. A precise water abundance measurement for the hot Jupiter WASP-43b. Astrophys. J. Lett. 739, L27 (2014).

25. 25.

Li, C. et al. The water abundance in Jupiter’s equatorial zone. Nat. Astron. 4, 609–616 (2020).

26. 26.

Atreya, S. K. et al. The origin and evolution of Saturn, with exoplanet perspective. Preprint at https://arxiv.org/abs/1606.04510 (2016).

27. 27.

Thorngren, D. & Fortney, J. J. Connecting giant planet atmosphere and interior modeling: constraints on atmospheric metal enrichment. Astrophys. J. Lett. 874, L31 (2019).

28. 28.

Burrows, A. & Sharp, C. M. Chemical equilibrium abundances in brown dwarf and extrasolar giant planet atmospheres. Astrophys. J. 512, 843–863 (1999).

29. 29.

Giacobbe, P. et al. Five carbon- and nitrogen-bearing species in a hot giant planet’s atmosphere. Nature 592, 205–208 (2021).

30. 30.

Line, M. R. et al. A systematic retrieval analysis of secondary eclipse spectra. I. A comparison of atmospheric retrieval techniques. Astrophys. J. 775, 137 (2013).

31. 31.

Line, M. R. et al. Uniform atmospheric retrieval analysis of ultracool dwarfs. II. Properties of 11 T dwarfs. Astrophys. J. 848, 83 (2017).

32. 32.

Tennyson, J. et al. The 2020 release of the ExoMol database: molecular line lists for exoplanet and other hot atmospheres. J. Quant. Spectrosc. Radiat. Transf. 255, 107228 (2020).

33. 33.

Coles, P. A., Yurchenko, S. N. & Tennyson, J. ExoMol molecular line lists – XXXV. A rotation-vibration line list for hot ammonia. Mon. Not. R. Astro. Soc. 490, 4638–4647 (2019).

34. 34.

Rothman, L. S. et al. HITEMP, the high-temperature molecular spectroscopic database. J. Quant. Spectrosc. Radiat. Transf. 111, 2139–2150 (2010).

35. 35.

Hargreaves, R. J. et al. An accurate, extensive, and practical line list of methane for the HITEMP database. Astrophys. J. Suppl. Ser. 247, 55 (2020).

36. 36.

Li, G. et al. Rovibrational line lists for nine isotopologues of the CO molecule in the X 1Σ+ ground electronic state. Astrophys. J. Suppl. Ser. 216, 15 (2015).

37. 37.

Azzam, A. A. A., Tennyson, J., Yurchenko, S. N. & Naumenko, O. V. ExoMol molecular line lists - XVI. The rotation-vibration spectrum of hot H2S. Mon. Not. R. Astron. Soc. 460, 4063–4074 (2016).

38. 38.

Barber, R. J. et al. ExoMol line lists - III. An improved hot rotation-vibration line list for HCN and HNC. Mon. Not. R. Astron. Soc. 437, 1828–1835 (2014).

39. 39.

Karman, T. et al. Update of the HITRAN collision-induced absorption section. Icarus 328, 160–175 (2019).

40. 40.

Grimm, S. L. & Heng, K. HELIOS-K: an ultrafast, open-source opacity calculator for radiative transfer. Astrophys. J. 808, 182 (2015).

41. 41.

Grimm, S. L. et al. HELIOS-K 2.0 opacity calculator and open-source opacity database for exoplanetary atmospheres. Astrophys. J. Suppl. 253, 30 (2021).

42. 42.

Polyansky, O. L. et al. ExoMol molecular line lists XXX: a complete high-accuracy line list for water. Mon. Not. R. Astron. Soc. 480, 2597–2608 (2018).

43. 43.

Gharib-Nezhad, E. et al. EXOPLINES: molecular absorption cross-section database for brown dwarf and giant exoplanet atmospheres. Astrophys. J. Suppl. Ser. 254, 34 (2021)

44. 44.

Madhusudhan, N. & Seager, S. A temperature and abundance retrieval method for exoplanet atmospheres. Astrophys. J. 707, 24–39 (2009).

45. 45.

Buchner, J. et al. X-ray spectral modelling of the AGN obscuring region in the CDFS: Bayesian model selection and catalogue. Astron. Astrophys. 564, A125 (2014)

46. 46.

Feroz, F., Hobson, M. P. & Bridges, M. MULTINEST: an efficient and robust Bayesian inference tool for cosmology and particle physics. Mon. Not. R. Astron. Soc. 398, 1601–1614 (2009).

47. 47.

Zucker, S. Cross-correlation and maximum-likelihood analysis: a new approach to combiningcross-correlation functions. Mon. Not. R. Astron. Soc. 342, 1291–1298 (2003).

48. 48.

Gibson, N. P. et al. Detection of Fe I in the atmosphere of the ultra-hot Jupiter WASP-121b, and a new likelihood-based approach for Doppler-resolved spectroscopy. Mon. Not. R. Astron. Soc. 493, 2215–2228 (2020).

49. 49.

Line, M. R., Knutson, H., Wolf, A. S. & Yung, Y. L. A systematic retrieval analysis of secondary eclipse spectra. II. A uniform analysis of nine planets and their C to O ratios. Astrophys. J. 783, 70 (2014).

50. 50.

Hoeijmakers, H. J. et al. Atomic iron and titanium in the atmosphere of the exoplanet KELT9b. Nature 560, 453–455 (2018).

51. 51.

Brogi, M. et al. Detection of molecular absorption in the dayside of exoplanet 51 Pegasi b? Astrophys. J. 767, 27 (2013).

52. 52.

Beltz, H., Rauscher, E., Brogi, M. & Kempton, E. M. R. A significant increase in detection of high-resolution emission spectra using a three-dimensional atmospheric model of a hot Jupiter. Astron. J. 161, 1 (2021).

53. 53.

Piskorz, D. et al. Ground- and space-based detection of the thermal emission spectrum of the transiting hot Jupiter KELT-2Ab. Astron. J. 156, 133 (2018).

54. 54.

Gharib-Nezhad, E. & Line, M. R. The influence of H2O pressure broadening in High-metallicity exoplanet atmospheres. Astrophys. J. 872, 27 (2019).

55. 55.

Arcangeli, J. et al. H opacity and water dissociation in the dayside atmosphere of the very hot gas giant WASP-18b. Astrophys. J. Lett. 855, L30 (2018).

56. 56.

Perez-Becker, D. & Showman, A. P. Atmospheric heat redistribution on hot Jupiters. Astrophys. J. 776, 134 (2013).

57. 57.

Tsai, S.-M. et al. Toward consistent modeling of atmospheric chemistry and dynamics in exoplanets: validation and generalization of the chemical relaxation method. Astrophys. J. 862, 31 (2018).

58. 58.

Fortney, J. J., Lodders, K., Marley, M. S. & Freedman, R. S. A unified theory for the atmospheres of the hot and very hot Jupiters: two classes of irradiated atmospheres. Astrophys. J. 678, 1419–1435 (2008).

59. 59.

Parmentier, V., Showman, A. P. & Fortney, J. J. The cloudy shape of hot Jupiter thermal phase curves. Mon. Not. R. Astron. Soc. 501, 78–108 (2021).

60. 60.

Fortney, J. J. et al. A framework for characterizing the atmospheres of low-mass low density transiting planets. Astrophys. J. 775, 80 (2013).

61. 61.

Pinhas, A., Madhusudhan, N., Gandhi, S. & MacDonald, R. H2O abundances and cloud properties in ten hot giant exoplanets. Mon. Not. R. Astron. Soc. 482, 1485–1498 (2019).

62. 62.

Fisher, C. & Heng, K. Retrieval analysis of 38 WFC3 transmission spectra and resolution ofthe normalization degeneracy. Mon. Not. R. Astron. Soc. 481, 4698–4727 (2018).

63. 63.

Feng, Y. K. et al. The impact of non-uniform thermal structure on the interpretation of exoplanet emission spectra. Astrophys. J. 829, 52 (2016).

64. 64.

Line, M. R. et al. Information content of exoplanetary transit spectra: an initial look. Astrophys. J. 749, 93 (2012).

65. 65.

Guillot, T. On the radiative equilibrium of irradiated planetary atmospheres. Astron. Astrophys. 520, A27 (2010).

66. 66.

Gandhi, S. et al. Molecular cross-sections for high-resolution spectroscopy of super-Earths, warm Neptunes, and hot Jupiters. Mon. Not. R. Astron. Soc. 495, 224–237 (2020).

67. 67.

Woods, P. M. & Willacy, K. Carbon isotope fractionation in protoplanetary disks. Astrophys. J. 693, 1360–1378 (2009).

68. 68.

Marboeuf, U., Thiabaud, A., Alibert, Y. & Benz, W. Isotopic ratios D/H and 15N/14N in giant planets. Mon. Not. R. Astron. Soc. 475, 2355–2362 (2018).

69. 69.

Molliere, P. & Snellen, I. A. G. Detecting isotopologues in exoplanet atmospheres using ground-based high-dispersion spectroscopy. Astron. Astrophys. 622, A139 (2019).

## Acknowledgements

M.R.L., J.J.F., J.L.B. and P.S. acknowledge support from NASA XRP grant 80NSSC19K0293. M.R.L. and E.S. acknowledge support from the Nexus for Exoplanet System Science and NASA Astrobiology Institute Virtual Planetary Laboratory (no. 80NSSC18K0829). M.B. and S.G. acknowledge support from the UK Science and Technology Facilities Council (STFC) research grant ST/S000631/1. J.Z. acknowledges support from the NASA FINESST grant 80NSSC19K1420. E.M.-R.K. and E.R. thank the Heising-Simons Foundation for support. J.P.W. acknowledges support from the Wolfson Harrison UK Research Council Physics Scholarship and the UK Science and Technology Facilities Council (STFC). This work used the Immersion Grating Infrared Spectrometer (IGRINS) that was developed under a collaboration between the University of Texas at Austin and the Korea Astronomy and Space Science Institute (KASI) with the financial support of the Mount Cuba Astronomical Foundation, of the US National Science Foundation under grants AST-1229522 and AST-1702267, of the McDonald Observatory of the University of Texas at Austin, of the Korean GMT Project of KASI, and Gemini Observatory. This program, GS-2020B-Q-249, is based on observations obtained at the international Gemini Observatory, a program of NSF’s NOIRLab, which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation on behalf of the Gemini Observatory partnership: the National Science Foundation (United States), National Research Council (Canada), Agencia Nacional de Investigación y Desarrollo (Chile), Ministerio de Ciencia, Tecnología e Innovación (Argentina), Ministério da Ciência, Tecnologia, Inovações e Comunicações (Brazil), and Korea Astronomy and Space Science Institute (Republic of Korea). Finally, we acknowledge Research Computing at Arizona State University for providing HPC and storage resources that have significantly contributed to the research results reported within this manuscript.

## Author information

Authors

### Contributions

M.R.L. conceived of the idea, performed the data analysis and modelling, and wrote the manuscript. J.Z. (principal investigator) and M.R.L. wrote the original IGRINS proposal. M.B. provided guidance on the cross-correlation analysis and conceptual framework. J.L.B. provided guidance on the context of the results. S.G. performed an independent Bayesian analysis to confirm the result. G.N.M. ran the PLP pipeline and also assisted in the IGRINS specific observational setup. V.P., P.S., G.M., M.M., E.M.-R.K., J.J.F., E.S., J.P., E.R., J-M.D., J.P.W. and L.P. helped with the original proposal/and or provided valuable insight/comments on the manuscript or through discussions.

### Corresponding author

Correspondence to Michael R. Line.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Neale Gibson and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data figures and tables

### Extended Data Fig. 1 Summary of the data and PCA procedure.

a, The median per-resolution element signal-to-noise for each order for the night (in red). The blue curve is the median SNR in both time and over an individual order. b, Example raw data cubes (top row)—spectra versus time/frame for representative two orders (25, 5). Stationary tellurics show up as vertical dark streaks. Wavelength dependent gradient is due to the echelle blaze throughput. The PCA/SVD method can remove these stationary features, leaving behind the planetary signal buried in the noise (bottom row). We use these ‘post-PCA’ frames for the subsequent cross-correlation/retrieval analysis (repeated for all 43 use orders).

### Extended Data Fig. 2 Summary of the key opacity sources used in the retrieval analysis.

Absorption cross-sections for the molecules considered in the retrieval analysis (for 0.01 bar, 1,600 K).

### Extended Data Fig. 3 Corner plot summary of the posterior probability distribution from the main-text retrieval analysis.

Note the bounded constraints on water, CO and the isotopic ratio, but upper limits only on the other species. Note, we retrieve [13C16O/12C16O] but plot the inverse, [12C16O/13C16O] to facilitate comparisons to literature reported values (in Extended Data Fig. 6) The inset shows the molecular components of the maximum likelihood model spectrum. Figure generated with corner.py.

### Extended Data Fig. 4 Classic cross-correlation analysis data products.

The model template used to in this cross-correlation analysis is the spectrum resulting from the maximum likelihood solution found by the retrieval analysis. The left column illustrates the gas detections (all gases, H2O, CO and other—NH3+H2S+HCN+CH4) in the standard Kp–ΔVsys plane, with a slice in Vsys along the literature reported Kp at the bottom. The detection maps are constructed by subtracting the mean total CC, then dividing by an ‘off peak’ (a boxed region in the lower left corner of each panel) CC standard deviation. Using this method, only H2O is strongly detected, with a hint of CO present at the expected velocities. The right column reproduces analogous products using the log-likelihood formalism7 (∆logL relative to the minimum), resulting in a stronger presence of CO. We emphasize that while such maps may be instructive for ‘detecting’ species or ‘atmosphere’, they do not marginalize over all of the degeneracy, nor do they maximize the information content in the data. This is why in our analysis we focus on the results arising from the more comprehensive log-likelihood/retrieval formalism.

### Extended Data Fig. 5 Robustness test analyses summary using the H2O, CO and temperature profile constraints as the metrics for assumption impact.

The top row of histograms and first TP profile histogram demonstrate the lack of impact of temperature profile parameterization. The middle panel of histograms and middle temperature profile panel show that there is little impact due to any presence of temperature heterogeneities on the hemisphere(s) observed during the sequence. Finally, the bottom panel of histograms and last temperature profile panel illustrate the lack of impact of various data analysis and other minor modelling assumptions. In short, the retrieved abundances and temperature profile constraints are largely resilient against most common assumptions.

### Extended Data Fig. 6 Bayesian inference/retrieval tool comparison on the IGRINS data.

The temperature profiles are compared in the left most panel and a subset of the abundances in the corner plot on the right. Each model uses slightly different atmospheric parameterization assumptions with the core radiative transfer aspects (solver, opacities) independently developed.

### Extended Data Fig. 7 Carbon isotopic abundance analysis.

The top row of histograms compares the constraints from a nominal simplified retrieval model applied to the true data (red) and the reverse-injected data reinjected with 13C isotope removed model (black). The upper limit on the simulated data and bounded constraint arising from the true dataset suggests that there is indeed isotopic information in these IGRINS data. The bottom panel compares the retrieved 12C to 13C ratio (red) to common Solar System bodies (blue, after ref. 68) and various reference values (galactic interstellar medium (ISM) components, and Earth (terrestrial), black dashed lines). WASP-77Ab sits anomalously low (enhanced 13C) compared to most Solar System objects.

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Line, M.R., Brogi, M., Bean, J.L. et al. A solar C/O and sub-solar metallicity in a hot Jupiter atmosphere. Nature 598, 580–584 (2021). https://doi.org/10.1038/s41586-021-03912-6

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Public Group

# endl error

This topic is 4458 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

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I'm working on an exercise program in my C++ book. Here is the source code: // Listing 2.2 using cout #include <iostream> int main() { std::cout << "Hello there.\n"; std::cout << "Here is 5: " << 5 << "\n"; std::cout << "The manipulator endl writes a new line to the screen."; std::cout << endl; std::cout << "Here is a very big number:\t" << 7000 << endl; std::cout << "Here is the sum of 8 and 5:\t" << 8 + 5 << endl; std::cout << "Here's a fraction:\t\t" << (float) 5/8 << endl; std::cout << "And a very very big number:\t"; std::cout << (double) 7000 * 7000 << endl; std::cout << "Don't forget to replace Jesse Liberty with your name...\n"; std::cout << "Jesse Liberty is a C++ Programmer!\n"; return 0; } However, I keep getting this error: "9 C:\Documents and Settings\Joey\My Documents\cpp\exercise2.cpp endl' undeclared (first use this function) (Each undeclared identifier is reported only once for each function it appears in.) " The book doesn't tell me anything about an error. Line's 8 and 9 are confusing though, so I deleted them, but the same problem with endl; came up for the previous line. Any help would be greatly appreciated, thanks.

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You should use either std::endl or put 'using namespace std' at the top of your code after the header include and drop the std:: prefixes all together.

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endl is in namespace std, just like cout, so it's called std::endl

Corrected code:
#include <iostream>int main(){std::cout << "Hello there.\n";std::cout << "Here is 5: " << 5 << "\n";std::cout << "The manipulator endl writes a new line to the screen.";std::cout << std::endl;std::cout << "Here is a very big number:\t" << 7000 << std::endl;std::cout << "Here is the sum of 8 and 5:\t" << 8 + 5 << std::endl;std::cout << "Here's a fraction:\t\t" << (float) 5/8 << std::endl;std::cout << "And a very very big number:\t";std::cout << (double) 7000 * 7000 << std::endl;std::cout << "Don't forget to replace Jesse Liberty with your name...\n";std::cout << "Jesse Liberty is a C++ Programmer!\n";return 0;}`

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ItsNotATumaaa,

endl is also part of the 'std' namespace. Make sure to either write "using namespace std;"

at the start of your file. Or add "std::" to the beginning of endl.

ie:
std::cout << "Here is a very big number:\t" << 7000 << std::endl;

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Ahh, thanks, I wasn't sure where the std:: was necessary.

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Quote:
 Original post by ItsNotATumaaaAhh, thanks, I wasn't sure where the std:: was necessary.

std is required for all functions and classes in the standard library, cout, cin, vector, list, deque, map, sort, etc.

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Thanks for all the help, I went ahead and added using namespace std; below my header and removed std:: all together, added a system pause (Because the window disappears after a split second) and it worked.

I think I'm starting to get to the hang of this, (Barely) couldn't do it without all your help though, thanks!

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BTW, you should replace all you "\n" with std::endl.

Regards,

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Quote:
 Original post by Emmanuel DelogetBTW, you should replace all you "\n" with std::endl.Regards,

why? whats wrong with
std::cout <

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hmmm missing most of the last post

std::cout <

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JoeJ
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5. 5

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# Playing with Powers of 2

Number Theory Level pending

Let $$P\left( x \right)$$ be the sum of the digits of $$x$$. We define $$T\left( x\right)$$ as applying $$P\left( x \right)$$ to the number $$x$$, and then to the result (repeatedly), until the outcome is a single digit. For example, $$T\left( 249 \right) :\quad P(249)=15,\quad P(15)=6$$ so $$T\left( 249 \right) =6$$.

Let $$T({ 2 }^{ 2016 })=N$$. Find the least possible value for $$x>1$$ that satisfy $${ 2 }^{ P(x) }\equiv N \pmod x$$.

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# 1.3 Levels of measurement

 Page 4 / 14

## Try it

[link] represents the amount, in inches, of annual rainfall in a sample of towns. What fraction of towns surveyed get between 11.03 and 13.05 inches of rainfall each year?

## Try it solutions

$\frac{9}{50}$

[link] contains the total number of deaths worldwide as a result of earthquakes for the period from 2000 to 2012.

Year Total Number of Deaths
2000 231
2001 21,357
2002 11,685
2003 33,819
2004 228,802
2005 88,003
2006 6,605
2007 712
2008 88,011
2009 1,790
2010 320,120
2011 21,953
2012 768
Total 823,356

Answer the following questions.

1. What is the frequency of deaths measured from 2006 through 2009?
2. What percentage of deaths occurred after 2009?
3. What is the relative frequency of deaths that occurred in 2003 or earlier?
4. What is the percentage of deaths that occurred in 2004?
5. What kind of data are the numbers of deaths?
6. The Richter scale is used to quantify the energy produced by an earthquake. Examples of Richter scale numbers are 2.3, 4.0, 6.1, and 7.0. What kind of data are these numbers?
1. 97,118 (11.8%)
2. 41.6%
3. 67,092/823,356 or 0.081 or 8.1 %
4. 27.8%
5. Quantitative discrete
6. Quantitative continuous

## Try it

[link] contains the total number of fatal motor vehicle traffic crashes in the United States for the period from 1994 to 2011.

Year Total Number of Crashes Year Total Number of Crashes
1994 36,254 2004 38,444
1995 37,241 2005 39,252
1996 37,494 2006 38,648
1997 37,324 2007 37,435
1998 37,107 2008 34,172
1999 37,140 2009 30,862
2000 37,526 2010 30,296
2001 37,862 2011 29,757
2002 38,491 Total 653,782
2003 38,477

Answer the following questions.

1. What is the frequency of deaths measured from 2000 through 2004?
2. What percentage of deaths occurred after 2006?
3. What is the relative frequency of deaths that occurred in 2000 or before?
4. What is the percentage of deaths that occurred in 2011?
5. What is the cumulative relative frequency for 2006? Explain what this number tells you about the data.

## Try it solutions

1. 190,800 (29.2%)
2. 24.9%
3. 260,086/653,782 or 39.8%
4. 4.6%
5. 75.1% of all fatal traffic crashes for the period from 1994 to 2011 happened from 1994 to 2006.

## References

“State&County QuickFacts,” U.S. Census Bureau. http://quickfacts.census.gov/qfd/download_data.html (accessed May 1, 2013).

“State&County QuickFacts: Quick, easy access to facts about people, business, and geography,” U.S. Census Bureau. http://quickfacts.census.gov/qfd/index.html (accessed May 1, 2013).

“Table 5: Direct hits by mainland United States Hurricanes (1851-2004),” National Hurricane Center, http://www.nhc.noaa.gov/gifs/table5.gif (accessed May 1, 2013).

“Levels of Measurement,” http://infinity.cos.edu/faculty/woodbury/stats/tutorial/Data_Levels.htm (accessed May 1, 2013).

Courtney Taylor, “Levels of Measurement,” about.com, http://statistics.about.com/od/HelpandTutorials/a/Levels-Of-Measurement.htm (accessed May 1, 2013).

David Lane. “Levels of Measurement,” Connexions, http://cnx.org/content/m10809/latest/ (accessed May 1, 2013).

## Chapter review

Some calculations generate numbers that are artificially precise. It is not necessary to report a value to eight decimal places when the measures that generated that value were only accurate to the nearest tenth. Round off your final answer to one more decimal place than was present in the original data. This means that if you have data measured to the nearest tenth of a unit, report the final statistic to the nearest hundredth.

In addition to rounding your answers, you can measure your data using the following four levels of measurement.

• Nominal scale level: data that cannot be ordered nor can it be used in calculations
• Ordinal scale level: data that can be ordered; the differences cannot be measured
• Interval scale level: data with a definite ordering but no starting point; the differences can be measured, but there is no such thing as a ratio.
• Ratio scale level: data with a starting point that can be ordered; the differences have meaning and ratios can be calculated.

When organizing data, it is important to know how many times a value appears. How many statistics students study five hours or more for an exam? What percent of families on our block own two pets? Frequency, relative frequency, and cumulative relative frequency are measures that answer questions like these.

#### Questions & Answers

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
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
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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# Sayyed Hashem Rasouli

سید هاشم رسولی
Email:  s.h.rasouli[at]nit.ac.ir
Website:  http://bs.nit.ac.ir/?s.h.rasouli

Associate Professor

Personal Information:
Name: Sayyed Hashem Rasouli
Date and Place of Birth:20 Sep 1980, Amol, Iran
Nationality: Iranian

Department of Mathematics, Faculty of Basic science, Babol University of Technology, Babol, Iran.
Post Code: 71167-47148
Tel: (+98) 111 323 4203
Fax: (+98) 111 3234201
E-mail: s.h.rasouli@nit.ac.ir

Qualifications
B.S. in Pure Mathematics : 1999-2003, University of Tabriz (Branch of Mohaghegh Ardabili), Iran.

M.S. in Pure Mathematics-Analysis : 2003-2005, University of Mazandaran, Iran.
* Title of M.S.Thesis : On the Existence and Stability Properties of positive solutions for a Population Model.
* Supervisor : Professor Ghasem Alizadeh Afrouzi.

Ph.D. in Pure Mathematics-Applied Nonlinear Functional Analysis : 2005-2009, University of Mazandaran, Babolsar-Iran, & University of West Bohemia, Pilzen, Czech Republic.
* Title of Ph.D.Thesis : Methods of Nonlinear Analysis for Solving Some Boundary Value Problems Involving The p-Laplasian Operator.
* Supervisors : Professor Ghasem Alizadeh Afrouzi ( University of Mazandaran ) & Professor Pavel Drabek ( University of West Bohemia, Czech Republic ).
* Advisor : Professor Hossein Torabi Tehrani ( University of Nevada, USA ).

Research Interests
Nonlinear Functional Analysis (Applications to Nonlinear Boundary Value Problems)

Honors and Awards

First Rank Graduated, M.S. Degree, Mazandaran University, 2005.
• Acceptance In Ph.D By quota Of Distinguished Student.
First Rank Graduated, Ph.D. Degree, Mazandaran University, 2009.
• Member of National Elite Foundation.
• Member of The American Mathematical Socity.
• Reviewer for Mathematical Reviews.
•  Editoril Board of : The Journal of Mathematics and Computer Sciences.

Province Distinguished Researcher, 2010.

University Distinguished Researcher, 2013.

Previous and Present Positions

1. Head of the Dep. Basic Science, Pardisan University, 2009.

2. Vice Chancellor for Financial and Administrative, Babol University of Technology, 2010-at present.

Professional Membership

1. Member of the American Mathematical Society.

2. Member of the Iranian National Elite Foundation.

Teaching Experiences

Real analysis, Functional analysis, Operator Theory, Applied Functional analysis.

Publications

# [96] Yazdani, Somayeh; Alizadeh Afrouzi, Ghasem; Rezaee Roshan, Jamal; Rasouli, Sayed Hashem, Multiple Positive Solutions for p-Kirchhoff Problems with Sign-Changing Potential, Med.J.MAth,  Published Online 13 March 2018.

[95]  S.H. Rasouli and H. Fani, An Existence Result for p-Kirchhoff-type Problems with Singular Nonlinearity, Accepted for publication, AMEN, 2018.

[94] S.H. Rasouli, On a nonlinear system arising in a theory of thermal explosion, Accepted for publication, BSPdM, 2017.

[93] S.H. Rasouli, M. Fani, S. Khademloo, Existence of sign-changing solutions for a nonlocal problem of  $p$-Kirchhoff-type, Accepted for publication, MJOM, 2017.

[92] S.H. Rasouli, On a Picone's identity for the $mathcal{A}_{p(x)}$-Laplacian and its applications , Accepted for publication, BIMS, 2017.

[91] S.H. Rasouli, On the existence and multiplicity results for a class of elliptic
problems with singular weights and failing zeroes, accepted for publication, Bul. Tra.Uni. Bra, Series III: Mathematics, Informatics, Physics, 2017.

[90] S.H. Rasouli and H. Norouzi, On a nonlinear system involving the variable exponent operator, Stu.Sci.Math.Hun,accepted for publication, 2017.

[89]  S.H. Rasouli and K. Fallah, The Nehari manifold approach for a  p(x)-Laplacian problem with nonlinear boundary conditions, UMZH, Accepted for publication, 2017.

[88] ON THE EXISTENCE OF POSITIVE WEAK SOLUTIONS FOR A CLASS OF CHEMICALLY REACTING SYSTEMS WITH SIGN-CHANGING WEIGHTS, Bul. Tra.Uni. Bra • Vol 9(58), No. 2 - 2016 Series III: Mathematics, Informatics, Physics, 71-78.

[87] S. Khademloo, S.H. Rasouli and M. Mirzaee, Multiple solutions for a perturbed fourth-order problem on $\mathbb{R}^{N}$", accepted for publication ,  Int. J. Appl. Com. Math, 2016.

[86] S.H. Rasouli, On a class of infinite semipositone
nonlinear systems with multiple parameters, accepted for publication, JIMS, 2016.

[85] S.H. Rasouli, Z. Firouzjahi, ON A CLASS OF NONLINEAR INFINITE SEMIPOSITONE PROBLEMS WITH SIGN-CHANGING WEIGHTS, ROMAI J., v.11, no.2(2015), 201–206.

# [46] S.H. Rasouli , "On the existence of positive solution for a class of nonlinear elliptic system with multiple parameters and singular weights" , CKMS ,27 ,2012, 557-564.

[45]S.H. Rasouli and G.A. Afrouzi , "A note on the existence of positive  solution  for a class of  nonlinear Laplacian systems with multiple parameters and sign-changing weight" , JIMS , 79 ( 2012), 153-159.

[44S.H. Rasouli, G.A. Afrouzi and J. Vahidi , "On positive weak solutions for some nonlinear elliptic boundary value problems involving the p-Laplacian" , TJMCS , 94-101 , 2011.

[43S.H. Rasouli , Z. Halimi and Z. Mashhadban , "A remark on positive solution for a class of (p,q)-Laplacian nonlinear system with sign-changing weight and combined nonlinear effects" , TJMCS , 126-134 , 2011.

 [42] G. A. Afrouzi, S. Shakeri, S. H. Rasouli , "ON THE FUZZY METRIC SPACES" , TJMCS , 475-482 , 2011.[41] S.H. Rasouli and G.A. Afrouzi , "On the existence, nonexistence and uniqueness of positive weak solutions for nonlinear multiparameter elliptic systems involving the (p,q)-Laplacian" , JIMS , 78 ( 2011), 163-172.[40] S.H. Rasouli , Z. Halimi and Z. Mashhadban , "A note on the existence of positive weak solution for a class of Laplacian nonlinear system with sign-changing weight" , The 1 Regional Conference on Mathematics and its Applications in Engineering Sciences , 2010.[39] S.H. Rasouli and G.A. Afrouzi , "On the nonexistence and uniqueness of positive weak solutions for nonlinear multiparameter elliptic systems involving the (p,q)-Laplacian" , International Conference on Mathematical Science, Bolu, Turkey , 2010.[38] Pavel Drabek and S.H. Rasouli , "A quasilinear eigenvalue problem with Robin conditions on the non smooth domain of finite measure" , journal for analysis and its applications , 469-485 , 2010.[37] S.H. Rasouli , Z. Halimi and Z. Mashhadban , "A remark on the existence of positive weak solution for a class of $(p,q)$-Laplacian nonlinear system with sign-changing weight " , Nonlinear Analysis , 385-389 , 2010.[36] S.H. Rasouli and G.A. Afrouzi , "The Nehari manifold for a class of concave–convex elliptic systems involving the p-Laplacian and nonlinear boundary condition" , Nonlinear Analysis , 3390-3401 , 2010.[35] G.A.Afrouzi and S.H.Rasouli , "A remark on the existence of multiple solutions to a multiparameter nonlinear elliptic system" , Nonlinear Analysis , 445-455 , 2009.[34] G.A.Afrouzi and S.H.Rasouli , "A variational approach to a quasilinear elliptic problem involving the p Laplacian and nonlinear boundary condition" , Nonlinear Analysis , 2447-2455 , 2009.[33] G.A.Afrouzi and S.H.Rasouli , "A remark on the existence and multiplicity result for a nonlinear elliptic problem involving the p-Laplacian " , NoDEA : Nonlinear Differential Equations and Applications , 2009.[32] G. A. Afrouzi, J. Vahidi and S.H.Rasouli , "On critical exponent for existence of positive solutions for some semipositone problems involving the weight function" , IJMA , 987-991 , 2008.[31] G. A. Afrouzi, J. Vahidi and S.H.Rasouli , "On critical exponent for existence of positive weak solutions for a class of semipositone problems involving the p-Laplacian operator" , IJMA , 993-998 , 2008.[30] G. A. Afrouzi, J. Vahidi and S.H.Rasouli , "A note on the existence of positive solution for a nonlinear semipositone system" , , IJMA , 1015-1021 , 2008.[29] G. A. Afrouzi, J. Vahidi and S.H. Rasuli , "A remark on the existence of positive solution to a nonlinear semipositone system involving the weight function" , IJMA , 1023-1029 , 2008.[28] G. A. Afrouzi and S.H.Rasouli , "A remark on the linearized stability of positive solutions for systems involving the p-Laplacian" , POSITIVITY , 351-356 , 2007.[27] G. A. Afrouzi, S. Heidarkhani and S.H.Rasouli , "On the minimax inequality for a special class of functionals" , WJMS , 220-224 , 2007.[26] G. A. Afrouzi and S.H. Rasouli , "On the existence and stability properties of positive solution for some p-Laplacian Dirichlet problems" , WJMS , 21-26 , 2007.[25] G. A. Afrouzi and S.H. Rasouli , ", A remark on a nonlinear system of reaction-diffusion equations" , IMJ , 179-185 , 2007.[24] G. A. Afrouzi and S.H. Rasouli , "A note on the existence and stability properties of positive solution for some Dirichlet problems" , IMJ , 195-201 , 2007.[23] G. A. Afrouzi and S.H.Rasouli , "On the instability of positive solution of an elliptic equation" , IMJ , 137-142 , 2007.[22] G. A. Afrouzi and S. H. Rasouli , "Population models involving the P-Laplacian with indefinite weight and constant yeild harvesting" , Chaos, Solitons & Fractals , 404-408 , 2007.[21] G. A. Afrouzi, S.H. Rasouli and M. Bagheri , "On positive weak solutions for a class of semipositone equations" , WJMS , 286-288 , 2007.[20] G. A. Afrouzi and S.H.Rasouli , "On the instability of positive solution of an BV elliptic equation" , IJMS , 23-27 , 2007.[19] G. A. Afrouzi and S.H. Rasouli , "On a Nonlinear system of Reaction-Diffusion Equations " , Nonlinear Analysis: Modelling and Control , 115-121 , 2006.[18] G. A. Afrouzi and S.H. Rasouli , "A remark on the existence of positive solutions for a reaction-diffusion system" , Int. J. Contemp. Math. Sciences , 673-678 , 2006.[17] G. A. Afrouzi and S. H. Rasouli , "Stability properties of nonnegative solutions to a non- attonomous p-Laplacian equation" , , Chaos, Solitons & Fractals , . 1095-1099 , 2006.[16] G. A. Afrouzi, S. h. Rasouli and R. Sedaghat , "Population models with indefinite weight and constant yeild harvesting" , Far East Journal of mathematical Sciences , 141-135 , 2006.[15] G. A. Afrouzi, S. H. Rasouli and R. Sedaghat , "Diffusive logistic equation with indefinite weight and constant yield harvesting" , J. Basic Science , 7-9 , 2006.[14] G. A. Afrouzi and S. H. Rasouli , "Instability of positive solutions for population models involving P-Laplacian operator" , GJPAM , 51-54 , 2006.[13] G. A. Afrouzi and S. H. Rasouli , "An existence results on positive solutions for a quasilinear reaction-diffusion system" , IJAER , 71-76 , 2006.[12] G. A. Afrouzi and S.H.Rasouli , "A remark on the existence of positive solutions for some elliptic systems" ,ATAM , 109-113 , 2006.[11] G. A. Afrouzi and S.H. Rasouli , "On critical exponent for instability of positive solutions to a reaction- diffusion system involving the (p,q)-Laplacian" , IJNS , 61-64 , 2006.[10] G. A. Afrouzi and S.H.Rasouli , "On positive solutions for some nonlinear semipositone elliptic boundary value problems" , , Nonlinear Analysis: Modelling and Control , 323-329 , 2006.[9] G. A. Afrouzi and S. H. Rasouli , "A remark on the uniqueness of positive solution for some Dirichlet problems" , Nonlinear Analysis , 2773-2777 , 2006.[8] G. A. Afrouzi and S. H. Rasouli , ", Stability properties of positive solutions for a boundary value problem" ,IJCMS , 213-217 , 2006.[7] G. A. Afrouzi and S. H. Rasouli , "A remark on the instability of positive solutions to a diffusive logistic equation" , , IJCMS , 219-222 , 2006.[6] G. A. Afrouzi and S. H. Rasouli , ", Existence of solutions to a non-autonomous P-Laplacian equation" , , IJNS, 124-128 , 2006.[5] G. A. Afrouzi and S.H.Rasouli , "On Dirichlet boundary value problem for some quasilinear Elliptic systems" ,IJDE , 177-180 , 2006.[4] G. A. Afrouzi and S. H. Rasouli , "A note on the stability and uniqueness of positive solutions for some boundary value problems " , , Far East Journal of Dynamical systems , 145-151 , 2005.[3] G. A. Afrouzi and S. H. Rasouli , "A remark on the nonexistence of positive solutions for some P-Laplacian systems" , Global J. Pure & Appl. Math , 197-201 , 2005.[2] G. A. Afrouzi and S. H. Rasouli , "Instability of nonnegative solutions for a boundary value problem with indefinite weight function" , , Global J. Pure & Appl. Math , 9-12 , 2005.[1] G. A. Afrouzi and S. H. Rasouli , "Instability and existence results to a non-autonomous two points boundary value problems" , Global J. Pure & Appl. Math , 151-155 , 2005.

Supervised Dissertations and Theses

1. A.B. Kafshgari, 2012.

2. Z. Nekonam, 2011.

3. F.Y. Darzi, 2011.

4. M. Aalam, 2012.

5. S. Kanjani, 2013.

6. M. Tahmasebi, 2013.

7. K. Rahmati, 2014

b) Supervisor of M.Sc Theses:

1) M. Nategh.

2) F. Rezvani.

3) A. Ghourbani, 2013.

4) M. H. Malekshah, 2013.

5) Z. Firouzjahi, 2014.

6) H. Norouzi, 2014.

7) B. Salehi, 2014

Research Projects

1. On the existence of positive solution for a class of nonlinear singular elliptic

system with multiple parameters. 2011 ( supported by Iranian National Elite Foundation).


text:
SMS scnews item created by Anthony Henderson at Mon 29 Jul 2019 1220
Type: Seminar
Modified: Fri 2 Aug 2019 0954
Distribution: World
Expiry: 2 Aug 2019
Calendar1: 2 Aug 2019 1105-1255
CalLoc1: Quad Room S418
CalTitle1: SMRI Seminar: Parusinski - New methods of real algebraic geometry
Auth: anthonyh@124.180.39.249 (ahen2753) in SMS-SAML

# SMRI Seminar: Parusinski -- New methods of real algebraic geometry

UPDATE (2 August): We have moved this talk to the room next door, Quadrangle Room S418.

-----

This semester we will run a somewhat irregular SMRI seminar series, in which SMRI
visiting researchers will speak about their own research or other topics of interest,
complementing their contributions to the School’s existing seminar series.  We will
experiment with some venues in the Quadrangle as well as more customary locations.  All
are welcome, and please send feedback on the series to me at smri.exec@sydney.edu.au .

The first speaker in this SMRI seminar will be former School staff member Adam
Parusinski, details below.  Adam will also speak about a different topic in the Geometry
& Topology seminar on 19 August.

Anthony

--------------------

Speaker: Adam Parusinski (University of Nice)

Date: Friday 2 August 2019

Time: 11.05am - 12.55pm (with a break in the middle)

Venue: Quadrangle Room S418, in the corner of the quadrangle closest to Carslaw (i.e.
the one with the jacaranda tree), up a flight of stairs from ground level.

Title: New methods of real algebraic geometry: continuous rational functions and
arc-analytic geometry

Abstract:

We give a fairly elementary introduction to two recent techniques specific to real
algebraic geometry.  Continuous rational functions were introduced recently
independently by W.  Kucharz, J.  Kollar, and G.  Fichou, J.  Huisman, F.  Mangolte, and
J.-P.  Monnier.  The arc-analytic functions form a wider class, in particular, every
rational continuous function is arc-analytic.  The arc-analytic functions and related
arc-symmetric sets were introduced by K.  Kurdyka.

We discuss some recently obtained results on equisingularity, additive invariants and
motivic integration, approximation of continuous maps, and classification of vector
bundles.

Actions:
Calendar (ICS file) download, for import into your favourite calendar application
UNCLUTTER for printing
AUTHENTICATE to mark the scnews item as read
School members may try to .


text:
# Radon Transform reducing the number of parallel beams (MATLAB)

I am trying to understand different filters' and other things' effects on Radon Transform by using MATLAB. First I upload an image, then take its Radon transform with radon function and then reconstruct it with iradon function.

Now I wanted to see the difference between undersampling the projection data by reducing the number of parallel beams by a factor of 4 and reducing the number of rotation angles by a factor of 4. However according to what I understood from radon and iradon functions' descriptions, I can only change the number of rotation angles. Is not it true? If not, what is the way to do it?

Here is what I do to decrease the number of rotation angles by a factor of 4:

I = imread ('asdasd.tif');

Unfortunately you can't do this with the radon function as it comes. However, the function is written in MATLAB form (as opposed to being a compiled function), so you could extend the function yourself. This would also be a good way to learn more about the process.

To reconstruct properly, you would also need to perform edits on the iradon function.

An alternative way to get what you're looking for would be to get projections as they come from radon, then reduce the array size by averaging the projection rays in groups of 4. You would probably want the reconstruction to be the same size, so you'd need to repeat the averaged values 4 times in the argument to iradon. So maybe something like this:

p = phantom ();


text:
## Error in creation of view translation

I m trying to translate a view but when I hit the button in order to add a language translation nothing happens and the attached error appears in my console.

How could I solve this?

## Translation functor on parabolic Verma module

I want to prove that following proposition by using Theorems/propositions in Representations of Semisimple Lie Algebras in the BGG Category $$\mathcal{O}$$.

Define $$\Lambda := \{\nu \in \mathfrak{h}^* : \langle\nu,\alpha^\lor\rangle \in \mathbb{Z} \ \text{for all }\alpha \in \Phi^+\}.$$

Define $$\Lambda^+ := \{\nu \in \mathfrak{h}^* : \langle\nu,\alpha^\lor\rangle \in \mathbb{Z}^{\ge 0} \ \text{for all }\alpha \in \Phi^+\}.$$

Define $$\Lambda^+_I := \{\nu \in \mathfrak{h}^* : \langle\nu,\alpha^\lor\rangle \in \mathbb{Z}^{\ge 0} \ \text{for all }\alpha \in \Phi^+_I\}.$$

The $$\mathbb{Z}$$-span $$\Lambda_r$$ of $$\Phi$$ is called the root lattice.

Recall that a weight $$\eta\in \mathfrak{h}^*$$ is antidominant if $$\langle \eta+\rho,\alpha^{\lor}\rangle\not\in\mathbb{Z}^{>0}$$ for all $$\alpha\in \Phi^+$$.

For $$w \in W$$ and $$\eta\in \mathfrak{h}^*$$, define a shifted action of $$W$$ (called the dot action) by $$w \cdot \eta := w(\eta + \rho) – \rho$$. If $$\eta, \nu \in \mathfrak{h}^*$$, then we say that $$\eta$$ and $$\nu$$ are linked if for some $$w \in W$$, we have $$\nu = w \cdot \eta$$.

The weight $$\eta \in \mathfrak{h}^*$$ is regular if $$|W \cdot \eta| = |W|$$ or, equivalently, if $$\langle \eta + \rho,\alpha^\lor\rangle \neq 0$$ for all $$\alpha\in\Phi$$

By exercise 1.13, $$M\in\mathcal{O}_{\chi_\lambda}$$ has a direct sum decomposition $$M=\bigoplus M_i$$ such that all weights of each $$M_i$$ are contained in a single coset of the root lattice $$\Lambda_r$$ in $$\mathfrak{h}^*$$. Therefore, the category $$\mathcal{O}_{\chi_\lambda}$$ decomposes as a direct sum of full subcategories, which can be indexed by the nonempty intersection of the orbit $$W\cdot\lambda$$ with the cosets $$\mathfrak{h}^*/\Lambda_r$$. We use the antidominant weight $$\mu$$ in the intersection to parameterize the corresponding subcategory of $$\mathcal{O}_{\chi_\lambda}$$. We denote this subcategory by $$\mathcal{O}_{\mu}$$.

We say $$\eta$$ and $$\nu$$ are compatible if $$\nu – \eta \in\Lambda$$.

Fix $$\eta, \nu \in \mathfrak{h}^*$$ such that $$\eta,\nu$$ are compatible and write $$pr_\eta$$ and $$pr_\nu$$ for the natural projections of the category $$\mathcal{O}$$ onto $$\mathcal{O}_{\chi_\eta}$$ and $$\mathcal{O}_{\chi_\nu}$$. Let $$\overline{\nu-\eta}$$ be the unique $$W$$-conjugate in $$\Lambda^+$$ of $$\nu-\eta$$. If $$M \in \mathcal{O}$$, then $$M \mapsto pr_ \nu \left(L(\overline{\nu-\eta}) \otimes (pr_\eta M)\right)$$ followed by inclusion into $$\mathcal{O}$$ defines an exact functor $$\mathcal{O} \to \mathcal{O}$$. Its restriction to $$\mathcal{O}_{\chi_\eta}$$ (without the inclusion) relates the two subcategories $$\mathcal{O}_{\chi_\eta}$$ and $$\mathcal{O}_{\chi_\nu}$$. Write $$T^\nu_\eta$$ for the resulting functor on $$\mathcal{O}$$ (or on $$\mathcal{O}_{\chi_\eta}$$). We call $$T^\nu_\eta$$ a translation functor.

Proposition: Let $$\eta,\nu\in \Lambda_I^+$$, Suppose $$\eta,\nu\in \Lambda_I^+$$ are integral, regular and antidominant. Then there is an equivalence of categories between $$\mathcal{O}_\nu$$ and $$\mathcal{O}_\eta$$ such that (i) $$T^{\eta}_{\nu}(L(x\cdot \nu))\cong L(x\cdot \eta)$$ and $$T^{\eta}_{\nu}(M(x\cdot \nu))\cong M(x\cdot \eta)$$ for $$x\in W$$. (ii) If $$x\cdot\nu$$ is in $$\Lambda_I^+$$ then $$T^{\eta}_{\nu}(M_I(x\cdot \nu))\cong M_I(x\cdot \eta)$$.

Proof: Since $$\eta,\nu\in \Lambda_I^+$$ are integral, regular and antidominant, it holds that $$\eta,\nu$$ are compatible. Since $$\eta,\nu$$ are integral, we have $$\eta^\natural=\eta,\nu^\natural=\nu$$ and hence $$\eta^\natural,\nu^\natural\in F$$ where $$\Phi_F^-=\Phi^+$$, $$\Phi_F^0=\Phi_F^+=\emptyset$$. Applying Theorem 7.6, Proposition 7.7 and Theorem 7.8, we deduce that there is an equivalence of categories $$T^{\eta}_{\nu}$$ between $$\mathcal{O}_{\nu}$$ and $$\mathcal{O}_{\eta}$$ satisfying (i).

For a proof of (ii) it suffices to show that $$T^{\eta}_{\nu}(M_I(x\cdot \nu))\cong M_I(x\cdot \eta)$$ by the properties of the full subcategory. In fact, there is an exact sequence (Theorem 9.4) $$$$\label{longexact1} \bigoplus_{\alpha\in I} M(s_\alpha x \cdot \nu) \xrightarrow{f} M(x \cdot \nu) \xrightarrow{g} M_I (x \cdot \nu) \to 0. \quad\quad(1)$$$$ Applying $$T^{\eta}_{\nu}$$ to (1), we get another exact sequence $$$$\label{longexact2} \bigoplus_{\alpha\in I} M(s_\alpha x \cdot \eta) \xrightarrow{T^{\eta}_{\nu}(f)} M(x \cdot \eta) \xrightarrow{T^{\eta}_{\nu}(g)} T^{\eta}_{\nu}(M_I(x \cdot \nu)) \to 0. \quad\quad(2)$$$$ On the other hand, by replacing $$\nu$$ in (1) with $$\eta$$, we can get an exact sequence in $$\mathcal{O}_{\eta}$$: $$$$\label{longexact3} \bigoplus_{\alpha\in I} M(s_\alpha x \cdot \eta) \xrightarrow{f’} M(x \cdot \eta) \xrightarrow{g’} M_I (x \cdot \eta) \to 0. \quad\quad(3)$$$$

Since (2) is exact, it holds that $$T^{\eta}_{\nu}(g)$$ is surjective and $$\ker(T^{\eta}_{\nu}(g))=\mathrm{Im}(T^{\eta}_{\nu}(f))$$, we have $$T^{\eta}_{\nu}(M_I(x \cdot \nu))= \mathrm{Im}(T^{\eta}_{\nu}(g)) \cong M(x\cdot\eta)/\ker(T^{\eta}_{\nu}(g)) =M(x\cdot\eta)/\mathrm{Im}(T^{\eta}_{\nu}(f)).$$

Since (3) is exact, it holds that $$g’$$ is surjective and $$\ker(g’)=\mathrm{Im}(f’)$$, we have $$M_I(x \cdot \eta)=\mathrm{Im}(g’) \cong M(x\cdot\eta)/\ker(g’) =M(x\cdot\eta)/\mathrm{Im}(f’).$$

My question: How to show $$T^{\eta}_{\nu}(f)=f’$$?

## Translation of diagnosis problem to SAT

I have the following diagnosis problem:
h(A): z1 = not(in1)
h(D): z2 = not(in2)
h(B): z3 = z1 or z2
h(C): out1 = not(z3)
h(E): out2 = not(z3)

This is an image of the system:

I have an observation where I know that:
in1 = false
in2 = false
out1 = true
out2 = true

I want to check if {B} is a diagnosis of the system, meaning that I assume that A,D,C,E are valid, while I don’t assume the same about B.
This I want to turn into a sat problem. So first I map each variable in my system to a literal:
in1: 1
in2: 2
z1 (the output of A): 3
z2 (the output of D): 4
z3 (the output of B): 5
out1: 6
out2: 7

So to check if {B} is a diagnosis of the system (meaning that if I remove the assumption about {B} the system will be OK) I create a CNF like so:

not(1) AND not(2) AND 6 AND 7 – this represents my observations, the variables whose value I know for sure.

Now I want to add a representation for my constraints. For example, I know that 6 = not(5), but I don’t know the value of 5 (because I can’t assume the validity of component B).
My question is how do I add this knowledge to my CNF representation? If I add “not(5)” to my CNF then I assume the output of B is always false, and this isn’t correct.

Thank you very much.

## User registration email translation

I am working on an English/Arabic website, the user can switch between the two languages using the language switch block, I wanted to translate the email sent to the user after registration. So after some digging, I figured out I could do this using the account setting (translate tab), I added the Arabic translation of the email; then, after testing, I found out that the registration email is still sent in English.

Shouldn’t a user registered in the Arabic language get an Arabic registration email?

I also found out that the user’s preferred language is English, even after registering in the Arabic language.

These are my language detection settings.

## Do I need provide translation for an UI library

I have a library for a lockscreen in Android, that includes diferent dilogs for fingerprints, texts and all that stuff. My question is: What the best practice to provide localization. Should I have instuments that provides developers eho use this library to set up localization outside of library, which means if developer wants to support different languages it will be necessary to set up all the strings that being used in the library.

Or should I add localiation for those strings inside tha app?

To have better idea: https://github.com/thealeksandr/PFLockScreen-Android

## Not able to enable ‘Configuration Translation’ module gives error

I am trying to enable MULTILINGUAL -> Configuration Translation.

It gives below error.

Error: Call to a member function getPath() on null in Drupal\config_translation\ConfigNamesMapper->getOverviewRoute() (line 247 of /var/www/project/docroot/core/modules/config_translation/src/ConfigNamesMapper.php) #0 /var/www/project/docroot/core/modules/config_translation/src/Routing/RouteSubscriber.php(39): Drupal\config_translation\ConfigNamesMapper->getOverviewRoute() #1 /var/www/project/docroot/core/lib/Drupal/Core/Routing/RouteSubscriberBase.php(37): Drupal\config_translation\Routing\RouteSubscriber->alterRoutes(Object(Symfony\Component\Routing\RouteCollection)) #2 [internal function]: Drupal\Core\Routing\RouteSubscriberBase->onAlterRoutes(Object(Drupal\Core\Routing\RouteBuildEvent), ‘routing.route_a…’, Object(Drupal\Component\EventDispatcher\ContainerAwareEventDispatcher)) #3 /var/www/project/docroot/core/lib/Drupal/Component/EventDispatcher/ContainerAwareEventDispatcher.php(111): call_user_func(Array, Object(Drupal\Core\Routing\RouteBuildEvent), ‘routing.route_a…’, Object(Drupal\Component\EventDispatcher\ContainerAwareEventDispatcher)) #4 /var/www/project/docroot/core/lib/Drupal/Core/Routing/RouteBuilder.php(184): Drupal\Component\EventDispatcher\ContainerAwareEventDispatcher->dispatch(‘routing.route_a…’, Object(Drupal\Core\Routing\RouteBuildEvent)) #5 /var/www/project/docroot/core/lib/Drupal/Core/ProxyClass/Routing/RouteBuilder.php(83): Drupal\Core\Routing\RouteBuilder->rebuild() #6 /var/www/project/docroot/core/lib/Drupal/Core/Extension/ModuleInstaller.php(322): Drupal\Core\ProxyClass\Routing\RouteBuilder->rebuild() #7 /var/www/project/docroot/core/lib/Drupal/Core/ProxyClass/Extension/ModuleInstaller.php(83): Drupal\Core\Extension\ModuleInstaller->install(Array, true) #8 /var/www/project/docroot/core/modules/system/src/Form/ModulesListForm.php(458): Drupal\Core\ProxyClass\Extension\ModuleInstaller->install(Array) #9 [internal function]: Drupal\system\Form\ModulesListForm->submitForm(Array, Object(Drupal\Core\Form\FormState)) #10 /var/www/project/docroot/core/lib/Drupal/Core/Form/FormSubmitter.php(111): call_user_func_array(Array, Array) #11 /var/www/project/docroot/core/lib/Drupal/Core/Form/FormSubmitter.php(51): Drupal\Core\Form\FormSubmitter->executeSubmitHandlers(Array, Object(Drupal\Core\Form\FormState)) #12 /var/www/project/docroot/core/lib/Drupal/Core/Form/FormBuilder.php(589): Drupal\Core\Form\FormSubmitter->doSubmitForm(Array, Object(Drupal\Core\Form\FormState)) #13 /var/www/project/docroot/core/lib/Drupal/Core/Form/FormBuilder.php(318): Drupal\Core\Form\FormBuilder->processForm(‘system_modules’, Array, Object(Drupal\Core\Form\FormState)) #14 /var/www/project/docroot/core/lib/Drupal/Core/Controller/FormController.php(93): Drupal\Core\Form\FormBuilder->buildForm(‘system_modules’, Object(Drupal\Core\Form\FormState)) #15 [internal function]: Drupal\Core\Controller\FormController->getContentResult(Object(Symfony\Component\HttpFoundation\Request), Object(Drupal\Core\Routing\RouteMatch)) #16 /var/www/project/docroot/core/lib/Drupal/Core/EventSubscriber/EarlyRenderingControllerWrapperSubscriber.php(123): call_user_func_array(Array, Array) #17 /var/www/project/docroot/core/lib/Drupal/Core/Render/Renderer.php(582): Drupal\Core\EventSubscriber\EarlyRenderingControllerWrapperSubscriber->Drupal\Core\EventSubscriber{closure}() #18 /var/www/project/docroot/core/lib/Drupal/Core/EventSubscriber/EarlyRenderingControllerWrapperSubscriber.php(124): Drupal\Core\Render\Renderer->executeInRenderContext(Object(Drupal\Core\Render\RenderContext), Object(Closure)) #19 /var/www/project/docroot/core/lib/Drupal/Core/EventSubscriber/EarlyRenderingControllerWrapperSubscriber.php(97): Drupal\Core\EventSubscriber\EarlyRenderingControllerWrapperSubscriber->wrapControllerExecutionInRenderContext(Array, Array) #20 /var/www/project/vendor/symfony/http-kernel/HttpKernel.php(151): Drupal\Core\EventSubscriber\EarlyRenderingControllerWrapperSubscriber->Drupal\Core\EventSubscriber{closure}() #21 /var/www/project/vendor/symfony/http-kernel/HttpKernel.php(68): Symfony\Component\HttpKernel\HttpKernel->handleRaw(Object(Symfony\Component\HttpFoundation\Request), 1) #22 /var/www/project/docroot/core/lib/Drupal/Core/StackMiddleware/Session.php(57): Symfony\Component\HttpKernel\HttpKernel->handle(Object(Symfony\Component\HttpFoundation\Request), 1, true) #23 /var/www/project/docroot/core/lib/Drupal/Core/StackMiddleware/KernelPreHandle.php(47): Drupal\Core\StackMiddleware\Session->handle(Object(Symfony\Component\HttpFoundation\Request), 1, true) #24 /var/www/project/docroot/core/modules/page_cache/src/StackMiddleware/PageCache.php(99): Drupal\Core\StackMiddleware\KernelPreHandle->handle(Object(Symfony\Component\HttpFoundation\Request), 1, true) #25 /var/www/project/docroot/core/modules/page_cache/src/StackMiddleware/PageCache.php(78): Drupal\page_cache\StackMiddleware\PageCache->pass(Object(Symfony\Component\HttpFoundation\Request), 1, true) #26 /var/www/project/docroot/core/lib/Drupal/Core/StackMiddleware/ReverseProxyMiddleware.php(47): Drupal\page_cache\StackMiddleware\PageCache->handle(Object(Symfony\Component\HttpFoundation\Request), 1, true) #27 /var/www/project/docroot/core/lib/Drupal/Core/StackMiddleware/NegotiationMiddleware.php(52): Drupal\Core\StackMiddleware\ReverseProxyMiddleware->handle(Object(Symfony\Component\HttpFoundation\Request), 1, true) #28 /var/www/project/vendor/stack/builder/src/Stack/StackedHttpKernel.php(23): Drupal\Core\StackMiddleware\NegotiationMiddleware->handle(Object(Symfony\Component\HttpFoundation\Request), 1, true) #29 /var/www/project/docroot/core/lib/Drupal/Core/DrupalKernel.php(669): Stack\StackedHttpKernel->handle(Object(Symfony\Component\HttpFoundation\Request), 1, true) #30 /var/www/project/docroot/index.php(19): Drupal\Core\DrupalKernel->handle(Object(Symfony\Component\HttpFoundation\Request)) #31 {main}.

I am not sure what exactly cause of this. Anyone faced?

## How to find the shortest route between (0,0) and (4,4) in a 5×5 matrix, given one horizontal or vertical translation per step [on hold]

Consider the following matrix:

Input: The entire list of coordinates ranging from (0,0) to (4,4).

A list indicating certain coordinates which cannot be used to generate a path reached.

So,

• each position on the grid is a node
• nodes share an edge if exactly one coordinate differs by exactly 1
• X nodes (and their associated edges) are deleted

The problem then becomes, find the shortest path in the graph between two nodes. If the nodes are not in the same connected component, there is no such path.

Output: The shortest path between S and E, considering the positions of the X nodes, given by a sequence of coordinates.

So in the above picture, a possible route may be the following: (0,0)->(0,1)->(0,2)->(0,3)->(1,3)->(2,3)->(3,3)->(4,3)->(4,4)

A total of eight steps.

If the Xs occur in a way that prevents any movement (i.e, Xs at (0,1),(1,1), and (1,0), it should return -1 or indicate in some other way no path is possible.)

I have received advice that the A* search algorithm (pseudocode in this link) is relevant to this problem, but I am having difficulty seeing how to apply it.

## Issue with JPA statement “translation”

I have a JPA statement which is like this

select p from Proposal p where p.creationTime > :startDate AND p.creationTime < :stopDate AND ((p.owner = :owner) OR (:member MEMBER OF p.sharedWithTeam.members)) ORDER BY p.creationTime DESC

But it never generates any result. I use EclipseLink.

After digging a bit into the generated SQL, I found out that it translates the query into something that can never be true!

WHERE ((((t0.CREATIONTIME > ?) AND (t0.CREATIONTIME < ?)) AND ((t0.OWNER_username = ?) OR (? = t1.username))) AND ((t2.ID = t0.SHAREDWITHTEAM_ID) AND ((t3.teams_ID = t2.ID) AND (t1.username = t3.members_username)))) ORDER BY t0.CREATIONTIME DESC LIMIT ? OFFSET ?

(I only included the where clause to make it shorter…)

I can’t see what is wrong with my JPQL query. Could it be my use of “OR”? or my “bold” use of the member of condition?

Thanks!

## Exporting content translation to similar server

I have 2 instances of the same site built using Drupal. Both need to be translated, and most of the work of the translation has been done on site A and we need to take the translations from site A to site B. Site B will have slightly newer content, but not a lot and a new version of Drupal (both sites are/will be 8.6+).

I can export translation but they’re just for the interface, the content is not getting exported. Is there a way to export or send the translations in site A to site B without having to translate everything again one by one in site B?

Thanks.

## Offline translation files not recognized

When I try to use Google Translate offline, I get an error:

Translation failed. Offline translation file not available. Please check SD card is inserted.

In Settings-> Storage I could see that the Translate app was stored in the phone’s internal memory. I tried moving it to the SD card, and even after restarting the device, the same error was still there.

Using a file browser, I am able to look at the SD card and see that /storage/extSdCard/Android/data/com.google.android.apps.translate/files/olpv3/v5/25/r11 contains folders like dict.en_pt_25, lang.en_pt, and lang.pt_en where “pt” is also replaced by some other two-letter language codes. .../r12 contains the files for French.

How do I get Translate to work?


text:
### Homes

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

### Number Squares

Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?

### I'm Eight

Find a great variety of ways of asking questions which make 8.

# Two Dice

##### Stage: 1 Challenge Level:

If one dice shows $6$, what could the other dice be showing?
What totals would they give?
What could the other dice be if one is a $5$? A $4$?
How do you know you've found all the totals?