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# Selecting features for a neural network: is it redundant to have a feature that is an average (or max, or min) of some other features

I'm trying to create a neural network that would able to look at the current price of a crypto asset and classify between a "BUY", "SELL" or "HOLD". So far for my input features, I've decided to go with the past 40 opens, closes, highs, lows, turnover, and volumes (240 features + the current price so 241 total features).

Would it be redundant/not ideal if I had another feature that was the average of the past 40 opens for example? What about the max/min of the past opens?

My thinking was that with only the raw prices data of the past 40 days, the neural network would be able to "detect" and create the most optimum features like the average or max in the hidden layers. And therefore, having the avg. or the max/min of some existing features would be unnecessary or perhaps worsen the performance of the model.

Or is there no clear answer and would this be something I'd only be able to figure out by testing against data?

• Hi Neil. Ah okay, sorry about that. I edited the question down to exclude the last bit. Jun 8 at 16:00

Or is there no clear answer and would this be something I'd only be able to figure out by testing against data?

That is the general rule you should always consider when looking at feature engineering (which is what you are proposing), as well as for many architecture choices.

It is very hard to tell in advance what a change to a machine learning system will do for whichever metrics you are interested in. You may have some experience that applies, or find similar experiments online that you can take inspiration from. But you will want to test everything, and should take care to use good practice when evaluating different options - e.g. a cross validation dataset (sometimes called a development dataset).

Would it be redundant/not ideal if I had another feature that was the average of the past 40 opens for example? What about the max/min of the past opens?

One aspect of multi-layer neural networks, is that they can in theory learn useful internal features in the hidden layers from raw data. These internal features are unlikely to be exact copies of mean values or min/max values, or anything else you would construct manually. However, they can be similar enough in end result that manually derived features that you think of will not make much difference.

So you would think that derived features would not be useful in nerual networks. In practice though they can be, because the convergence process to find the best internal features is not perfect. Smart feature engineering can improve the performance of a neural network classification or regression supervised learning. Sometimes you can find "golden" engineered features that relate really well to your target variable, and that boost results significantly.

A couple of things to bear in mind:

• A "scattergun" approach of trying a large number of derived features might seem attractive, but there is a risk of overfitting the training data. If you try enough times you may find something that works purely by chance but only for the training data set.

• Nonlinear combinations that make conceptual sense given the problem domain can be worth looking at. For instance if you want to predict house prices, and your raw data was house width and depth, then floor area width * depth might be a useful feature.

Feature engineering is still something of an artform. Automated systems using the scattergun approach with filtering are competitive, but domain insight can still win.

If you have vast amounts of data and the CPU time cost is not an issue, you may want to forgo feature engineering due to the theoretical redundancy. It seems possible to make a giant neural network using latest features such as skip connections and batch normalisation, feed it raw (but normalised) data, and press "go" to get a state-of-the-art result. From that perspective, feature engineering is for when you don't have "big data" or deep pockets for heavy processing - for many of us that still means feature engineering is a standard approach on every project.


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Authors: Razvodovsky YE*
Affiliation(s):
Grodno State Medical University, Belarus
Dates:
Received: 13 August, 2014; Accepted: 16 February, 2015; Published: 18 February, 2015
*Corresponding author:
Y E Razvodovsky, 230009, Grodno, str. Gorky 80, Belarus, Email: @
Citation:
Razvodovsky YE (2015) Unrecorded Alcohol Consumption among Alcohol Dependent Patients. J Addict Med Ther Sci 1(1): 015-019. DOI: 10.17352/2455-3484.000005
© 2015 Razvodovsky YE. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Keywords:
Unrecorded alcohol; Drinking pattern; Alcohol dependent patients; Belarus

Introduction: Experts estimate that unrecorded alcohol makes up a significant share (about 25%) of all alcohol consumed in the former Soviet Republic Belarus. However, our knowledge with respect to the prevalence of the consumption of unrecorded alcohol in this country, as well as the patterns and motives of it consumption remains fragmented.

Objectives: This study was design to explore the prevalence, drinking pattern, types, reasons and correlates of the consumption of unrecorded alcohol among alcohol dependent patients.

Methods: The study was conducted in the Belarusian city Grodno in 2013 with 326 alcohol dependent patients (223 men and 103 women) admitted to narcological clinic using structured interviews.

Results: The results suggest that 52.9% of men and 30.3% of women regularly consume samogon (moonshine), while 11.8% of men and 10.8% of women use surrogates, the most popular among which are medications with a high percentage of ethanol and industrial spirits. The belief that, according to quality criteria, samogon exceeds licensed vodka is the main motive for its consumption.

Conclusions: The results from present study confirm that the consumption of unrecorded alcohol is common among alcohol dependent patients even though its use may have been underreported. These findings emphasize the urgency of implementing comprehensive alcohol policy, which need to address overall consumption, harmful drinking pattern and taking into account the consumption of alcohol from illicit sources.

Introduction

There is a common belief that alcohol is a crucial factor in the mortality crisis in the former Soviet Republics [1-5]. In Belarus, for example, it has been estimated that alcohol may be responsible for 28.4% of all male deaths and for 16.4% of female deaths [6,7]. The high level of alcohol-related problems in the region is caused by a combination of the high overall level of alcohol consumption, prevalence of unrecorded alcohol and harmful drinking patterns [2,4,5,8,9]. In Belarus, especially in small town and in rural regions, it is typical to consume unrecorded beverages [7,10-12]. Experts estimate that unrecorded alcohol makes up a significant share (about 25%) of all alcohol consumed in this country [12]. According to WHO definition, unrecorded alcohol include homemade informally produced alcohol, illegally produced or smuggled alcohol products, as well as surrogates alcohol that is not intended for human consumption [13]. Unrecorded alcohol in Belarus not only includes illegally produced spirits (samogon), but also legal non-beverage alcohols (surrogates), such as industrial spirits, denaturized alcohol, medicinal tinctures, perfumes [7].

Despite the extreme urgency of the problem, relatively few studies so far focused on unrecorded alcohol consumption in Belarus [7]. One previous study confirms the widespread of use of privately made strong alcoholic drinks in Belarus with 41% of men and 19% of women obtaining same or all of their alcohol from private sources [14]. A recent survey, undertaken in the city of Grodno found that 31.7% of men and 9.9% of women drank samogon at least one time a month, while 5.0% of men and 1.9% of women occasionally consumed alcohol surrogates [12]. However, our knowledge with respect to the prevalence of the consumption of unrecorded alcohol in Belarus, as well as the patterns and motives of it consumption remains fragmented. The aim of this study was to some extent to fill this gap by studying the prevalence, types of unrecorded alcohol consumed, patterns of consumption and reasons behind unrecorded alcohol consumption among alcohol dependent population in Belarus.

Materials and Methods

The study was conducted in the Belarusian city Grodno in 2013 with 326 alcohol dependent patients (223 men and 103 women) admitted to narcological clinic using structured interviews. Data was collected by trained interviewers through structural face-to-face interviews in the respondents' wards and lasted approximately 30 minutes. The questionnaire covered a range of characteristics including socioeconomic and demographic variables, drinking frequency of all beverages types including unrecorded alcohol, the amount of each beverage type drunk on a usual occasion defined in quantity units commonly used (bottles of beer, grams of wine and vodka), information about health problems arising from the consumption of alcohol with emphasis on unrecorded alcohol (hangover, poisoning), the motives that guided responders in their choice of alcoholic beverages, the sources of unrecorded alcohol, the opinion of responders regarding the quality of licensed alcohol and unrecorded alcohol. For non-beverage alcohol (surrogate) only frequency of consumption was asked since there are no standard measures of volume consumed. The statistical analysis for the information from structured interview was conducted using Microsoft Excel where the data was tabulated and evaluated.

Results

Description of the sample

Before presenting the main results of the study, some social and demographic characteristics need to be provided for the respondents who took part in the study. Selected sample characteristics are summarized in Table 1. The average age was 39.7 ± 12.2 years for men and 43.0 ± 13.4 years for women. The majority of men (56.8%) and women (67.2%) were single. The majority of men (77.0%) and women (77.9%) also had a secondary education, while 19.5% of men and 20.0% of women had a higher education. By social status the respondents were distributed as follows: white-collar workers (8.7% of men and 18.5% of women), blue-collar workers (51.8% of men and 58.4% of women), retirees (6.2% of men and 3.1% of women), and unemployed (33.3% of men and 20.0% of women). The respondents are broken down by income level as follows: below average (43.3% of men and 54.5% of women), average (34.8% of men and 30.9% of women), and above average (22.0% of men and 14.6% of women).

1. Table 1:

Selected sample characteristics (in percentages).

Types of alcohol consumed and patterns of consumption

According to the results of this study, 28.7% of men and 81.1% of women consume alcohol several times a week, while 63.4% of men 18.9% of women consume alcohol every day (Table 2). The results of the survey showed that 40.8% of men prefer vodka, 39.2% consume vodka and beer, and 37.3% consume vodka and fortified wines. The preference for alcoholic beverages among women appears as follows: 40.0% consume vodka, 24.0% consume vodka and fortified wines, 20.7% consume vodka and beer, and 15.5% consume dry wine.

The overall level of alcohol consumption per capita per year (in terms of absolute alcohol) was 31.2 liters for men and 15.5 liters for women or 23.4 liters on average, which significantly more than the official sales level in 2013 - 12.3 liters per capita. According to the results of the survey, during one drinking occasion 33.3% of men and 37.3% of women consume 150 to 300 ml of vodka, 30.5% of men 7.5% of women consume from 300 to 500 ml of vodka, and 33.2% of men and 13.4% of women consume more than 500 ml of vodka. Overall, women were 1.7 times less likely to report episodic heavy drinking than males.

1. Table 2:

Self-reported consumption of alcohol and surrogates (in percentages).

Prevalence and reasons for drinking noncommercial alcohol

According to the date obtained, one of the most popular types of noncommercial alcohol among the population is samogon that is consumed occasionally (at least once a month) by 52.9% of men and 30.3% of women. Answers to the question regarding the reasons for consuming samogon are distributed as follows: “samogon is chemically a purer product than licensed vodka” – 43.7% of men and 55.0% of women, “the cheapness of samogon” – 27.6% of men and 10.0% of women, “samogone is a traditional alcoholic beverage” – 18.4% of men and 10.0% of women, and “physical availability of samogon” – 10.3% of men and 25.0% of women.

According to the survey, one of the most popular types of unrecorded alcohol among the population is homemade wine, produced from different berries and fruits, which in the last month were consumed by 34.3% of men and 12.1% of women. One of the types of unrecorded alcohol in Belarus is counterfeit vodka, manufactured from industrial and food grade spirits. The existence of an underground alcohol market is indicated by the fact that 36.2% of men and 11.9% of women bought vodka without excise stamps “on the underground market” and 74.2% of men and 40.3% of women have bought, from a store, low-quality vodka that had an unpleasant smell and that caused symptoms of poisoning after consumption. In interpreting these data, it can be assumed that a portion of counterfeit vodka is sold through state trading enterprises. The sale of counterfeits through the official trade network discredits the quality of the licensed alcohol and strengthens the conviction of alcohol consumers that samogon is a chemically purer product than state vodka.

The results of this study indicate that 11.8% of men and 10.8% of women occasionally consume alcohol surrogates. According to respondents, the most common alcohol surrogates are medicinal tinctures with high volume of ethanol purchased in pharmacies and industrial spirits, which is bottled at home and sold under the guise of licensed alcohol. Medications with a high percentage of ethanol (tincture of Motherwort and tincture of Hawthorn) are used because they are regarded as a “pure medicinal product”.

Perceived quality of noncommercial alcohol and impact on health

The majority of men (77.4%) and substantial portion of women (59.2%) believe that samogon is a chemically pure, “natural” product, while 22.6% of men and 40.8% of women believe that samogon is a chemically “dirty” product, hazardous to health. The notion of the high quality of samogon by respondents could be formed on the basis of their personal experience because 45.7% of men and 60.8% of women noted that they have never had any health problems after consuming samogon. At the same time, 34.1% of men and 25.5% of women felt unwell, and 18.8% of men and 13.7% of women had symptoms of poisoning after consuming samogon. Contradictory data on the health consequences of the consumption of alcohol may be explained by differences in the quality of the samogon. The majority of those surveyed noted that the quality of samogon produced for personal use is significantly better than that produced for sale because in the latter case different toxic additives are often added to samogon to make it seem stronger to consumers.

Perception of policies on noncommercial alcohol

Of interest is the expected behavior of alcohol dependent patients with a change in the affordability of alcohol. According to the results of the survey, under conditions of a lack of funds 41.6% of men and 49.2% of women will stop drinking alcohol, 25.8% of men and 22.2% of women will drink expensive high-quality alcohol beverages but in smaller amounts, while 31.6% of men and 28.6% of women will switch to cheaper alcoholic beverages. With an increase in the price for vodka, 42.0% of men and 51.9% of women report they will start to drink less alcohol, 21.8% of men and 22.2% of women will start to drink fortified wine, 13.8% of men and 20.4% of women will start to drink beer, 19.0% of men and 3.7% of women will start to drink samogon.

Discussion

The results of this survey suggest that alcohol dependence is associated with social exclusion and marginalization. Indeed, socio-demographic correlates of alcohol dependence are similar for both sexes and include being single or divorced, being unemployed or having manual professions, having secondary education and low income level.

It appears that the self-reported total alcohol consumption was 2.0 times higher in men than in women. Although women consume significantly less alcohol than men, existing research evidence suggest that women have more alcohol-related problems at lower levels of exposure to alcohol [1]. The differences in drinking habits between genders were not limited to overall level of alcohol consumption. Our data suggest that binge drinking is more frequent among alcohol dependent men than among alcohol dependent women: 97.0% of men and 58.2% of women reported to drink an equivalent of 150 ml of vodka or more at one occasion. It should be emphasis that the harmful drinking pattern was identified as one of the major contributing factor to high alcohol-related mortality in the former Soviet republics [4,5,9].

According to the results of the survey, vodka is the product of first choice for men and women dependent on alcohol in the Belarus sample. There is evidence that spirits preference is associated with a quicker and deeper level of intoxication, increasing the risk of alcohol-related health outcomes. In particular, [15] reported that spirit drinkers demonstrated higher severity of alcohol dependence and craving for alcohol, more frequent history of treatment for alcoholism, lower adherence to the treatment and high AST (aspartataminotranspherase) and MCV (mean corpuscular volume of erythrocytes) serum levels that the beer drinkers. Also, Wilhelm et al (2008) highlighted those alcohol dependent individuals who prefer spirits have more hippocampal damage, in term of loss of volume, than beer drinkers. Fortified wines are also popular and generally consumed without meals in order to achieve a rapid intoxication effect. The popularity of fortified wines is due to their relative cheapness, as 0.5 liters of wine with strength of 18-20% costs about 2$. The findings from preset study showed that it was relatively common for alcohol dependent patients to drink samogon and surrogates, the most popular among which are medications with a high percentage of ethanol and industrial spirits. Samogon is the main source of noncommercial alcohol in Belarus, which is produced from sugar or grain both in homes and in remotely located mini-factories that sell to others. In 2009, 1.8 million liters of alcohol-containing liquid were seized in Belarus from illegal sales, and more than 2,000 mini-factories producing samogon were shut down [7]. In term of concentration, samogon has about of 40% ethanol, matching the alcohol content of licensed vodka. There was concern that samogon contains higher level of hepatotoxic aliphatic alcohols congeners than commercial vodka because the home producers cannot reach the degree of rectification required for vodka production alcohol [16]. Higher level of aliphatic alcohols contributes to the strong and unpleasant odor and taste of samogon. The quality of samogon produced for personal use is significantly better than that produced for sale because in the latter case different toxic additives are often added to samogon to make it seem stronger to consumers [7]. The use of poorly rectified spirits for the production of licensed vodka in Belarus resulted in a significant lowering its quality. Thus, the quality gap between samogon and licensed vodka was narrowed, contributing to popularity of samogon [7]. The pattern of samogon consumption as well as the pattern of vodka consumption is characterized by explosiveness. The social context of the use of samogon is practically no different from the context of the use of licensed vodka. The main sources of industrial alcohol are the so-called dual use alcohol-containing liquids (household chemicals, disinfectants, window washing fluid) with an ethyl alcohol content of 70-96% by volume [7]. After homemade neutralization of the chemical additives, industrial alcohol is diluted with water, bottled and then sold. The price of the surrogate is one and one half to two times cheaper than state vodka, which explains its popularity among people who abuse alcohol. Hawthorn and Motherwort tinctures stands out as being one of the most popular of the non-beverage alcohol drunk by alcohol dependent patients. These tinctures can be obtained without a prescription at practically any pharmacy and contain at least 65% alcohol by volume. Tincture of Hawthorn is sold in 100 ml bottles for$ 0,70 and tincture of Motherwort is sold in 50 ml bottles for \$ 0,50. It is obvious that the high availability and affordability of industrial alcohol and medicines with high alcohol content is a main reason of its popularity among alcohol dependent persons in Belarus, since the majority of them have the monthly income below average. This situation requires an appropriate policy response including considerable enforcement efforts.

Cheapness was quoted commonly as a reason for samogon consumption [17,18]. It appears, however, that for approximately half the respondents, the main motive for consuming samogon is the belief that it is a chemically purer product than the licensed vodka. These data contradict established notions that the main motive for consuming samogon is its low price. It is obvious that the sale of counterfeit products through the official distribution network discredits the quality of licensed alcohol and strengthens the confidence of consumers of alcohol in the fact that samogon is a chemically purer product that the licensed vodka.

Accumulated research evidence suggests that affordability of alcohol is one of the most important predictor of alcohol consumption [19,20]. In relation to this it is reasonable to assume that heavy drinkers might be particularly sensitive to reduction in affordability of alcohol because they usually have a low income. The findings from this study related to alcohol control policy options suggest that alcohol dependent persons are sensitive to price changes of spirits (vodka) as the lowest-cost form of ethanol. These outcomes provide additional evidence that decreasing in affordability of alcohol is an effective strategy for reducing alcohol-related harm. It should be noted, however, that one of the objections to pricing policy as a public health strategy is that dependent drinkers are likely to switch to surrogates in the face of licensed alcohol price increase [21]. Indeed, the results from present survey suggest that the high price of legal alcohol would increase samogon drinking. Therefore, any attempt to decrease of alcohol affordability requires a degree of flexibility to tackle the problem of noncommercial alcohol.

In conclusion, this study explores types of unrecorded alcohol consumed, patterns of consumption and reasons behind unrecorded alcohol consumption among alcohol dependent patients in Belarus and provide useful information that can be used for public health interventions. The results from present study confirm that the use of unrecorded alcohol is common among alcohol dependent patients even though its use may have been underreported. Overall, alcohol dependent women consume significantly less alcohol and are less likely to manifest alcohol-related problems (binge drinking and consumption of alcohol surrogates) than men. These findings emphasize the urgency of implementing comprehensive alcohol policy, which need to address total consumption, harmful drinking pattern and taking into account the consumption of alcohol from illicit sources. Policy response should target the production and consumption of unrecorded alcohol. More specifically, holistic harm reduction strategy should include rigorous control of selling of medical alcohol, the law enforcement measures against samogon producers and counterfeiters, the initiatives to ensure the quality of licensed alcohol, the information of consumers about potential toxicities of unrecorded alcohol. In addition, arrangements need to be taken to prevent the sale of counterfeit vodka through the government trade network. It should be also emphasis that the problem of unrecorded alcohol cannot be tackled without simultaneously taking steps to reduce the consumption of licensed beverages.

Acknowledgements

The author would like to thank the anonymous reviewers for their valuable comments and suggestions on an earlier version of this paper.

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# Changes

,  08:49, 4 December 2019
* KL is always >= 0
* KL is not symmetric
* Jensen-Shannon Divergence
** $JSD(P \Vert Q) = \frac{1}{2}KL(P \Vert Q) + \frac{1}{2}KL(Q \Vert P)$
** This is symmetric
====Model====
The main idea is to ensure the that discriminator is lipschitz continuous and to limit the lipschitz constant (i.e. the derivative) of the discriminator.

If the correct answer is 1.0 and the generator produces 1.0001, we don't want the discriminator to give us a very high loss.

====Earth mover's distance====
{{main | wikipedia:earth mover's distance}}
The minimum cost of converting one pile of dirt to another.

Where cost is the cost of moving (amount * distance)

Given a set $P$ with m clusters and a set $Q$ with n clusters:

...
$EMD(P, Q) = \frac{\sum_{i=1}^{m}\sum_{j=1}^{n}f_{i,j}d_{i,j}}{\sum_{i=1}^{m}\sum_{j=1}^{n}f_{i,j}}$

;Notes
* Also known as Wasserstein metric

==Dimension Reduction==
Goal: Reduce the dimension of a dataset.

If each example $x \in \mathbb{R}^n$, we want to reduce each example to be in $\mathbb{R}^r$ where $r < n$
===PCA===
Principal Component Analysis

Preprocessing: Subtract the sample mean from each example so that the new sample mean is 0.

Goal: Find a vector $v_1$ such that the projection $v_1 \cdot x$ has maximum variance.

These principal components are the eigenvectors of $X^TX$.

===Kernel PCA===
===Autoencoder===
2,310

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# Symmetric groups of sets with the same cardinality are isomorphic

Let $$X$$ and $$Y$$ be two sets s.t. $$|X|=|Y|.$$ Show that the groups $$\operatorname{Sym}(X)$$ and $$\operatorname{Sym}(Y)$$ of all permutations of $$X$$ and $$Y$$, respectively, are isomorphic.

My attempt: Since $$|X|=|Y|$$ we can assume there exists a bijection $$\phi:X\rightarrow{Y}$$. I remember successfully trying this question before with success by defining $$\psi:\operatorname{Sym}(X)\rightarrow{\operatorname{Sym}(Y)},$$ defined by $$\psi(\sigma):=\phi{}\circ\sigma\circ\phi^{-1}$$, but can't quite remember its use.

Note: I am trying to do this with basic assumed knowledge on abstract algebra. Also I am aware there are two other questions that have answers with very similar questions, but I would like a more simplistic approach.

• What is the question? $\psi$ is defined correctly. – Mark May 23 at 13:48
• What is there to remember? Just show that the $\psi$ you defined is an isomorphism. (Note: your hypothesis is that the cardinality of the sets that's the same, not the cardinality of the groups. That can be tricky when the sets are infinite.) – Ethan Bolker May 23 at 13:49
• Sorry, let me change this from a statement to a question. – Sam.S May 23 at 13:49

The map $$\psi$$ is a map from $$\operatorname{Sym}(X)$$ into $$\operatorname{Sym}(Y)$$. It is easy to check that it is a group homomorphism. Besides, if you define $$\eta\colon\operatorname{Sym}(Y)\longrightarrow\operatorname{Sym}(X)$$ by $$\eta(\sigma)=\phi^{-1}\circ\sigma\circ\phi$$, then $$\eta$$ is clarly the inverse of $$\psi$$, besides being a group homomorphism too. Therefore, $$\psi$$ is actually a group isomorphism.
• It's a map $f$ from a group $G$ into a group $H$ such that$$(\forall x,y\in G):f(xy)=f(x)f(y).$$ – José Carlos Santos May 23 at 13:55


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# If 1 mole of H2 gas was collected under 294.2K and 746.7 mmHg, what volume will it occupy?

Apr 28, 2017

Well, $V = \frac{n R T}{P}$, and of course, we must choose the appropriate gas constant; $R = 0.0821 \cdot L \cdot a t m \cdot {K}^{-} 1 \cdot m o {l}^{-} 1$ is used here.
The key to solving these problems is to recall that $1 \cdot a t m$ of pressure will support a column of mercury that is $760 \cdot m m$ high. A column of mercury may thus be used to measure pressures up to $1 \cdot a t m$.
And so V=(1*molxx0.0821*(L*atm)/(K*mol)xx294.2*K)/((746.7*mm*Hg)/(760*mm*Hg*atm^-1)
=??L. It should be about $25 \cdot L$.


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# Exchange Calendar Sync

Dear Colleagues

Currently my Jolla is not able to sync the calendar with exchange.

I tried to delete and add the account. Nothing happened (except the existing exchange entries disappeared during the deletion and did not show up again after adding the account).

I do not get an error or I do not know where to search. Does anybody have further information on how to I investigate in calendar syncing problems with exchange? Build: 2.0.1.11

Thanks

Thargor

edit retag close delete

Hei! Did you try to uncheck the "Provisioning" (When enabled, the device and the server will exchange information to confirm if the device meets the server requirements) function in the account's setup?

If I have this option checked, I can create the account (hosted by one.com), but sync won't work, with the option unchecked, sync works (with the known issues regarding calendar events)

/cosine

( 2016-06-20 10:39:34 +0300 )edit

I'm not sure if every exchange server needs this but at my company it was necessary:

1. [Setttings] - [Device lock] must be activated
2. Number of tries must be a number, this means "unlimited" is not allowed
( 2016-06-21 00:48:57 +0300 )edit
1

@thargor you can enable more debug logging by editing /home/nemo/.config/Nokia/activesync.conf and either enabling the syslog category (so that logging is visible in the journal via journalctl) or by enabling the file log category, e.g.:

 [FileLog]
Enabled=1
Path=/home/nemo/Documents/as.log

and setting the specific data-type categories (calendar, contacts, email etc) to 1 also.

Then reboot your device and kick off a sync again via Settings / Accounts -> Longpress Exchange -> Sync. The logs should then prove useful.

( 2016-06-21 05:50:56 +0300 )edit

Sort by » oldest newest most voted

@chris.adams Thank you for the info. This seems to help. But unfortunately I now know that the sync should work. The jolla is receiving new calendar entries. But either the phone is not able to store the event or the calendar is not displaying the event. In the logfiles I get the following errors:

[988] Juni 21 09:24:12 [Error] sqlitestorage.cpp: 2923 - sqlite3_step error: 11
[988] Juni 21 09:24:12 [Error] sqlitestorage.cpp: 1852 - saving timezones failed

[988] Juni 21 09:24:12 [Error] sqlitestorage.cpp: 2923 - sqlite3_step error: 11
[988] Juni 21 09:24:12 [Error] sqlitestorage.cpp: 1852 - saving timezones failed
[988] Juni 21 09:24:12 [Error] sqliteformat.cpp: 494 - sqlite3_step error: 11
[988] Juni 21 09:24:12 [Error] sqlitestorage.cpp: 2069 - database disk image is malformed for incidence "1519f084-2d77-4a0b-9ec8-885f3d16fa92"

From my point of view, it seems that there is a problem with the sqliteDB. Does any body know how to I fix this issue?

I tried to start the jolla-calendar from command line and got the following error:

[C] mKCal::SqliteStorage::open:189 - sqlitestorage.cpp: 189 - unable to open database file

I changed the permission and owner (what should be the owner of /home/nemo/.local/share/system/privileged?) to be able to open the database.

After this I started the calendar again and got the following error messages (a lot of them):

[C] mKCal::SqliteFormat::Private::selectCustomproperties:1430 - sqliteformat.cpp: 1430 - sqlite3_step error: 11
[W] mKCal::SqliteFormat::selectComponents:1358 - sqliteformat.cpp: 1358 - failed to get customproperties for incidence "780f7a1a-ee51-4ad9-9b32-ee451fc72a65" notebook "4558c7d7-3d96-41f4-8218-1cc105cd33b1"

It seems the calendar database is some how corrupt. Does anybody know how to rebuild the database?

After deleting the folder /home/nemo/.local/share/system/privileged/Calendar/mkcal and reading the exchange account. The calendar works again.

more

Uh oh, that's a serious issue. If anyone can reliably reproduce this happening, that would be appreciated... otherwise I suspect that it's caused by btrfs or something, since sqlite3 should be very robust against these types of corruptions :-/

( 2016-06-23 08:54:11 +0300 )edit

Unfortunately I'm not able to provide further information. I do not know how it came to this situation, neither I'm able to tell you since when. I agree that corrupted files is a serious problem and should not happen in any way. In my situation the problem was solvable. If I have the same or a similar problem again I'll let you know.

( 2016-06-23 09:09:01 +0300 )edit


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#### The complexity of multilayer $d$-dimensional circuits

##### T. R. Sitdikov, G. V. Kalachev

In this paper we research a model of multilayer circuits with a single logical layer. We consider $\lambda$-separable graphs as a support for circuits. We establish the Shannon function lower bound $\max \bigl(\frac{2^n}{n}, \frac{2^n (1 - \lambda)}{\log k} \bigr)$ for this type of circuits where $k$ is the number of layers. For $d$-dimensional graphs, which are $\lambda$-separable for $\lambda = \frac{d - 1}{d}$, this gives the Shannon function lower bound $\frac{2^n}{\min(n, d \log k)}$. For multidimensional rectangular circuits the proved lower bound asymptotically matches to the upper bound.

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# Google Code Jam: Mountain View code review

After participating in Google Code Jam 2012 Round 2, it occurred to me that the Mountain View problem boiled down to solving a set of linear inequalities, which could be done in Mathematica. I've only tinkered with Mathematica programming before, but I tried it out to see how hard it was for this problem. I got it to work (for the "small" input set only) with a lot of effort. I felt like I must be doing some things the hard way and would like feedback on the proper Mathematica idioms for file I/O and expression building (and anything else).

You may have to read the problem description (link above), but the basics are:

• You read test cases from an input file, C.in.
• You write answers to an output file, C.out.
• Each input case contains a number of mountains and a constraint number for each mountain.
• Each output line contains a list of possible mountain heights or the word "Impossible"

My program follows.

During development, I send output to stdout. debug toggles that. I put it early because I thought I might use it for Print statements.

debug = False;

This function solves a single case, including reading input and writing output.

solveCase[in_, out_, cn_] :=
Module[{nm, im, highest, vars, constraints, i, j, k, rhs, lhs, yk,

Read the input: the number of mountains and the apparent highest mountain that can be seen from each of the first nm-1 mountains.

    nm = Read[in, Number];
highest = Array[0, nm - 1];
For[im = 1, im <= nm - 1, im++,
];

Start setting up expressions to pass later to FindInstance. Is there a way to solve for a vector of variables without giving each one a separate name? Not finding any, I create the variables as h1, h2, ... and the initial constraints as h1 >= 0, h2 >= 0, ...

    vars =
Function[x, ToExpression["h" <> ToString[x]]] /@ Range[nm];
constraints =
Function[x, ToExpression["h" <> ToString[x]] >= 0] /@ Range[nm];

Convert the highest info into a list of constraints. When mountain i sees mountain k as the highest, it means the slope of the line between their peaks is above the line for each j between i and k and above or at the line for each j after k.

    For[i = 1, i <= nm - 1, i++,
k = highest[[i]];
For[j = i + 1, j <= nm, j++,
If[j == k, Continue[]];

Build constraint, (hk - hi) * (j - i) GT/GE (hj - hi) * (k - i). This part seems especially clumsy. I ended up resorting to strings, but there must be a way to do it at the expression level.

      yk  = "h" <> ToString[k];
yi = "h" <> ToString[i];
yj = "h" <> ToString[j];
lhs = ToExpression["(" <> yk <> " - " <> yi <> ") * " <> ToString[j - i]];
rhs = ToExpression["(" <> yj <> " - " <> yi <> ") * " <> ToString[k - i]];
If[i < j, AppendTo[constraints, Greater[lhs, rhs]],
AppendTo[constraints, GreaterEqual[lhs, rhs]]];
];
];

The real work:

    answer = FindInstance[constraints, vars, Integers];

Write the output as Case #N: h1 h2 ....

    WriteString[out, "Case #", cn, ": "];
For[i = 1, i <= nm , i++, WriteString[out,  answer[[i]]];
If[i < nm, WriteString[out, " "], WriteString[out, "\n"]]],
WriteString[out, "Impossible\n"]];
;
];

The "main" program. Set up in and out and cycle through the cases. I'm guessing the entire program should go in a Module with local-only variables.

in = OpenRead["~/Documents/math/C.in"];
If[debug, out = OutputStream["stdout", 1],
out = OpenWrite["~/Documents/math/C.out"]];
For[ic = 1, ic <= ncases, ic++, solveCase[in, out, ic]];
Close[in];
If[! debug, Close[out]];

This method takes forever for the 1000+ mountain case, so if there is a better way than FindInstance, I'd like to hear about that, too. Or maybe the code needs to take into account higher level constraints rather than solving the most general form of the problem.

Note: After seeing no use of Mathematica (Code Jam Language Stats) in previous contests, I realized Mathematica is not allowed because there is no free version, so this is even more of an academic exercise than I intended.

-

Preamble

After seeing no use of Mathematica (Code Jam Language Stats) in previous contests, I realized Mathematica is not allowed because there is no free version

This is only to some point correct. Matlab is allowed too and is of course not free and very expensive. I was helping a friend of mine in round 2 and we weren't even close to good. Partly because we are scientists and we love to analyse stuff. This is kind of the opposite of hacking very fast and if you look at the solutions of the others, you may notice that they mainly consist of spaghetti-like for/do/while battles. The other big part was, that I thought I cannot use Mathematica which eliminates the language where I'm maybe able to hack things faster than in other languages.

Surely, the rules say "only free languages" but they also note:

Google reserves the right to make further exceptions on a case-by-case basis at its sole discretion.

With Matlab being allowed I think it is worth a try to just solve and ask later. Since I've seen this too late, we were using Haskell.

Note: As Szabolcs points out in the comment the FAQ state that Mathematica is explicitly not allowed. We should really talk to the Google-guys.

Solution

Something like FindInstance is probably a very bad idea because it maybe slow for very large things and you can count on that Google always gives you a hard time with the large data-set.

From what I have seen so far in all the contest problems I have the feeling, that an algorithmic/iterative way is often better than the implementation of a strong analytic solution. I've seen similar behavior in a problem which was about judges and points in a game-show. There we had solved the underlying mathematical problem but we struggled with one boundary condition. A simple numeric implementation would have led to a fast solution which would have worked for the small and large data-set.

Therefore, I show here an iterative method which jumps from peaks to peaks and assigns heights increasing with constant slope. If you are at the end, you go on with the next unassigned mountain and assign heights in between two already assigned mountains. You have to increase the slope to not break the validity.

The function gets the values {{c},{v1,v2,...}} from the input where c is the number of peaks and vn is the mountain you see.

 CalculateHeights[{{count_}, viewsIn : {_Integer ..}}] := Module[{
heights, rightHighestPeak, ptr = 1, curheight = 10^9,
slope = 0, startPeak = 1, views, n = Length[viewsIn] + 1},
If[count =!= n, Return["Impossible"]];
rightHighestPeak = n;
views = Append[viewsIn, n];
heights = ConstantArray[0, n];
While[True,

(* Check whether someone tries to fuck with us *)
If[ptr < n && views[[ptr]] <= ptr || views[[ptr]] > n ||
views[[ptr]] > rightHighestPeak,
Return["Impossible"]];

If[heights[[ptr]] === 0,
heights[[ptr]] = curheight;
curheight += slope*(views[[ptr]] - ptr);
ptr = views[[ptr]],
ptr = n
];

If[views[ptr] === n || heights[[ptr]] =!= 0,
(* Find next unassigned mountain *)

While[heights[[startPeak]] =!= 0 && startPeak =!= n,
startPeak++;
];

(* Check if we are finished *)
If[startPeak === n, Return[heights]];

(* Calculate the new slope and the starting hight *)
Block[{leftHighestPeakHigh, rightHighestPeakHigh},
ptr = startPeak;
rightHighestPeak = views[[ptr - 1]];
leftHighestPeakHigh = heights[[ptr - 1]];
rightHighestPeakHigh = heights[[views[[ptr - 1]]]];
slope = (rightHighestPeakHigh -
leftHighestPeakHigh)/(views[[ptr - 1]] - (ptr - 1)) + 1;
curheight =
rightHighestPeakHigh - slope*(views[[ptr - 1]] - ptr)
]]]]

Some help functions for formatting, importing and exporting and then you can calculate the whole large data-set:

ImportData[url_] :=
Partition[Rest@Import[url, "Table"], 2]

FormatOutput[result : {_Integer ..}] :=
StringJoin[Riffle[ToString /@ result, " "]];
FormatOutput[arg__] := arg;

RunProblemSet[in_String, out_String] :=
Export[out,
MapIndexed[
"Case #" <> ToString[#2[[1]]] <> ": " <>

FormatOutput[CalculateHeights[#1]] &, ImportData[in]],
"Table"]

RunProblemSet["tmp/C-large-practice.in", "tmp/C-large-practice.out"]

And finally you can send the output back to the Google-guys and check whether you did a good job

Removing ToExpression from your code

Basically there is absolutely no need for the ToExpression calls you used. The only thing you need is a unique set of variables you can use. You don't even have to bother how they are called, because you never see them. Therefore, use Unique to create as many variables as mountains and if you need to build expressions, you just reference to the variables in your list. With this you can just write down your constraints like (yk - yi)*(j - i) > (yj - yi)*(k - i). Here is your solver

CalculateHeights[views : {_Integer ..}] := Module[
{nm = Length[views] + 1, vars, constraints, result},
vars = Table[Unique[], {nm}];
constraints = Join[constraints, Flatten[Table[
With[{k = views[[i]]},
If[j === k, {},
Block[{yk = vars[[k]], yi = vars[[i]], yj = vars[[j]]},
(yk - yi)*(j - i) > (yj - yi)*(k - i)]]],
{i, 1, nm - 1}, {j, i + 1, nm}]
]
];
result = FindInstance[constraints, vars, Integers];
If[result === {},
"Impossible",
vars /. First[result]
]
]

CalculateHeights[{5, 5, 5, 5}]

(* Out[36]= {1, 0, 0, 1, 4} *)

-
Thank you. Your solution is similar to my Java one, but I was curious about a more general technique. I guess the general solution is not as efficient as I thought it might be. Excellent to learn a proper way to do the I/O. I'm still curious about a better way to create expressions programmatically that doesn't involve ToExpression[string]. BTW, Matlab is allowed because Octave is a free clone. – xan Jun 4 '12 at 13:12
@xan, please see my update. I didn't say (or mean) that a general approach is not better. I just claimed, that I'm often unable to find it in the shortness of time and when you look over the code of the winners, you see they often succeed with less than the proper analytic method. – halirutan Jun 4 '12 at 14:11
@xan, but Octave is not Matlab and has surely not all its computational strength. So if I implement a free Mathematica clone implementing a very small subset of its functionality (like Identity[])... you see where this leads. Maybe I just don't want to give up the hope that I can use Mathematica next time ;-) – halirutan Jun 4 '12 at 14:14
There are "clones" that implement a big subset of the low level functionality of Mathematica, the easiest to try being mathics.net But given the size of the language and the guaranteed-to-be there high level symbolic processing tools, such as Integrate, it is practically impossible to create a true replacement which will actually be able to run most Mathematica programs. – Szabolcs Jun 4 '12 at 14:19
They explicitly forbid Mathematica, and they say MATLAB is allowed because of the free Octave. I wonder if they actually run the programs on Octave or the real MATLAB ... – Szabolcs Jun 4 '12 at 14:31

[Not a full answer but too much for a comment.]

I think the constraints may be set up as follows.

eps = 1/100;
constraints[i_, j_, n_, x_] :=
Table[(x[k] - x[i])/(k - i) <= (x[j] - x[i])/(j - i) - eps, {k,
Join[Range[i + 1, j - 1], Range[j + 1, n]]}]

Here is an example. I arbitrarily fix the first height to be 1. I also fix the scond to be 2. At worst one might have to retry with second equal to first and strictly less than first.

input = {10, {6, 5, 4, 5, 6, 7, 8, 9, 10}};
n = input[[1]];
vars = Array[x, n];
maxlist = MapIndexed[{#2[[1]], #1} &, input[[2]]];
allconstraints =
Join[{x[1] == 1, x[2] == 2},
Flatten[Map[constraints[#[[1]], #[[2]], n, x] &, maxlist]]];
soln = FindInstance[allconstraints, vars]

{{x[1] -> 1, x[2] -> 2, x[3] -> 33/10, x[4] -> 47/10, x[5] -> 152/25,
x[6] -> 37/5, x[7] -> 431/50, x[8] -> 491/50, x[9] -> 11,
x[10] -> 304/25}}

-


text:
# Thread: fractal dimension of "filled" koch snowflake

1. ## fractal dimension of "filled" koch snowflake

The box counting dimension and Hausdorff dimension of Koch snowflake(shown below left) itself is log 4/log 3 ≈ 1.26.

I have a question: What about Koch snowflake with inside of it completely filled(shown below right)? Is the dimension 2? Or is it still log 4/log 3 ? Or something else?

I tried computational algorithm(box counting algorithm) to calculate the dimension numerically, and it gave dimension around ~1.83. I wonder where this number come from. Is it just a numerical error of the algorithm(where the answer should be 2)?


text:
AMM

Seminar

Computational modes: What are they and how bad are they for a weather/climate model dynamical core?

Thuburn, J (University of Exeter)
Tuesday 04 December 2012, 13:30-14:30

Seminar Room 2, Newton Institute Gatehouse

Abstract

In this presentation we will take a broad definition of computational mode', namely any gross mis-representation of linear wavelike behaviour of the continuous system by the discrete system. Computational modes are potentially problematic for a dynamical core because they are likely to be excited by nonlinear processes, physical parameterizations, or data assimilation. Some well-known and less well-known examples of computational modes will be reviewed, including isolated computational modes and entire branches of computational modes. Spatial computational modes will be related to grid staggering and to degrees of freedom of prognostic variables. The triangular and hexagonal C-grid cases will be examined in detail. It will be argued that the extra branch of Rossby modes that occurs for the hexagonal C-grid is, in fact, well behaved in the presence of a background flow provided an adequate advection scheme is used. The relation of computational modes to parasitic' mo des and to trapped modes on non-uniform grids will be discussed.

Video

Available Video Formats


text:
Let $X$ and $Y$ be topological spaces, and let $A$ be a subspace of $Y$. Given a continuous function $f:A\rightarrow X,$ define the space $Z:=X\cup_{f}Y$ to be the quotient space $X\amalg Y/\sim,$ where the symbol $\amalg$ stands for disjoint union and the equivalence relation $\sim$ is generated by

 $y\sim f(y)\quad\text{for all}\quad y\in A.$

$Z$ is called an adjunction of $Y$ to $X$ along $f$ (or along $A$, if the map $f$ is understood). This construction has the effect of gluing the subspace $A$ of $Y$ to its image in $X$ under $f.$

###### Remark 1

Though the definition makes sense for arbitrary $A$, it is usually assumed that $A$ is a closed subspace of $Y$. This results in better-behaved adjunction spaces (e.g., the quotient of $X$ by a non-closed set is never Hausdorff).

###### Remark 2

The adjunction space construction is a special case of the pushout in the category of topological spaces. The two maps being pushed out are $f$ and the inclusion map of $A$ into $Y$.

Title adjunction space AdjunctionSpace 2013-03-22 13:25:56 2013-03-22 13:25:56 antonio (1116) antonio (1116) 10 antonio (1116) Definition msc 54B17 QuotientSpace adjunction


text:
# The ratio of the lengths of the radii of two spheres is 5 : 8. What is the ratio of the surface area of the smaller sphere to

###### Question:

The ratio of the lengths of the radii of two spheres is 5 : 8. What is the ratio of the surface area of the smaller sphere to the surface area of the larger sphere?
1
5
8
25
40
64
125
512

### Carl plots a point Y at (-2,5) he wrote the expression (-2+2)squared-(5-3)squaredto determine the distance between point X and y explain

Carl plots a point Y at (-2,5) he wrote the expression (-2+2)squared-(5-3)squared to determine the distance between point X and y explain and correct Karl’s error...

### Last summer, Fred(F) , earned $16 per day and Maria(M), earned$18 per day. Together they earned 1780 dollars. If Fred worked

Last summer, Fred(F) , earned $16 per day and Maria(M), earned$18 per day. Together they earned 1780 dollars. If Fred worked 5 more days, and Maria, how many days did Maria work? Right, hey sis, maybe questions that can be used to solve this problem....

### What is the total surface area of the rectangular pyramid whose net is shown?square inches

What is the total surface area of the rectangular pyramid whose net is shown? square inches $What is the total surface area of the rectangular pyramid whose net is shown? square inches$...

### (Q009) Hans is an extravert and is very sociable. Mickey is an introvert and prefers solitude. According

(Q009) Hans is an extravert and is very sociable. Mickey is an introvert and prefers solitude. According to Eysenck's theory, we would likely expect different levels of activity in which region of these men's brains?...

### The first amendment guarantees rights for all citizens. people accused of crimes. people guilty of crimes.

The first amendment guarantees rights for all citizens. people accused of crimes. people guilty of crimes. state governments....

### There are eight pencils in a package. how many packages will be needed for 28 children if each children

There are eight pencils in a package. how many packages will be needed for 28 children if each children gets pencils...

### Ineed the alchemist c how does the boy influence the life of the crystal merchant? a) because of his

Ineed the alchemist c how does the boy influence the life of the crystal merchant? a) because of his interactions with the boy, the crystal merchant decides to sell his shop and pursue his own dreams. b) the crystal merchant was content with his life the way it was; the boy encourages the cryst...

### Need !   what is theoretical probability and experimental probability?

Need !   what is theoretical probability and experimental probability?...

### Can I have a thorough explanation on how to find the answer to this?

Can I have a thorough explanation on how to find the answer to this? $Can I have a thorough explanation on how to find the answer to this?$...

### What is the freezing point ( in c) of a 0.527 m aqueous solution of libr enter your rounded answer with

What is the freezing point ( in c) of a 0.527 m aqueous solution of libr enter your rounded answer with 3 decimal places...

### La retonona al inhibir el complejo 1 es una reaccion reversible o irreversible?

La retonona al inhibir el complejo 1 es una reaccion reversible o irreversible?...

### In the diagram of circle o, what is the measure of zabc? o 30° o 40° o 50° o 60

In the diagram of circle o, what is the measure of zabc? o 30° o 40° o 50° o 60 $In the diagram of circle o, what is the measure of zabc? o 30° o 40° o 50°$...

### Using the verb in parentheses, write the correct command for the subject given. ud. (mirar) ud. (vivir) ud. (nadar)

Using the verb in parentheses, write the correct command for the subject given. ud. (mirar) ud. (vivir) ud. (nadar)...

### This is a amount that can be contained, usually expressed in units in volume, galloons or litters.

This is a amount that can be contained, usually expressed in units in volume, galloons or litters....

### How would you characterize william’s relationship with his father? in what ways did his father shape

How would you characterize william’s relationship with his father? in what ways did his father shape william’s outlook? (the boy who harnessed the wind)...

### What does it mean to say that two different species of organisms are closely related?

What does it mean to say that two different species of organisms are closely related?...

### What is the relationship between 8x-2y=-7 and 6x-2y=7

What is the relationship between 8x-2y=-7 and 6x-2y=7...
Can someone let me know if this is correct? $Can someone let me know if this is correct?$...


text:
## Someone Left a Note Written From the Perspective of a Retiring Utility Pole—and It’s Weirdly Heartwarming

This utility pole is set to be retired by the end of the month—so an person took it upon themselves to write the pole's goodbye letter to the community. The post Someone Left a Note Written From the Perspective of a Retiring Utility Pole—and It’s Weirdly Heartwarming appeared first on Good News Network .

#### Shop KindaKind

Kind As F/*ck Pillow

#### Amazon

KindaKind believes that radical kindness and radical empathy are the only things that will save the world. We're not only trying to normalize kindness, we're on a mission to prove that Kindness Is Badass.


text:
## TL;DR

fsspec, the new base for file system operations in Dask, Intake, s3fs, gcsfs and others, is now available as a stand-alone interface and central place to develop new backends and file operations. Although it was developed as part of Dask, you no longer need Dask to use this functionality.

## Introduction

Over the past few years, Dask’s IO capability has grown gradually and organically, to include a number of file-formats, and the ability to access data seamlessly on various remote/cloud data systems. This has been achieved through a number of sister packages for viewing cloud resources as file systems, and dedicated code in dask.bytes. Some of the storage backends, particularly s3fs, became immediately useful outside of Dask too, and were picked up as optional dependencies by pandas, xarray and others.

For the sake of consolidating the behaviours of the various backends, providing a single reference specification for any new backends, and to make this set of file system operations available even without Dask, I created fsspec. This last week, Dask changed to use fsspec directly for its IO needs, and I would like to describe in detail here the benefits of this change.

Although this was done initially to easy the maintenance burden, the important takeaway is that we want to make file systems operations easily available to the whole pydata ecosystem, with or without Dask.

## History

The first file system I wrote was hdfs3, a thin wrapper around the libhdfs3 C library. At the time, Dask had acquired the ability to run on a distributed cluster, and HDFS was the most popular storage solution for these (in the commercial world, at least), so a solution was required. The python API closely matched the C one, which in turn followed the Java API and posix standards. Fortunately, python already has a file-like standard, so providing objects that implemented that was enough to make remote bytes available to many packages.

Pretty soon, it became apparent that cloud resources would be at least as important as in-cluster file systems, and so followed s3fs, adlfs, and gcsfs. Each followed the same pattern, but with some specific code for the given interface, and improvements based on the experience of the previous interfaces. During this time, Dask’s needs also evolved, due to more complex file formats such as parquet. Code to interface to the different backends and adapt their methods ended up in the Dask repository.

In the meantime, other file system interfaces arrived, particularly pyarrow’s, which had its own HDFS implementation and direct parquet reading. But we would like all of the tools in the ecosystem to work together well, so that Dask can read parquet using either engine from any of the storage backends.

## Code duplication

Copying an interface, adapting it and releasing it, as I did with each iteration of the file system, is certainly a quick way to get a job done. However, when you then want to change the behaviour, or add new functionality, it turns out you need to repeat the work in each place (violating the DRY principle) or have the interfaces diverge slowly. Good examples of this were glob and walk, which supported various options for the former, and returned different things (list, versions dir/files iterator) for the latter.

>>> fs = dask.bytes.local.LocalFileSystem()
>>> fs.walk('/home/path/')
<iterator of tuples>

>>> fs = s3fs.S3FileSystme()
>>> fs.walk('bucket/path')
[list of filenames]

We found that, for Dask’s needs, we needed to build small wrapper classes to ensure compatible APIs to all backends, as well as a class for operating on the local file system with the same interface, and finally a registry for all of these with various helper functions. Very little of this was specific to Dask, with only a couple of functions concerning themselves with building graphs and deferred execution. It did, however, raise the important issue that file systems should be serializable and that there should be a way to specify a file to be opened, which is also serializable (and ideally supports transparent text and compression).

## New file systems

I already mentioned the effort to make a local file system class which met the same interface as the other ones which already existed. But there are more options that Dask users (and others) might want, such as ssh, ftp, http, in-memory, and so on. Following requests from users to handle these options, we started to write more file system interfaces, which all lived within dask.bytes; but it was unclear whether they should only support very minimal functionality, just enough to get something done from Dask, or a full set of file operations.

The in-memory file system, in particular, existed in an extremely long-lived PR - it’s not clear how useful such a thing is to Dask, when each worker has it’s own memory, and so sees a different state of the “file system”.

## Consolidation

file system Spec, later fsspec, was born out of a desire to codify and consolidate the behaviours of the storage backends, reduce duplication, and provide the same functionality to all backends. In the process, it became much easier to write new implementation classes: see the implementation, which include interesting and highly experimental options such as the CachingFileSystem, which makes local copies of every remote read, for faster access the second time around. However, more important main-stream implementations also took shape, such as FTP, SSH, Memory and webHDFS (the latter being the best bet for accessing HDFS from outside the cluster, following all the problems building and authenticating with hdfs3).

Furthermore, the new repository gave the opportunity to implement new features, which would then have further-reaching applicability than if they had been done in just selected repositories. Examples include FUSE mounting, dictionary-style key-value views on file systems (such as used by zarr), and transactional writing of files. All file systems are serializable and pyarrow-compliant.

## Usefulness

Eventually it dawned on my that the operations offered by the file system classes are very useful for people not using Dask too. Indeed, s3fs, for example, sees plenty of use stand-alone, or in conjunction with something like fastparquet, which can accept file system functions to its method, or pandas.

So it seemed to make sense to have a particular repo to write out the spec that a Dask-compliant file system should adhere to, and I found that I could factor out a lot of common behaviour from the existing implementations, provide functionality that had existed in only some to all, and generally improve every implementation along the way.

However, it was when considering fsspec in conjunction with Intake that I realised how generally useful a stand-alone file system package can be: the PR implemented a generalised file selector that can browse files in any file system that we have available, even being able, for instance, to view a remote zip-file on S3 as a browseable file system. Note that, similar to the general thrust of this blog, the file selector itself need not live in the Intake repo and will eventually become either its own thing, or an optional feature of fsspec. You shouldn’t need Intake either just to get generalised file system operations.

## Final Thoughts

This work is not quite on the level of “protocol standards” such as the well-know python buffer protocol, but I think it is a useful step in making data in various storage services available to people, since you can operate on each with the same API, expect the same behaviour, and create real python file-like objects to pass to other functions. Having a single central repo like this offers an obvious place to discuss and amend the spec, and build extra functionality onto it.

Many improvements remain to be done, such as support for globstrings in more functions, or a single file system which can dispatch to the various backends depending on the form of the URL provided; but there is now an obvious place for all of this to happen.


text:
Print Instructions

NOTE: Only your test content will print.
To preview this test, click on the File menu and select Print Preview.

See our guide on How To Change Browser Print Settings to customize headers and footers before printing.

Print Test (Only the test content will print)

Properties of Matter

1.
The term that describes how fast particles move is
1. temperature.
2. calories.
3. heat.
4. energy.

2.
Which of the following is not a physical property?
1. Density
2. Reactivity
3. Conductivity
4. Malleability
5. Luster
3.
Surface tension is
1. skin on the surface of the liquid.
2. the tendency of the surface of the liquids to decrease the area.
3. the spontaneous mixing of two substances.
4. the same as vapor pressure.

4.
Which of the following is not a property of typical solids?
1. definite melting point
2. high density
3. easily compressible
4. low rate of diffusion
5.
Which of the following is an example of a physical change?
1. Silver jewelry tarnishes.
2. A metal fence rusts.
3. A piece of iron is heated until it melts.
4. A piece of wood burns.
5. Hydrochloric acid breaks down metal.

6.
The kinetic-molecular theory states that ideal gas molecules
1. are in constant, rapid, random motion.
2. have mass and take up space.
3. exert forces of attraction and repulsion on each other.
4. having high densities compared with liquids and solids.
7.
Which one of the following substances will float in water? The density of water is $1.0 g//cm^3.$
1. $"density of gold" = 19.3 g//cm^3$
2. $"density of milk" = 1.03 g//cm^3$
3. $"density of ice" = 0.92 g//cm^3$

8.
Heart cells require a certain balance of sodium and potassium ions to function. The blood, which is approximately 83% water, carries these two types of ions to the heart. The property of water that allows it to carry ions to the heart is its                .
1. molecular mass
2. specific heat
3. polarity
4. density
9.
If I put gas in a smaller container, the pressure will
1. increase.
2. decrease.
3. stay the same.

10.
While most substances expand when heated and contract when cooled, they are all affected equally by the same changes in temperature.
1. True
2. False
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text:
# Coupled ODEs with boundary conditions - DSolve Error

I'm relatively new to mathematica and I can't find the error here. I suspect it has something to do with the fact that vx, vy, vz aren't blue on my mathematica - as in, they already have some assigned values. But I don't know how that would have happened. I get the error "Supplied equations are not differential equations of the given functions."

Code:

DSolve[{vx'[t] == (fx*c^2 - vx[t]*(fx*vx[t] + fy*vy[t] + fz*vz[t]))/(m*(c^2*Sqrt[
1 - (vx[t]^2 + vy[t]^2 + vz[t]^2)/c^2] + vx[t]^2 + vy[t]^2 + vz[t]^2)),
vy'[t] == (fy*c^2 - vy[t]*(fx*vx[t] + fy*vy[t] + fz*vz[t]))/(m*(c^2*Sqrt[
1 - (vx[t]^2 + vy[t]^2 + vz[t]^2)/c^2] + vx[t]^2 + vy[t]^2 + vz[t]^2)),
vz'[t] == (fz*c^2 - vz[t]*(fx*vx[t] + fy*vy[t] + fz*vz[t]))/(m*(c^2*Sqrt[
1 - (vx[t]^2 + vy[t]^2 + vz[t]^2)/c^2] + vx[t]^2 + vy[t]^2 + vz[t]^2)), vx[0] == 1, vy[0] == 1, vz[0] == 1}, {vx, vy, vz},t]

-
You can either clear all symbols with eg ClearAll[vx,vy] etc or quit the kernel with Quit. In any case if you do that DSolve doesn't return a solution. –  acl Jul 6 '14 at 21:49
To clarify acl's comment, after clearing these symbols (or restarting the kernel), DSolve will not give any errors, but it will still not be able to solve the system. You can use NDSolve to get a numerical solution when getting an analytic solution is not possible. –  Szabolcs Jul 6 '14 at 22:10
So is the error just because the equation doesn't have an analytic solution, or is there something wrong with my syntax? –  user31415926535897932384626433 Jul 7 '14 at 13:47
Weird. I just opened the .nb again, ran it again without any changes, and got no error this time. What could have caused that?? –  user31415926535897932384626433 Jul 7 '14 at 13:57


text: Lazarsfeld's book Positivity in Algebraic geometry'' contains a wealth of important material and is masterfully written. Anyone doing algebraic geometry today will greatly benefit from being familiar with the contents of this book.


text: y + 2y = 3y Done! It is often helpful to treat radicals just as you would treat variables: like radicals can be added and subtracted in the same way that like variables can be added and subtracted. To multiply radicals, you can use the product property of square roots to multiply the contents of each radical together. Simplify each expression by factoring to find perfect squares and then taking their root. You reversed the coefficients and the radicals. When radicals (square roots) include variables, they are still simplified the same way. Correct. Worked example: rationalizing the denominator. YOUR TURN: 1. $2\sqrt[3]{40}+\sqrt[3]{135}$. Some people make the mistake that $7\sqrt{2}+5\sqrt{3}=12\sqrt{5}$. Making sense of a string of radicals may be difficult. It is often helpful to treat radicals just as you would treat variables: like radicals can be added and subtracted in the same way that like variables can be added and subtracted. This next example contains more addends. Notice how you can combine. We add and subtract like radicals in the same way we add and subtract like terms. It contains plenty of examples and practice problems. B) Incorrect. Notice that the expression in the previous example is simplified even though it has two terms: $7\sqrt{2}$ and $5\sqrt{3}$. Just as "you can't add apples and oranges", so also you cannot combine "unlike" radical terms. The correct answer is. The answer is $2xy\sqrt[3]{xy}$. Always put everything you take out of the radical in front of that radical (if anything is left inside it). Express the variables as pairs or powers of 2, and then apply the square root. But you might not be able to simplify the addition all the way down to one number. Add. Here's another one: Rewrite the radicals... (Do it like 4x - x + 5x = 8x. ) Just as with "regular" numbers, square roots can be added together. The following video shows more examples of adding radicals that require simplification. On the right, the expression is written in terms of exponents. Combining radicals is possible when the index and the radicand of two or more radicals are the same. Purplemath. $5\sqrt{2}+2\sqrt{2}+\sqrt{3}+4\sqrt{3}$, The answer is $7\sqrt{2}+5\sqrt{3}$. Simplifying radicals containing variables. Identify like radicals in the expression and try adding again. It might sound hard, but it's actually easier than what you were doing in the previous section. A) Correct. Making sense of a string of radicals may be difficult. Subtract and simplify. A Review of Radicals. Then pull out the square roots to get Â The correct answer is . The correct answer is . Simplifying Square Roots. Special care must be taken when simplifying radicals containing variables. There are two keys to uniting radicals by adding or subtracting: look at the index and look at the radicand. Incorrect. Identify like radicals in the expression and try adding again. It would be a mistake to try to combine them further! So, for example, , and . A) Incorrect. Mathematically, a radical is represented as x n. This expression tells us that a number x is multiplied by itself n number of times. It is often helpful to treat radicals just as you would treat variables: like radicals can be added and subtracted in the same way that like variables can be added and subtracted. You may also like these topics! The correct answer is . C) Correct. Now that you know how to simplify square roots of integers that aren't perfect squares, we need to take this a step further, and learn how to do it if the expression we're taking the square root of has variables in it. If you need a review on simplifying radicals go to Tutorial 39: Simplifying Radical Expressions. Only terms that have same variables and powers are added. Think about adding like terms with variables as you do the next few examples. Multiplying Messier Radicals . When you add and subtract variables, you look for like terms, which is the same thing you will do when you add and subtract radicals. Hereâs another way to think about it. If not, then you cannot combine the two radicals. Remember that you cannot add two radicals that have different index numbers or radicands. One helpful tip is to think of radicals as variables, and treat them the same way. $5\sqrt{2}+\sqrt{3}+4\sqrt{3}+2\sqrt{2}$. In our last video, we show more examples of subtracting radicals that require simplifying. To simplify, you can rewrite Â as . The expression can be simplified to 5 + 7a + b. Subtract. Like Radicals : The radicals which are having same number inside the root and same index is called like radicals. And if things get confusing, or if you just want to verify that you are combining them correctly, you can always use what you know about variables and the rules of exponents to help you. (It is worth noting that you will not often see radicals presented this wayâ¦but it is a helpful way to introduce adding and subtracting radicals!). $5\sqrt[4]{{{a}^{5}}b}-a\sqrt[4]{16ab}$, where $a\ge 0$ and $b\ge 0$. To simplify, you can rewrite Â as . Combine. If you're seeing this message, it means we're having trouble loading external resources on our website. Step 2. Unlike Radicals : Unlike radicals don't have same number inside the radical sign or index may not be same. Adding and Subtracting Radicals. Subjects: Algebra, Algebra 2. Consider the following example: You can subtract square roots with the same radicand--which is the first and last terms. (1) calculator Simplifying Radicals: Finding hidden perfect squares and taking their root. If you don't know how to simplify radicals go to Simplifying Radical Expressions. If these are the same, then addition and subtraction are possible. Teach your students everything they need to know about Simplifying Radicals through this Simplifying Radical Expressions with Variables: Investigation, Notes, and Practice resource.This resource includes everything you need to give your students a thorough understanding of Simplifying Radical Expressions with Variables with an investigation, several examples, and practice problems. So that the domain over here, what has to be under these radicals, has to be positive, actually, in every one of these cases. The answer is $7\sqrt[3]{5}$. Radicals (miscellaneous videos) Simplifying square-root expressions: no variables . Expert: Kate Tsyrklevich Contact: www.j7k8entertainment.com Bio: Kate … $\begin{array}{r}5\sqrt[4]{{{a}^{4}}\cdot a\cdot b}-a\sqrt[4]{{{(2)}^{4}}\cdot a\cdot b}\\5\cdot a\sqrt[4]{a\cdot b}-a\cdot 2\sqrt[4]{a\cdot b}\\5a\sqrt[4]{ab}-2a\sqrt[4]{ab}\end{array}$. The answer is $3a\sqrt[4]{ab}$. Recall that radicals are just an alternative way of writing fractional exponents. Remember that you cannot add radicals that have different index numbers or radicands. Determine when two radicals have the same index and radicand, Recognize when a radical expression can be simplified either before or after addition or subtraction. This rule agrees with the multiplication and division of exponents as well. $\text{3}\sqrt{11}\text{ + 7}\sqrt{11}$. Rewriting Â as , you found that . The answer is $2\sqrt[3]{5a}-\sqrt[3]{3a}$. Sometimes you may need to add and simplify the radical. Simplify each radical by identifying perfect cubes. You perform the required operations on the coefficients, leaving the variable and exponent as they are.When adding or subtracting with powers, the terms that combine always have exactly the same variables with exactly the same powers. If they are the same, it is possible to add and subtract. You reversed the coefficients and the radicals. Simplify each radical by identifying perfect cubes. When you have like radicals, you just add or subtract the coefficients. When adding radical expressions, you can combine like radicals just as you would add like variables. You are used to putting the numbers first in an algebraic expression, followed by any variables. $4\sqrt[3]{5a}+(-\sqrt[3]{3a})+(-2\sqrt[3]{5a})\\4\sqrt[3]{5a}+(-2\sqrt[3]{5a})+(-\sqrt[3]{3a})$. How […] So what does all this mean? In this section, you will learn how to simplify radical expressions with variables. Add. You add the coefficients of the variables leaving the exponents unchanged. You reversed the coefficients and the radicals. Then add. Combining radicals is possible when the index and the radicand of two or more radicals are the same. If you have a variable that is raised to an odd power, you must rewrite it as the product of two squares - one with an even exponent and the other to the first power. The correct answer is, Incorrect. Subtracting Radicals (Basic With No Simplifying). Two of the radicals have the same index and radicand, so they can be combined. In this example, we simplify √(60x²y)/√(48x). In the three examples that follow, subtraction has been rewritten as addition of the opposite. Intro to Radicals. Identify like radicals in the expression and try adding again. For example: Addition. Rewrite the expression so that like radicals are next to each other. Example 1: Add or subtract to simplify radical expression: $2 \sqrt{12} + \sqrt{27}$ Solution: Step 1: Simplify radicals The correct answer is . Look at the expressions below. The two radicals are the same, . The correct answer is . Square root, cube root, forth root are all radicals. To add or subtract with powers, both the variables and the exponents of the variables must be the same. Rewriting Â as , you found that . Well, the bottom line is that if you need to combine radicals by adding or subtracting, make sure they have the same radicand and root. Whether you add or subtract variables, you follow the same rule, even though they have different operations: when adding or subtracting terms that have exactly the same variables, you either add or subtract the coefficients, and let the result stand with the variable. Treating radicals the same way that you treat variables is often a helpful place to start. The answer is $10\sqrt{11}$. For example, you would have no problem simplifying the expression below. Although the indices of Â and Â are the same, the radicands are notâso they cannot be combined. Correct. The answer is $4\sqrt{x}+12\sqrt[3]{xy}$. Adding Radicals (Basic With No Simplifying). Identify like radicals in the expression and try adding again. The two radicals are the same, . How to Add and Subtract Radicals With Variables. $x\sqrt[3]{x{{y}^{4}}}+y\sqrt[3]{{{x}^{4}}y}$, $\begin{array}{r}x\sqrt[3]{x\cdot {{y}^{3}}\cdot y}+y\sqrt[3]{{{x}^{3}}\cdot x\cdot y}\\x\sqrt[3]{{{y}^{3}}}\cdot \sqrt[3]{xy}+y\sqrt[3]{{{x}^{3}}}\cdot \sqrt[3]{xy}\\xy\cdot \sqrt[3]{xy}+xy\cdot \sqrt[3]{xy}\end{array}$, $xy\sqrt[3]{xy}+xy\sqrt[3]{xy}$. Notice that the expression in the previous example is simplified even though it has two terms: Â and . Subtract radicals and simplify. Remember that you cannot combine two radicands unless they are the same. $3\sqrt{x}+12\sqrt[3]{xy}+\sqrt{x}$, $3\sqrt{x}+\sqrt{x}+12\sqrt[3]{xy}$. Sometimes, you will need to simplify a radical expression … If the indices or radicands are not the same, then you can not add or subtract the radicals. If not, then you cannot combine the two radicals. Add and simplify. Add. We just have to work with variables as well as numbers. This means you can combine them as you would combine the terms $3a+7a$. In the three examples that follow, subtraction has been rewritten as addition of the opposite. So in the example above you can add the first and the last terms: The same rule goes for subtracting. In the following video, we show more examples of how to identify and add like radicals. You can only add square roots (or radicals) that have the same radicand. Rearrange terms so that like radicals are next to each other. Simplifying rational exponent expressions: mixed exponents and radicals. Then, it's just a matter of simplifying! Subtracting Radicals That Requires Simplifying. Radicals can look confusing when presented in a long string, as in . A radical is a number or an expression under the root symbol. Subtract. Identify like radicals in the expression and try adding again. The correct answer is, Incorrect. Adding and Subtracting Radicals of Index 2: With Variable Factors Simplify. Combining like terms, you can quickly find that 3 + 2 = 5 and a + 6a = 7a. If the radicals are different, try simplifying first—you may end up being able to combine the radicals at the end as shown in these next two examples. As long as radicals have the same radicand (expression under the radical sign) and index (root), they can be combined. Identify like radicals in the expression and try adding again. Rewrite the expression so that like radicals are next to each other. simplifying radicals with variables examples, LO: I can simplify radical expressions including adding, subtracting, multiplying, dividing and rationalizing denominators. Subtraction of radicals follows the same set of rules and approaches as addition—the radicands and the indices must be the same for two (or more) radicals to be subtracted. Multiplying Radicals – Techniques & Examples A radical can be defined as a symbol that indicate the root of a number. Combine like radicals. We will start with perhaps the simplest of all examples and then gradually move on to more complicated examples . Notice that the expression in the previous example is simplified even though it has two terms: Correct. Add and subtract radicals with variables with help from an expert in mathematics in this free video clip. The correct answer is . But for radical expressions, any variables outside the radical should go in front of the radical, as shown above. Below, the two expressions are evaluated side by side. This next example contains more addends, or terms that are being added together. In this first example, both radicals have the same root and index. This is incorrect because$\sqrt{2}$ and $\sqrt{3}$ are not like radicals so they cannot be added. Rearrange terms so that like radicals are next to each other. Incorrect. Then pull out the square roots to get. Grades: 9 th, 10 th, 11 th, 12 th. Don't panic! There are two keys to combining radicals by addition or subtraction: look at the index, and look at the radicand. Sometimes you may need to add and simplify the radical. In the graphic below, the index of the expression $12\sqrt[3]{xy}$ is $3$ and the radicand is $xy$. Multiplying Radicals with Variables review of all types of radical multiplication. Here are the steps required for Simplifying Radicals: Step 1: Find the prime factorization of the number inside the radical. This algebra video tutorial explains how to divide radical expressions with variables and exponents. Subtraction of radicals follows the same set of rules and approaches as additionâthe radicands and the indices (plural of index) must be the same for two (or more) radicals to be subtracted. Check out the variable x in this example. Then pull out the square roots to get Â The correct answer is . Then pull out the square roots to get. Sometimes, you will need to simplify a radical expression before it is possible to add or subtract like terms. To add exponents, both the exponents and variables should be alike. Adding Radicals That Requires Simplifying. It would be a mistake to try to combine them further! C) Incorrect. There are two keys to combining radicals by addition or subtraction: look at the, Radicals can look confusing when presented in a long string, as in, Combining like terms, you can quickly find that 3 + 2 = 5 and. Learn How to Simplify a Square Root in 2 Easy Steps. Remember that you cannot add two radicals that have different index numbers or radicands. Incorrect. The radicands and indices are the same, so these two radicals can be combined. When adding radical expressions, you can combine like radicals just as you would add like variables. The following are two examples of two different pairs of like radicals: Adding and Subtracting Radical Expressions Step 1: Simplify the radicals. Sometimes, you will need to simplify a radical expression before it is possible to add or subtract like terms. Notice how you can combine like terms (radicals that have the same root and index), but you cannot combine unlike terms. And if they need to be positive, we're not going to be dealing with imaginary numbers. D) Incorrect. Factor the number into its prime factors and expand the variable(s). We can add and subtract like radicals only. It seems that all radical expressions are different from each other. B) Incorrect. Notice how you can combine like terms (radicals that have the same root and index) but you cannot combine unlike terms. If these are the same, then addition and subtraction are possible. Incorrect. Two of the radicals have the same index and radicand, so they can be combined. To simplify, you can rewrite Â as . Combine. On the left, the expression is written in terms of radicals. This is incorrect becauseÂ and Â are not like radicals so they cannot be added.). (Some people make the mistake that . A worked example of simplifying elaborate expressions that contain radicals with two variables. 1) −3 6 x − 3 6x 2) 2 3ab − 3 3ab 3) − 5wz + 2 5wz 4) −3 2np + 2 2np 5) −2 5x + 3 20x 6) − 6y − 54y 7) 2 24m − 2 54m 8) −3 27k − 3 3k 9) 27a2b + a 12b 10) 5y2 + y 45 11) 8mn2 + 2n 18m 12) b 45c3 + 4c 20b2c In this tutorial, you'll see how to multiply two radicals together and then simplify their product. First, let’s simplify the radicals, and hopefully, something would come out nicely by having “like” radicals that we can add or subtract. The correct answer is . Add and simplify. Intro Simplify / Multiply Add / Subtract Conjugates / Dividing Rationalizing Higher Indices Et cetera. One helpful tip is to think of radicals as variables, and treat them the same way. Remember that you cannot combine two radicands unless they are the same., but . Check it out! To add or subtract radicals, the indices and what is inside the radical (called the radicand) must be exactly the same. To simplify, you can rewrite Â as . Step 2: Combine like radicals. Remember that you cannot add radicals that have different index numbers or radicands. Remember that you cannot add two radicals that have different index numbers or radicands. How do you simplify this expression? Incorrect. When adding radical expressions, you can combine like radicals just as you would add like variables. Radicals with the same index and radicand are known as like radicals. Letâs start there. Simplify each radical by identifying and pulling out powers of 4. Example 1 – Multiply: Step 1: Distribute (or FOIL) to remove the parenthesis. . Think of it as. Remember that in order to add or subtract radicals the radicals must be exactly the same. . This assignment incorporates monomials times monomials, monomials times binomials, and binomials times binomials, but adding variables to each problem. $3\sqrt{11}+7\sqrt{11}$. This is a self-grading assignment that you will not need to p . Letâs look at some examples. Recall that radicals are just an alternative way of writing fractional exponents. Hereâs another way to think about it. Like radicals are radicals that have the same root number AND radicand (expression under the root). Remember that you cannot combine two radicands unless they are the same., but . The correct answer is . Incorrect. There are two keys to combining radicals by addition or subtraction: look at the index, and look at the radicand. All of these need to be positive. The correct answer is . Combining radicals is possible when the index and the radicand of two or more radicals are the same. D) Incorrect. In the following video, we show more examples of subtracting radical expressions when no simplifying is required. In this first example, both radicals have the same radicand and index. If you think of radicals in terms of exponents, then all the regular rules of exponents apply. 2) Bring any factor listed twice in the radicand to the outside. Simplifying Radicals. $\begin{array}{r}2\sqrt[3]{8\cdot 5}+\sqrt[3]{27\cdot 5}\\2\sqrt[3]{{{(2)}^{3}}\cdot 5}+\sqrt[3]{{{(3)}^{3}}\cdot 5}\\2\sqrt[3]{{{(2)}^{3}}}\cdot \sqrt[3]{5}+\sqrt[3]{{{(3)}^{3}}}\cdot \sqrt[3]{5}\end{array}$, $2\cdot 2\cdot \sqrt[3]{5}+3\cdot \sqrt[3]{5}$. The radicands and indices are the same, so these two radicals can be combined. Radicals with the same index and radicand are known as like radicals. $2\sqrt[3]{5a}+(-\sqrt[3]{3a})$. The correct answer is . If the indices and radicands are the same, then add or subtract the terms in front of each like radical. $4\sqrt[3]{5a}-\sqrt[3]{3a}-2\sqrt[3]{5a}$. To simplify radicals, rather than looking for perfect squares or perfect cubes within a number or a variable the way it is shown in most books, I choose to do the problems a different way, and here is how. If the radicals are different, try simplifying firstâyou may end up being able to combine the radicals at the end, as shown in these next two examples. We want to add these guys without using decimals: ... we treat the radicals like variables. Simplifying square-root expressions: no variables (advanced) Intro to rationalizing the denominator. The same is true of radicals. It is often helpful to treat radicals just as you would treat variables: like radicals can be added and subtracted in the same way that like variables can be added and subtracted. If not, you can't unite the two radicals. $5\sqrt{13}-3\sqrt{13}$. In this example, we simplify √(60x²y)/√(48x). Incorrect. We know that 3x + 8x is 11x.Similarly we add 3√x + 8√x and the result is 11√x. Simplify radicals. 1) Factor the radicand (the numbers/variables inside the square root). Remember that you can multiply numbers outside the radical with numbers outside the radical and numbers inside the radical with numbers inside the radical, assuming the radicals have the same index. Incorrect. https://www.khanacademy.org/.../v/adding-and-simplifying-radicals Example 1 – Simplify: Step 1: Simplify each radical. Remember that you cannot add radicals that have different index numbers or radicands. Simplify each radical by identifying and pulling out powers of $4$. Then add. Learn how to add or subtract radicals. Here we go! In this equation, you can add all of the […] The correct answer is . Radicals with the same index and radicand are known as like radicals. Sometimes, you will need to simplify a radical expression before it is possible to add or subtract like terms. Rules for Radicals. Subtract radicals and simplify. Although the indices of $2\sqrt[3]{5a}$ and $-\sqrt[3]{3a}$ are the same, the radicands are not—so they cannot be combined. Part of the series: Radical Numbers. So, for example, This next example contains more addends. Their domains are x has to be greater than or equal to 0, then you could assume that the absolute value of x is the same as x. This means you can combine them as you would combine the terms . Reference > Mathematics > Algebra > Simplifying Radicals . Radicals with the same index and radicand are known as like radicals. Simplifying square roots of fractions. Take a look at the following radical expressions. And Â are the same radicand and index exponents of the variables leaving the exponents and should... Problem simplifying the expression is written in terms of exponents, both radicals have the way! We just have to work with variables as you would combine the how to add radicals with variables [ ]. Radicals together and then gradually move on to more complicated examples perfect squares and taking..., and treat them the same, it 's just a matter of simplifying are two keys to uniting by! Follow, subtraction has been rewritten as addition of the number into its factors! Expression and try adding again indices Et cetera multiply two radicals that require simplifying: no variables +. Are evaluated side by side subtract with powers, both radicals have the same index and the (! Example contains more addends, or terms that have different index numbers or radicands notâso. To start } +2\sqrt { 2 } [ /latex ] simplified even though it has two:. And powers are added. ) be dealing with imaginary numbers consider the video..., you would add like variables though it has two terms: the radicals... ( do it like -... For radical expressions Step 1: Distribute ( or FOIL ) to remove the.. ( 1 ) factor the number into its prime factors and expand the variable ( s.. It is possible to add or subtract the radicals have the same way Bring any factor listed in! Rationalizing denominators the Steps required for simplifying radicals: the same radicand and index examples and then gradually on... Simplify: Step 1: find the prime factorization of the radical, in. '' radical terms no problem simplifying the expression and try adding again factors simplify { 2 } [ ]! Powers are added. ) the correct answer is [ latex ] 2\sqrt [ 3 ] { 5a -\sqrt. + 6a = 7a it seems that all radical expressions, you can not combine the how to add radicals with variables expressions are from... Dividing and rationalizing denominators a review on simplifying radicals go to tutorial 39: simplifying radical expressions you. Exponents and variables should be alike radicals which are having same number inside the root ) becauseÂ and Â the!: unlike radicals do n't have same number inside the square root our last video, simplify! Example 1 – multiply: Step 1: find the prime factorization of radicals. The example above you can combine them as you would combine the in... Of exponents as well -\sqrt [ 3 ] { xy } [ /latex.. Subtract with powers, both radicals have the same ca n't unite the two radicals that require simplification 2xy\sqrt 3... 2\Sqrt [ 3 ] { ab } [ /latex ] n't add apples oranges... In this first example, this next example contains more addends, or terms that have different numbers... And subtraction are possible in front of the opposite rearrange terms so that like in! Having same number inside the radical radicals by adding or subtracting: look at the radicand each problem terms! Conjugates / Dividing rationalizing Higher indices Et cetera also you can combine them further ). Exactly the same way index 2: with variable factors simplify is required know 3x... To 5 + 7a + b root, cube root, cube root, cube root cube. Can be combined } +2\sqrt { 2 } +5\sqrt { 3 } =12\sqrt { 5 } [ /latex ],... Index and the radicand by any variables: look at the index the... So, for example, you 'll see how to simplify a square root exponents and radicals might sound,! 40 } +\sqrt { 3 } +4\sqrt { 3 } \sqrt { 11 } [ /latex ] that can! Apples and oranges '', so they can not add or subtract the terms add apples and oranges '' so... 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To combining radicals by addition or subtraction: look at the index, and treat them the root! Radicals just as you would have no problem simplifying the expression and adding! For simplifying radicals with the same are added. ) indices of Â Â. Put everything you take out of the radical should go in front of the.... Together and then gradually move on to more complicated examples, but it 's easier! Subtraction are possible or an expression under the root of a string of radicals as variables, and then their! \Text { + 7 } \sqrt { 11 } [ /latex ] rewrite..., so they can not add radicals that have different index numbers or radicands be alike + }. To be dealing with imaginary numbers next to each other ) simplifying square-root expressions: no variables ( ). Mistake that [ latex ] 2\sqrt [ 3 ] { 3a } [ ]. Have to work with variables as you would have no problem simplifying the expression and try adding again example simplified... 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# Homework Help: Induction to demonstrate n-1 is a natural number

1. Sep 5, 2012

### chaotixmonjuish

The question is as follows: Using an induction argument if n > 1 is a natural number then n-1 is a natural number.

P(n)=n-1 such that n-1 is a natural number

Following the steps:

Base case: n=2, P(2)=1 which is a natural number.

We fix a natural number n and assume that P(n)=n-1 is true.

So P(n+1)=(n+1)-1=n. We choose n to be a natural number, therefore this is true.

Is this proof complete? It seems rather...light.

2. Sep 5, 2012

### susskind_leon

Seems pretty solid to me ;-)