text:
# How to convert pressure (Bar) to flow rate (L/min)?

#### avishay

hii,

I'm try to calculate the pressure (in bar) needed for a certain flow rate 3 L/min of Argon gas given the following setup:
- I have a tank of Argon gas and the line pressure can be between 0 bar to 5 bar.
- The gas will flow out to the open air in the end.
- My pipe has an internal radius of 2.3mm.

I will be very happy if someone can also explain to me the process of getting to the answer...

Thanks for the help :)

Related Mechanical Engineering News on Phys.org

#### BvU

Science Advisor
Homework Helper
Hello avishay, $\qquad$ $\qquad$ !

Your problem statement isn't complete: for a short pipe the pressure drop is less than for a long pipe.

With the expressions in the link you can calculate $\Delta p$ for your pipe length.

#### avishay

I didnt realy understod how to calculate this prameter, I'm not realy sure why i need this...
any help?
:)

#### russ_watters

Mentor
I didnt realy understod how to calculate this prameter, I'm not realy sure why i need this...
Pressure drop is a function of length or rather is given per unit length.

#### BvU

Science Advisor
Homework Helper
calculate this parameter
It's not really a parameter: according to the link it's a result of a bunch of variables.

What have you calculated yourself so far ?

#### Chestermiller

Mentor
The methodology for solving a problem like this is presented in Chapter 7 of Transport Phenomena by Bird, Stewart, and Lightfoot. But, please note that, in a case like this where the gas pressure change can be as large as a factor of 6, you will need to take into account the compressibility of the gas, and, as such, will probably be working in terms of the square of the absolute pressure (rather than the absolute- or gauge pressure to the 1st power).

### Want to reply to this thread?

"How to convert pressure (Bar) to flow rate (L/min)?"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving


text:
# Why does spiped use both nonces and ephemeral keys?

Colin Percival's spiped utility uses a pre-shared key and Diffie-Hellman with ephemeral keys to provide forward secrecy. The protocol is summarized in the project's README under the section "Encrypted Protocol".

What is the purpose of the nonces (nonce_C and nonce_S)? How are they useful when x_C and x_S are already chosen at random?

Without the nonces, one could violate explicit authentication
by replaying the group_element || MAC_tag messages.

• Can you elaborate on the replay attack? I don't see how the attacker could actually replay packets, since the other party will end up computing a different shared secret every time. – Tim McLean May 7 '15 at 2:55
• The attacker would just send the same group_element || MAC_tag to the party that message $\hspace{.26 in}$ was sent to before, even though that "party will end up computing a different shared secret every time." $\hspace{.15 in}$ – user991 May 7 '15 at 3:06
• Right. So the receiver accepts group_element as valid, and computes a new y_SC (a new shared secret). The receiver then derives the new AES and HMAC keys. How does the attacker now produce a packet with a valid HMAC tag? The attacker can't simply replay packets because the HMAC key has changed, AFAICT. – Tim McLean May 7 '15 at 3:14
• The attacker doesn't "now produce a packet with a valid HMAC tag". $\;$ – user991 May 7 '15 at 3:23
• Yes. ${}{}{}\;$ – user991 May 7 '15 at 3:29

Without the initial exchange of nonces, an attacker could replay a recorded handshake. Although an attacker can't use this to replay actual packets, an attacker could possibly execute a denial of service attack if the process protected by spiped is not expecting a large number of connections.

The attack (assuming a modified spiped protocol that MACs the public keys directly with the long-term key):

1. Observe a handshake. Record y_C || h_C, where y_C is the client's ephemeral public key and h_C = HMAC(K, y_C) (K is the pre-shared key).
2. Open a new connection and replay y_C || h_C. The server sees a valid MAC, and presumably opens a connection to the protected process.
3. Repeat #2 until the protected process is overwhelmed.

Thanks to Ricky Demer for the discussion on his answer.

format: plain


text:
Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 29 May 2016, 06:37

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# GMAT Problem Solving (PS)

 new topic Question banks Downloads My Bookmarks Reviews Important topics Go to page  1   2   3   4   5   6   7   8   9   10   11  ...  249    Next Search for:
Topics Author Replies   Views Last post

Announcements

100
 150 Hardest and easiest questions for PS   Tags:
Bunuel

5

15873

20 May 2016, 07:55

698
 GMAT PS Question Directory by Topic & Difficulty
bb

0

257308

22 Feb 2012, 11:27

Topics

 A positive number x is multiplied by 2 and this product is then divide   Tags:
Lolaergasheva

0

1185

28 Sep 2015, 01:38

 DS:Coordinate Geometry   Tags:
EnterMatrix

0

1157

17 Jul 2010, 11:55

 A certain stock exchange designates each stock with a 1, 2   Tags:
chicagocubsrule

0

7138

12 May 2015, 07:26

 Set X consists of 100 numbers. The average (arithmetic mean) of set X   Tags:
Hussain15

0

5067

24 Sep 2015, 02:33

 Joshua and Jose work at an auto repair center with 4 other workers.   Tags:
Safiya

0

1473

05 Feb 2016, 12:02

 Mixture bleaching chemical   Tags:
coelholds

0

2181

27 Jun 2015, 06:10

 Lionel left his house and walked towards Walt's house, 48 miles away.   Tags:
shrive555

0

1412

04 Aug 2015, 09:20

 Percent Problem   Tags:
udaymathapati

0

970

30 Aug 2010, 11:32

 what is the tens digit of k?   Tags:
tarek99

0

4553

16 Jun 2015, 23:19

 combinations, alphabet   Tags:
noboru

0

1460

22 Feb 2010, 21:56

 If x and y are positive integers and 1 + x + y + xy = 15,   Tags:
mrwaxy

0

927

23 Jul 2015, 00:12

 Strange GMAT Prep Question   Tags:
nikhilbajaj

0

1217

20 Oct 2015, 17:28

 If 125% of j is equal to 25% of k, 150% of k is equal to 50% of l, and   Tags:
aiming4mba

0

1086

30 Sep 2015, 11:01

 The annual interest rate earned by an investment increased by 10 perce   Tags:
TOUGH GUY

0

1709

20 Jul 2015, 01:29

 If w + x < 0, is w - y > 0 ?   Tags:
naveenhv

0

1290

09 Nov 2015, 12:20

 X is planning a bus trip across town that involves three buses. Bus 1   Tags:
valencia

0

1611

25 Sep 2015, 08:22

 A convenience store currently stocks 48 bottles of mineral water. The   Tags:
dred

0

6236

08 Jul 2015, 19:53

 During a trip on an expressway, Don drove a total of x miles. His   Tags:
ludwigvb

0

1842

21 Jul 2015, 11:13

 At a certain food stand, the price of each apple is $0.4 and Tags: singh_amit19 0 2374 22 Jul 2015, 01:29  If k is an integer Tags: monirjewel 0 2901 27 Oct 2015, 05:29  During a trip on an expressway, Don drove x miles.His average speed on Tags: Yellow22 0 1946 16 Jan 2016, 16:37  walkway Area Tags: udaymathapati 0 995 26 Aug 2010, 08:23  If n is a positive integer, which of the following is a possible value Tags: alltimeacheiver 0 1713 07 Aug 2015, 07:09  10^50 - 74 Tags: dimitri92 0 4351 31 Jan 2016, 12:44  For a certain race, 3 teams were allowed to enter 3 members each. A Tags: vcbabu 0 1869 06 Sep 2015, 22:19  GMAT PREP (PS) Tags: LM 0 2385 23 Oct 2010, 10:08  Which of the following CANNOT be the median of the 3 positive integers Tags: kannn 0 3715 21 Nov 2015, 08:40  Poker question Tags: ursiddheart 0 1230 17 Jul 2015, 09:50  Probability; Equal number of boys & girls Tags: Hussain15 0 5319 17 Jun 2015, 03:18  College students Tags: MSDHONI 0 1359 08 May 2011, 07:52  For any positive integer n, the sum of the first n positive integers Tags: metallicafan 0 2370 24 Apr 2016, 13:03  If x, y, and z are positive integers and 3x = 4y = 7z, then the least Tags: MSDHONI 0 1769 01 Feb 2016, 07:00  The function f is defined by f(x) = √x – 10 for all positive Tags: IEsailor 0 2673 27 Oct 2015, 06:04  The figure shows a square patio surrounded by a walkway of Tags: amitdgr 0 6179 04 Jul 2015, 07:31  At a certain paint store "forest green" is made by mixing 4 parts blue Tags: tejhpamarthi 0 1449 22 Nov 2010, 11:15  ps 6.7 Tags: racejockey 0 1938 06 Jul 2011, 01:01  Tickets Tags: Madelaine88 0 1101 03 Mar 2011, 12:43  Right triangle PQR is to be constructed in the xy-plane so Tags: haas_mba07 0 1663 29 Apr 2016, 22:02  A small cubical aquarium has a depth of 1 foot. In the small aquarium Tags: MRHDK1 0 2684 25 Sep 2015, 08:15  probability that the # of men = # of women ? Tags: Alchemist1320 0 1347 26 Dec 2011, 06:01  If n is a positive integer and the product of all the integers from 1 Tags: SunnyDelight 0 2102 27 Jul 2015, 00:02 $686,000 in bonus money is to be divided among 6 employees. No employe   Tags:
martie11

0

2210

15 May 2016, 13:01

 If x > y^2 >z^4   Tags:
Baten80

0

1579

19 Aug 2015, 04:01

 # 35 Elevator with safety limit   Tags:
aalriy

0

961

10 Dec 2010, 10:07

 Problem from OG   Tags:
vasili

0

1512

17 May 2016, 19:30

 #204 OG PS   Tags:
tonebeeze

0

1513

17 May 2016, 19:36

 The y intercept of line l is 4. If the slope of line l is   Tags:
gautamsubrahmanyam

0

2276

27 Aug 2015, 07:52

 Function F(x)   Tags:
udaymathapati

0

1779

27 Jan 2016, 11:05

 What is the least possible product of 4 different integers, each of   Tags:
Acer86

0

2055

09 Nov 2015, 23:50

 As shown in the figure above, a thin conveyor belt 15 feet long is dra   Tags:

0

2812

16 Jul 2015, 06:07

 new topic Question banks Downloads My Bookmarks Reviews Important topics Go to page  1   2   3   4   5   6   7   8   9   10   11  ...  249    Next Search for:
 Who is online In total there are 3 users online :: 1 registered, 0 hidden and 2 guests (based on users active over the past 15 minutes) Users browsing this forum: HungNguyen and 2 guests Statistics Total posts 1490566 | Total topics 181094 | Active members 446260 | Our newest member nitishsingh400@gmail.com

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.


text:
# What is a section?

This question comes out of the answers to Ho Chung Siu's question about vector bundles. Based on my reading, it seems that the definition of the term "section" went through several phases of generality, starting with vector bundles and ending with any right inverse. So admittedly I'm a little confused about which level of generality is the most useful.

Some specific questions:

• Why can we think of sections of a bundle on a space as generalized functions on the space? (I'm being intentionally vague about the kind of bundle and the kind of space.)
• What's the relationship between sections of a bundle and sections of a sheaf?
• How should I think about right inverses in general? I essentially only have intuition for the set-theoretic right inverse.

-

To your first question, "function on a space" $X$ usually means a morphism from $X$ to one of several "ground spaces" of choice, for example the reals if you work with smooth manifolds, Spec(A) if you work with schemes over a ring, etc. (This is a fairly selective use of the word "function" which used to confuse me.) A section $\gamma$ of a (some-kind-of) bundle $E\to X$ is thought of as a "generalized function" on $X$ by thinking of it as a funcion with "varying codomain", i.e. at each point $x\in X$, it takes value in the fibre
$E_x\to x$. If one is talking about locally free / locally trivial bundles, meaning $E$ is locally (over open sets
$U\subset X$) isomorphic to some product $U\times T$, then we can locally identify the fibres with $T$. Thus locally a section just looks like a function with codomain $T$, which is often required to be nice.

To your second question, I generally take the "right-inverse" or "pre-inverse" definition from category theory, because it relates back to others in the following precise way:

Say $\pi: Y\to X$ is a space over $X$ (intentionaly vague). The word "over" is used to activate the tradition of suppressing reference to the map $\pi$ and refering instead to the domain $Y$. For $U\subseteq X$ open, the notation $\Gamma(U,Y)$ denotes sections of the map $\pi$ over $U$, i.e. maps $U\to Y$ such that the composition $U \to Y\to X$ is the identity (thus necessarily landing back in $U$). It's not hard to see that
$\Gamma(-,Y)$ actually forms a sheaf of sets on $X$.

Conversely, given any sheaf of sets $F$ on a space $X$, one can form its espace étalé, a topological space over $X$, say $\pi: \acute{E}t(F) \to X$. Then for an open $U\subseteq X$, the elements of $F(U)$ correspond precisely to sections of the map $\pi$, which by the above notation is written $\Gamma(U,\acute{E}t(F)$. That is to say,
$F(-)\simeq\Gamma(-,\acute{E}t(F))$ as sheaves on $X$. This explains why people often refer to sheaf elements as "sections" of the sheaf.

Moreover, what we now denote by $\acute{E}t(F)$ actually used to be the definition of a sheaf, so people tend to identify the two and write $\Gamma(-,F)$ a instead of $\Gamma(-,\acute{E}t(F))$. This explains the otherwise bizarre tradition of writing $\Gamma(U,F)$ instead of the the more compact notation $F(U)$.

$\Big($Unfortunate linguistic warning: Many people incorrectly use the term "étale space". However, the French word "étalé" means "spread out", whereas "étale" (without the second accent) means "calm", and they were not intended to be used interchangeably in mathematics. This is unfortunate, because the espace étalé has very little to with with étale cohomology. More unfortunate is the annoying coincidence that when dealing with schemes the projection map from the espace étalé happens to be an étale morphism, because it is locally on its domain an isomorphism of schemes, a much stronger condition.$\Big)$

To your third question, I think the observation that $\Gamma(-,Y)$ forms a sheaf on $X$ gives a nice context in which to think of sections $X$ to $Y$: they "live in" the sheaf $\Gamma(-,Y)$ as its globally defined elements.

-
Thank you! This explanation cleared up a lot of things for me. –  Qiaochu Yuan Dec 6 '09 at 23:03
Great :) I also just added a parenthetical linguistic warning about something that also tends to create confusion, albeit a mild sort. –  Andrew Critch Dec 6 '09 at 23:32
Adding to the confusion, Mac Lane calls a certain type of bundle an "$\'etale$ space or bundle, where $\'etale$ is now used as an adjective, but this is in fact in reference to something much close to the classical espace $\'etale\'e$. –  Harry Gindi Dec 7 '09 at 2:11

A section of a bundle $B$ over a space $S$ is just a map $\sigma: S \rightarrow B$ such that for each $x \in S$, $\sigma(x) \in B_x$, where $B_x$ is the fiber over $x$.

Functions correspond to the case where the base is the domain $D$ and the bundle is $D \times R$, where $R$ is the range. In that sense, sections are generalized functions.

The notion of a section of a sheaf is essentially the same, but has to be adapted appropriately.

It seems to me that any reference that defines a vector bundle or a sheaf would explain this. I guess I would recommend any modern introduction to Riemann surfaces, where there is a minimum of machinery and complication. Although I don't work with Riemann surfaces, I found them fun to learn about, because they have the advantages of being 1-dimensional but have the rich structure of a 2-dimensional object.

-
Of course, you must keep in mind that presheaves-bundles is only an adjunction, and the actual equivalence of categories happens only when we restrict to sheaves and "etale" bundles, as Mac Lane calls them. –  Harry Gindi Dec 6 '09 at 22:52
I do? I'm a differential geometer, so I've been able to survive even though I can't remember precisely the difference between a presheaf and a sheaf. And I have no idea what an "adjunction" is. But I am curious. Any chance you or someone else would care to elaborate on this comment, maybe using more old-fashioned mathematical English? –  Deane Yang Dec 7 '09 at 3:57

Bundles are usually defined as being locally trival thingamajigs. A trivial bundle with fiber $F$ looks like the projection map $U \times F \to U$. A section of a trivial bundle is just a function $U \to F$. A global function on a manifold is the same as a bunch of local functions that literally agree on the overlaps. Similarly a global section of a bundle is the same as a bunch of local sections (which, again, are just functions) that "agree" on the overlaps, where now "agree" does not mean literally agree, but "agree after a twist", where the "twists" comes from the transition functions of the vector bundle.

Whenever we have a bundle, we can form a sheaf out of it. The corresponding sheaf is the one which maps open sets $U$ to the set of sections of the bundle over $U$. Conversely, if we have a sheaf on a space $X$, it is possible to construct a space $Y$ and a map $Y \to X$ such that the "sections" of the sheaf correspond to the actual sections of the map $Y \to X$. This is called the espace étalé and is discussed here and somewhere in Hartshorne chapter II section 1.

You may also be interested in looking at Hartshorne chapter II exercise 5.18.

-
If $\pi: E \to M$ is a bundle over a topological space $M$, you can define a sheaf on $M$ that associates to each open set $U \subseteq M$ the set of sections over it, i.e., maps $\sigma: U \to E$ such that $\pi \circ \sigma = \mathrm{id}_{U}$. Conversely, given a sheaf $\mathcal{F}$ on $M$ you can construct a topological space such that your $\mathcal{F}$ is its sheaf of sections. This Wikipedia page has some information on it. You will also be able to find information on any introductory book an algebraic geometry (e.g., Hartshorne).


text:
# Homework Help: Motion along a line

1. May 24, 2012

### zebrastripes

1. The problem statement, all variables and given/known data

A particle P of unit mass moves along an x-axis under the influence of the force

F(x)=2(x$^{3}$-x)

Firstly, I find V(x)=x$^{2}$-x$^{4}$/2.
Where equilibrium points are F(x)=0 so x=0 with energy V(0)=0, x=1 with energy V(1)=V(-1)=1/2.
And I have also sketched the graph.

So here are the parts I'm stuck on:

1) Initially P is projected from the point x=1/2 with speed U. Using conservation of energy, find the turning points (where x'=0) as a function of U. Find the maximum value of U for which the resultant motion will be bounded.

2)Stating from Newton's second law, prove that a particle displaced by a small amount from x=0 will perform periodic oscillations with a frequency of $\sqrt{2}$

2. Relevant equations

T=mx'$^{2}$/2

T+V=E

3. The attempt at a solution

U$^{2}$/2+(1/2)$^{2}$-(1/2)$^{4}$/2=E

Giving E=U$^{2}$+7/16

Then, because energy is conserved and x'=0 at turning points:

x$^{2}$-x$^{4}$/2=U$^{2}$+7/16

And now I'm really stuck for how to find the turning points as functions of U?

And I have no idea what I'm supposed to be doing for 2)

Sorry this is long, but any help will be greatly appreciated

2. May 24, 2012

### Ray Vickson

If v = velocity (= dx/dt), then by conservation of energy we have
$$\frac{1}{2} v^2 + V(x) = \frac{1}{2} U^2 + V(1/2) = \frac{1}{2} U^2 + \frac{7}{32},$$ since $V(1/2) = 7/32.$ At turning points, $v = 0,$ so you get an equation in $x.$

For small |x| the potential V(x) is almost linear in x. If you neglect the x4 term in V(x) you get a simple harmonic oscillator.

RGV

3. May 25, 2012

### zebrastripes

Thanks RGV, but under what assumptions can I say for small |x|?

And would you mind giving me a hint about what to do for part 2)?

Thanks again!


text:
It is currently 08 Dec 2019, 20:20

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square

Author Message
TAGS:
GRE Instructor
Joined: 10 Apr 2015
Posts: 2612
Followers: 95

Kudos [?]: 2818 [1] , given: 45

If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square [#permalink]  11 Aug 2019, 10:18
1
KUDOS
Expert's post
00:00

Question Stats:

58% (03:40) correct 41% (01:55) wrong based on 12 sessions
If $$(\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})$$, then $$x=$$

A) $$\frac{1}{8}$$

B) $$\frac{1}{2}$$

C) $$1$$

D) $$\sqrt[3]{2}$$

e) $$2$$
[Reveal] Spoiler: OA

_________________

Brent Hanneson – Creator of greenlighttestprep.com

GRE Instructor
Joined: 10 Apr 2015
Posts: 2612
Followers: 95

Kudos [?]: 2818 [1] , given: 45

Re: If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square [#permalink]  11 Aug 2019, 10:21
1
KUDOS
Expert's post
GreenlightTestPrep wrote:
If $$(\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})$$, then $$x=$$

A) $$\frac{1}{8}$$

B) $$\frac{1}{2}$$

C) $$1$$

D) $$\sqrt[3]{2}$$

e) $$2$$

Useful root property: $$\frac{\sqrt[n]{x}}{\sqrt[n]{y}}=\sqrt[n]{\frac{x}{y}}$$

Given: $$(\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})$$

Divide both sides by $$\sqrt{5.5}$$ to get: $$\sqrt[3]{4}=\frac{(\sqrt{22})(\sqrt[3]{x})}{\sqrt{5.5}}$$

Divide both sides by $$\sqrt[3]{x}$$ to get: $$\frac{\sqrt[3]{4}}{\sqrt[3]{x}}=\frac{\sqrt{22}}{\sqrt{5.5}}$$

Apply above property to both sides to get: $$\sqrt[3]{\frac{4}{x}}=\sqrt{\frac{22}{5.5}}$$

Simplify right side: $$\sqrt[3]{\frac{4}{x}}=\sqrt{4}$$

Simplify right side: $$\sqrt[3]{\frac{4}{x}}=2$$

Raise both sides to the power of 3 to get: $$(\sqrt[3]{\frac{4}{x}})^3=2^3$$

Simplify: $$\frac{4}{x} = 8$$

Solve: $$x = \frac{4}{8} = \frac{1}{2}$$

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Senior Manager
Joined: 22 Jun 2019
Posts: 379
Followers: 0

Kudos [?]: 51 [0], given: 137

Re: If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square [#permalink]  12 Aug 2019, 01:42
GreenlightTestPrep wrote:
GreenlightTestPrep wrote:
If $$(\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})$$, then $$x=$$

A) $$\frac{1}{8}$$

B) $$\frac{1}{2}$$

C) $$1$$

D) $$\sqrt[3]{2}$$

e) $$2$$

Useful root property: $$\frac{\sqrt[n]{x}}{\sqrt[n]{y}}=\sqrt[n]{\frac{x}{y}}$$

Given: $$(\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})$$

Divide both sides by $$\sqrt{5.5}$$ to get: $$\sqrt[3]{4}=\frac{(\sqrt{22})(\sqrt[3]{x})}{\sqrt{5.5}}$$

Divide both sides by $$\sqrt[3]{x}$$ to get: $$\frac{\sqrt[3]{4}}{\sqrt[3]{x}}=\frac{\sqrt{22}}{\sqrt{5.5}}$$

Apply above property to both sides to get: $$\sqrt[3]{\frac{4}{x}}=\sqrt{\frac{22}{5.5}}$$

Simplify right side: $$\sqrt[3]{\frac{4}{x}}=\sqrt{4}$$

Simplify right side: $$\sqrt[3]{\frac{4}{x}}=2$$

Raise both sides to the power of 3 to get: $$(\sqrt[3]{\frac{4}{x}})^3=2^2$$

Simplify: $$\frac{4}{x} = 8$$

Solve: $$x = \frac{4}{8} = \frac{1}{2}$$

Cheers,
Brent

I think,seems little mistake in the last portion. It will be
Corrected line: Raise both sides to the power of 3 to get: $$(\sqrt[3]{\frac{4}{x}})^3=2^3$$
VP
Joined: 20 Apr 2016
Posts: 1087
WE: Engineering (Energy and Utilities)
Followers: 16

Kudos [?]: 942 [1] , given: 226

Re: If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square [#permalink]  12 Aug 2019, 07:12
1
KUDOS
GreenlightTestPrep wrote:
If $$(\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})$$, then $$x=$$

A) $$\frac{1}{8}$$

B) $$\frac{1}{2}$$

C) $$1$$

D) $$\sqrt[3]{2}$$

e) $$2$$

Here,
$$(\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})$$

or $$(\sqrt[3]{4}) * 2.3 = 4.6* (\sqrt[3]{x})$$ { use of calculator to find $$\sqrt{5.5}$$ and $$\sqrt{22}$$ }

or $$(\sqrt[3]{4}) = 2 * (\sqrt[3]{x})$$ (dividing both sides by 2.3)

Cubing both sides
$$4 = 8* x$$

or $$x = \frac{1}{2}$$
_________________

If you found this post useful, please let me know by pressing the Kudos Button

Rules for Posting

Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months GRE Prep Club tests

Senior Manager
Joined: 22 Jun 2019
Posts: 379
Followers: 0

Kudos [?]: 51 [0], given: 137

Re: If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square [#permalink]  12 Aug 2019, 07:37
pranab01 wrote:
GreenlightTestPrep wrote:
If $$(\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})$$, then $$x=$$

A) $$\frac{1}{8}$$

B) $$\frac{1}{2}$$

C) $$1$$

D) $$\sqrt[3]{2}$$

e) $$2$$

Here,
$$(\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})$$

or $$(\sqrt[3]{4}) * 2.3 = 4.6* (\sqrt[3]{x})$$ { use of calculator to find $$\sqrt{5.5}$$ and $$\sqrt{22}$$ }

or $$(\sqrt[3]{4}) = 2 * (\sqrt[3]{x})$$ (dividing both sides by 2.3)

Cubing both sides
$$4 = 8* x$$

or $$x = \frac{1}{2}$$

I THINK GRE CALCULATOR DOES NOT ALLOW TO CALCULATE ROOT EITHER, SO WE NEED TO PASS IT.
GRE Instructor
Joined: 10 Apr 2015
Posts: 2612
Followers: 95

Kudos [?]: 2818 [0], given: 45

Re: If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square [#permalink]  12 Aug 2019, 08:20
Expert's post
huda wrote:
I think,seems little mistake in the last portion. It will be
Corrected line: Raise both sides to the power of 3 to get: $$(\sqrt[3]{\frac{4}{x}})^3=2^3$$

Good catch - thanks!
I've changed the exponent.

Kudos for you!!

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

GRE Instructor
Joined: 10 Apr 2015
Posts: 2612
Followers: 95

Kudos [?]: 2818 [1] , given: 45

Re: If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square [#permalink]  12 Aug 2019, 08:24
1
KUDOS
Expert's post
huda wrote:
pranab01 wrote:
GreenlightTestPrep wrote:
If $$(\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})$$, then $$x=$$

A) $$\frac{1}{8}$$

B) $$\frac{1}{2}$$

C) $$1$$

D) $$\sqrt[3]{2}$$

e) $$2$$

Here,
$$(\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})$$

or $$(\sqrt[3]{4}) * 2.3 = 4.6* (\sqrt[3]{x})$$ { use of calculator to find $$\sqrt{5.5}$$ and $$\sqrt{22}$$ }

or $$(\sqrt[3]{4}) = 2 * (\sqrt[3]{x})$$ (dividing both sides by 2.3)

Cubing both sides
$$4 = 8* x$$

or $$x = \frac{1}{2}$$

I THINK GRE CALCULATOR DOES NOT ALLOW TO CALCULATE ROOT EITHER, SO WE NEED TO PASS IT.

pranab01 is estimating those roots.
It's a good strategy.

By the way, the GRE's onscreen calculator does have a square root button.
Here's my video on this
[you-tube]https://youtu.be/qvL9uwnR0v8[/you-tube]

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square   [#permalink] 12 Aug 2019, 08:24
Display posts from previous: Sort by

If [m](\sqrt[3]{4})([square_root]5.5[/square_root])=([square

 Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.


text:
ceTk: Cuzick and Edwards T_k Test statistic In nnspat: Nearest Neighbor Methods for Spatial Patterns

Description

This function computes Cuzick and Edwards T_k test statistic based on the number of cases within `k`NNs of the cases in the data.

For disease clustering, \insertCitecuzick:1990;textualnnspat suggested a `k`-NN test based on number of cases among `k` NNs of the case points. Let z_i be the i^{th} point and d_i^k be the number cases among `k` NNs of z_i. Then Cuzick-Edwards' `k`-NN test is T_k=∑_{i=1}^n δ_i d_i^k, where δ_i=1 if z_i is a case, and 0 if z_i is a control.

The argument `cc.lab` is case-control label, 1 for case, 0 for control, if the argument `case.lab` is `NULL`, then `cc.lab` should be provided in this fashion, if `case.lab` is provided, the labels are converted to 0's and 1's accordingly. Also, T_1 is identical to the count for cell (1,1) in the nearest neighbor contingency table (NNCT) (See the function `nnct` for more detail on NNCTs).

Usage

 `1` ```ceTk(dat, cc.lab, k = 1, case.lab = NULL, ...) ```

Arguments

 `dat` The data set in one or higher dimensions, each row corresponds to a data point. `cc.lab` Case-control labels, 1 for case, 0 for control `k` Integer specifying the number of NNs (of subject i), default is `1`. `case.lab` The label used for cases in the `cc.lab` (if `cc.lab` is not provided then the labels are converted such that cases are 1 and controls are 0), default is `NULL`. `...` are for further arguments, such as `method` and `p`, passed to the `dist` function.

Value

Cuzick and Edwards T_k test statistic for disease clustering

Elvan Ceyhan

References

\insertAllCited

`Tcomb`, `seg.ind`, `Pseg.coeff` and `ceTkinv`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```n<-20 #or try sample(1:20,1) Y<-matrix(runif(3*n),ncol=3) cls<-sample(0:1,n,replace = TRUE) #or try cls<-rep(0:1,c(10,10)) ceTk(Y,cls) ceTk(Y,cls,method="max") ceTk(Y,cls,k=3) ceTk(Y,cls+1,case.lab = 2) #cls as a factor na<-floor(n/2); nb<-n-na fcls<-rep(c("a","b"),c(na,nb)) ceTk(Y,fcls,case.lab="a") #try also ceTk(Y,fcls) ############# n<-40 Y<-matrix(runif(3*n),ncol=3) cls<-sample(1:4,n,replace = TRUE) # here ceTk(Y,cls) gives an error message ```


text:
Volume 18, issue 4 (2018)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
Quasiautomorphism groups of type $F_\infty$

Samuel Audino, Delaney R Aydel and Daniel S Farley

Algebraic & Geometric Topology 18 (2018) 2339–2369
Abstract

The groups $QF\phantom{\rule{0.3em}{0ex}}$, $QT\phantom{\rule{0.3em}{0ex}}$, $\stackrel{̄}{Q}T\phantom{\rule{0.3em}{0ex}}$, $\stackrel{̄}{Q}V$ and $QV$ are groups of quasiautomorphisms of the infinite binary tree. Their names indicate a similarity with Thompson’s well-known groups $F\phantom{\rule{0.3em}{0ex}}$, $T$ and $V\phantom{\rule{0.3em}{0ex}}$.

We will use the theory of diagram groups over semigroup presentations to prove that all of the above groups (and several generalizations) have type ${F}_{\infty }$. Our proof uses certain types of hybrid diagrams, which have properties in common with both planar diagrams and braided diagrams. The diagram groups defined by hybrid diagrams also act properly and isometrically on $CAT\left(0\right)$ cubical complexes.

We have not been able to recognize your IP address 3.238.250.73 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

or by using our contact form.

Keywords
quasiautomorphism group, Thompson's groups, Houghton groups, finiteness properties of groups, CAT(0) cubical complexes
Primary: 20F65
Secondary: 57M07


text:
# Why is the output from Stata different from the output from ggeffect?

Stata’s equivalent to the marginal effects produced by ggeffects is the margins-command. However, the results are not always identical. For models from non-gaussian families, point estimates for the marginal effects are identical, but the confidence intervals differ.

Here is an explanation, why there is a difference. First, we fit a logistic regression model.

library(magrittr)
set.seed(5)

data <- data.frame(
outcome = rbinom(100, 1, 0.5),
var1 = rbinom(100, 1, 0.1),
var2 = rnorm(100, 10, 7)
)

m <- glm(
outcome ~ var1 * var2,
data = data,
)

## Example with graphical output

### The Stata plot

This is the code in Stata to produce a marginal effects plot.

use data.dta, clear
quietly logit outcome c.var1##c.var2
quietly margins, at(var2 = (-8(0.5)28) var1 = (0 1))
marginsplot

The resulting image looks like this.

### The ggeffects plot

When we use ggeffects, the plot slighlty differs.

library(ggeffects)
ggpredict(m, c("var2", "var1")) %>% plot()

As we can see, the confidence intervals in the Stata plot are outside the plausible range of [0, 1], which means that the predicted uncertainty from the Stata output has a probability higher than 1 and lower than 0, while ggpredict() computes confidence intervals within the possible range.

## Conclusion

It seems like Stata is getting the confidence intervals wrong. Predictions and standard errors returned in Stata are on the (transformed) response scale. Obviously, the confidence intervals are then computed by estimate +/- 1.96 * standard error, which may lead to confidence intervals that are out of reasonable bounds (e.g. above 1 or below 0 for predicted probabilities).

The transformed estimate (on the response scale) is always between 0 and 1, and the same is true for the transformed standard errors. However, adding or substracting approx. 2 * transformed SE to the transformed estimate does no longer ensure that the confidence intervals are within the correct range.

The more precise way to do the calculation is to calculate estimates, standard errors and confidence intervals on the (untransformed) scale of the linear predictor and then back-transform.


text:
Volume 380 - Particles and Nuclei International Conference 2021 (PANIC2021) - QCD, spin physics and chiral dynamics
Extraction of the worm-gear TMD $g_{1T}$ from COMPASS, HERMES and JLab data on semi-inclusive DIS
S. Bhattacharya*, Z.B. Kang, A. Metz, G. Penn and D. Pitonyak
Full text: pdf
Pre-published on: March 02, 2022
Published on:
Abstract
Transverse momentum dependent parton distributions (TMDs) are an important class of functions required to understand the 3D structure of hadrons in terms of their underlying partons. One of the least known TMDs in terms of a global QCD analysis is the worm-gear TMD $g_{1T}$. It carries the probabilistic interpretation of finding longitudinally polarized quarks inside transversely polarized hadrons. In this proceedings, we present the first-ever global QCD analysis of the semi-inclusive DIS $A^{\textrm{cos}(\phi_{h} -\phi_{S})}_{LT}$ data using Monte Carlo techniques to extract the worm-gear TMD $g_{1T}$. The relevant data are available from COMPASS, HERMES and JLab. We compare our results for $g_{1T}$ with different theoretical approaches, including the large-$N_c$ approximation, the Wandzura-Wilczek-type approximation, and lattice QCD.
DOI: https://doi.org/10.22323/1.380.0361
How to cite

Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.

Open Access


text:
×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Are you an
Engineering professional?
Join Eng-Tips Forums!
• Talk With Other Members
• Be Notified Of Responses
• Keyword Search
Favorite Forums
• Automated Signatures
• Best Of All, It's Free!

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

#### Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

# Welding with a little bit of paint after grinding5

## Welding with a little bit of paint after grinding

(OP)
We have an existing beam to column connection that we now have to weld the shear plate to the beam web.
The existing connection has been painted.
The welders can grind most of the paint away, but cant grind all the paint at the joint.
Please, all the CWI's respond, anyone else with experience, any suggestions?

### RE: Welding with a little bit of paint after grinding

lsmfse:
After grinding and other prep., burn the remaining paint off with a torch, clean up the ash with a powered wire brush and a hand brush, then wipe the surface down. There are some fluxes and rod coverings which are somewhat tolerant of slight surface impurities. I don’t intend to mean you can weld through a puddle of paint, oil or water, but you don’t need a shot blasted clean surface either. Talk with a few local welding material suppliers for their weld prep. recommendations.

### RE: Welding with a little bit of paint after grinding

Agree with dhengr.

The devil is in the details; she also wears prada.

### RE: Welding with a little bit of paint after grinding

Sounds like a plan.

"Everyone is entitled to their own opinions, but they are not entitled to their own facts."

### RE: Welding with a little bit of paint after grinding

In practice, GTAW will almost always fail (porosity, inclusions, surface defects) if anything but a very clean newly-ground surface is welded.
SMAW is more forgiving to very small bits of paint left on the surface - if, for example, paint is removed by simple hand wire brushing or impact hammer (needle gun). Your best weld requires the weld to be melting together clean filler, clean base metal, and new clean metal.

### RE: Welding with a little bit of paint after grinding

3
While the SMAW or even FCAW will tolerate a little residual paint and still produce a respectable weld, I find it interesting few people consider the age of the paint to be a concern. If the structure was built before the 1980's, I would question whether the paint was lead based. Grind, burning, or welding is going to "release" the lead into the worker's breathing area. Then again, some people consider their workers to be expendable. Can't say I agree with that approach. Get the paint tested if it has been in place for 30 years.

Best regards - Al

### RE: Welding with a little bit of paint after grinding

There are no welding fumes that are safe to breathe, so what are you going to do differently after you get test results?

### RE: Welding with a little bit of paint after grinding

You can't protect the welder if you don't know what you're dealing with.

Best regards - Al

### RE: Welding with a little bit of paint after grinding

Maybe use paint stripper and a wire brush once the paint has lifted.

### RE: Welding with a little bit of paint after grinding

A good old stick/arc/SMAW welder will weld straight through the paint/rust easily. I'm glad at least some people know the health concerns...

you're going to need less than $100. The mask that will actually protect from lead and mold and any, ANY other unknown particles is called: -3M 60926 Multi-Gas/P100 (HEPA) The 3M 6000 series is the one you want, the p100 is a hepa filter is needed whenever you are using heat or vaporizing these bad chemicals, the 926 version has an extra charcoal filtering so they won't be inhaling vaporised lead. This is a cheap mask... please do not make them wear a cotton mask that will only serve to capture particles and force the user to breathe all their air through a blackened cancerous cotton ball (been there done that found a new job). Replacement filters are below$30 by the way. also they make a half face version so it's small and will fit under the welders hood. It must fit under the mask or the welder will complain and not use it

#### Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

#### Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

#### Resources

Low-Volume Rapid Injection Molding With 3D Printed Molds
Learn methods and guidelines for using stereolithography (SLA) 3D printed molds in the injection molding process to lower costs and lead time. Discover how this hybrid manufacturing process enables on-demand mold fabrication to quickly produce small batches of thermoplastic parts. Download Now
Examine how the principles of DfAM upend many of the long-standing rules around manufacturability - allowing engineers and designers to place a partâ€™s function at the center of their design considerations. Download Now
Taking Control of Engineering Documents
This ebook covers tips for creating and managing workflows, security best practices and protection of intellectual property, Cloud vs. on-premise software solutions, CAD file management, compliance, and more. Download Now

Close Box

# Join Eng-Tips® Today!

Join your peers on the Internet's largest technical engineering professional community.
It's easy to join and it's free.

Here's Why Members Love Eng-Tips Forums:

• Talk To Other Members
• Notification Of Responses To Questions
• Favorite Forums One Click Access
• Keyword Search Of All Posts, And More...

Register now while it's still free!


text:
# Is $\sin^2 n$ bounded away from zero?

Can one find a number $m$ such that $\sin^2 n \geq m > 0$ for all integers $n$?

By continuity of $\sin x$, it is enough to say that $|n - k \pi| \geq m^{\prime} > 0$ for all integers $n,k$.

Since $\pi$ can be approximated arbitrarily closely by rationals, for any $\epsilon > 0$, we can find integers $n$ and $k$ such that $|n−k\pi| < k \epsilon$. But this is not enough to disprove the existence of the lower bound $m$.

It seems like one needs to use more delicate Diophantine approximation here.

-
oeis.org/A004112 –  Charles Feb 23 '12 at 21:29

Since the set $\{\sin n:n\in\mathbb N\}$ is dense in $[-1,1]$, the set of the squares of its elements is also dense there. In particular, you can approximate zero as much as you want.
A minor correction: the set $\{ \sin^2 n,\ n\in \mathbb{N}\}$ is not dense in $[-1,1]$ as $\{ \sin n,\ n\in \mathbb{N}\}$, but it is dense in $[0,1]$. –  Pacciu Mar 28 '11 at 8:47
The set $\{n-2\pi m; m,n\in\mathbb{Z}\}$ is dense in $\mathbb{R}$ so $\sin(n-2\pi m )=\sin(n)$ can get close to any number in $[-1,1].$ Therefore zero is the only lower bound for $\sin^2n$, which is not interesting obviously.


text:
INVESTIGACIÓN ORIGINAL ORIGINAL RESEARCH

Gender inequalities in health among older Brazilian adults

Sandhi Maria BarretoI, *; Luana GiattiI; Alexandre KalacheII

IUniversidade Federal de Minas Gerais, Faculdade de Medicina, Belo Horizonte, Minas Gerais, Brasil
IIWorld Health Organization, Ageing and Life Course Unit, Geneva, Switzerland

ABSTRACT

OBJECTIVE: To investigate gender differences among older Brazilians in their health status and their use of health services.
METHODS: Participants were individuals aged 60 years and older included in a national household survey conducted in Brazil in 1998. Data were analyzed by multiple logistic regression, taking into account the design effect due to multistage sampling.
RESULTS: There were differences in the health and living conditions of older men and older women that were not explained by age or place of residence. Older women had worse indicators of schooling and personal income but better indicators of housing standards and per capita household income. The older women also reported more chronic diseases, had poorer indicators of independence and physical mobility, sought health services more often, and reported more medical visits in the previous year. Despite their apparent worse health conditions, elderly women in urban areas had lower hospitalization rates in the previous year (odds ratio = 0.89; 95% confidence interval, 0.820.96) than did elderly men in urban areas.
CONCLUSIONS: Our results indicate that among older Brazilians there are gender inequalities in health that cannot be explained by age and place of residence. The findings raise questions on how health, socioeconomic, and cultural factors influence gender patterns of seeking and using health care in later life in the country. As pressures on health care and health funding increase in Brazil as a result of the aging of the population, there is a need to take a gender perspective into account.

Key words: Age factors; aged; aged, 80 and over; sex factors; health status; socioeconomic factors; Brazil.

RESUMEN

OBJETIVO: Investigar las diferencias halladas en función del género en el estado de salud y en el uso de servicios de salud en personas brasileñas de edad avanzada.
MÉTODOS: Los participantes fueron personas de 60 años de edad o más que habían sido incluidas en una encuesta domiciliaria nacional realizada en el Brasil en 1998. Los datos se analizaron mediante regresión logística multifactorial, teniendo en cuenta el efecto del diseño basado en un muestreo polietápico.
CONCLUSIONES: Nuestros resultados indican que entre las personas de edad avanzada en el Brasil hay desigualdades de salud entre los sexos que no pueden explicarse en función de la edad o del lugar de residencia. Estos hallazgos dan lugar a interrogantes acerca de la influencia de factores sanitarios, socioeconómicos y culturales sobre la forma en que las personas de un sexo u otro en el país buscan y utilizan la atención de salud en etapa avanzada de la vida. A medida que se incrementan las presiones sobre el sistema de atención de la salud y su financiamiento como resultado del envejecimiento de la población, se torna necesario mirar el asunto desde el punto de vista del género.

The process of rapid aging in developing country populations brings about the need to address how gender inequalities affect health in later life. Although the gender gap in life expectancy favors women by more than three years in most developed and developing countries, the gender gap in healthy life expectancy is much narrower, with women sometimes presenting lower healthy expectancy than men do (1, 2). In Brazil the gender gap in life expectancy at birth is very high (nearly eight years), but women's higher life expectancy is offset by their lower healthy life expectancy at almost all ages, particularly among lower socioeconomic groups (3).

In spite of its importance, the gender gap in health in later life remains underresearched, particularly in developing countries. Gender analysis seeks to differentiate the influence of biological, behavioral, and social factors on health and to assess how these factors might interact with gender, viewed as the social, cultural, and symbolic construction of femininity and masculinity in any given society (4). In that sense the roots of gender inequalities in health in later life cannot be separated from men's and women's past experiences in all areas that relate to gains and losses in health (5, 6).

Over the last few decades in Brazil, increases in life expectancy have occurred in all age groups, particularly among women. Figure 1 shows, for men and women, the increases in life expectancies at birth in the last 50 years and United Nations projections for the next 50 years. Between 1991 and 2000 the difference in life expectancy at birth between men and women increased from 7.2 to 7.8 years. The underlying excess male mortality occurs in all age groups, but it is greatest among young adults due to young men's unacceptably high risk of death from violence and accidents. The widening of the gender gap in life expectancy in the country is contributing to the relative enlargement of the female contingent among the aged. In the last census (2000), older women (60+ years) outnumbered men by 1.5 million (6.5 million men vs. 8.0 million women). In common with many other countries, female preponderance increases with age, from 54% in those 6069 years old to 59% in those 80 and older. Among Brazilian centenarians, there were more than seven times as many women as men in 2000. An inevitable consequence of this preponderance is the increase in the number of elderly women living alone and having to cope with loneliness in later life.

Data from Russia on gender inequalities in longevity clearly indicate that the gender gap can increase in adverse social and economic conditions (7), and Brazil has one of the worst income distributions in the world. The feminization of old age and the trend towards an increased gender gap in health status in the years to come reinforce the need to study gender dimensions of health inequalities in later life in Brazil. The purpose of this study was to investigate gender differences in several aspects related to health and life conditions in a representative sample of the Brazilian population aged 60 years and older.

MATERIAL AND METHODS

The study included all individuals aged 60 years and over who participated in the National Household Survey (Pesquisa Nacional por Amostra de Domicílios) that took place in 1998. Conducted by the Brazilian Foundation on Geography and Statistics, each of the annual surveys has a different thematic focus. In 1998 the National Household Survey investigated, through household interviews, several aspects related to population health and health care use in the country. Further details are published elsewhere (8).

Men and women were compared in relation to several characteristics and factors associated with their life conditions, health status, and pattern of using health services. Sociodemographic characteristics included age, urban or rural residence, residence or not in a metropolitan region (the state capital and surrounding towns), position within the household (head of the household or not), schooling, personal income, household income per capita, number of people per bedroom, sanitation (piped water, bathroom in the house, trash collection service), electricity, and color television in the home.

The health indicators studied were: self-rated health, absence from ordinary activities due to a health problem in the previous two weeks, staying in bed some time in the last two weeks because of illness, report of chronic illness, the number of doctor visits during the previous year, the number of hospitalizations in the previous year, and private health plan coverage. In addition, the following indicators of mobility and independence were studied, in terms of difficulties in: eating, bathing, or using the toilet; walking uphill or climbing stairs; stooping down, kneeling, or bending; and walking at least 100 meters.

The data were analyzed using the survey commands of Stata statistical software (StataCorp, College Station, Texas, United States of America). In order to represent the entire population of Brazil, the estimates were weighted using the National Household Survey weights to allow for differences in sampling probabilities of participants. A special algorithm provided by the Brazilian Institute of Geography and Statistics was also incorporated in the analysis process to take into account the sampling design effects due to multistage sampling. Existing differences between elderly men and elderly women in relation to the variables included in the study were estimated using Pearson's chi-square and adjusted odds ratios with confidence intervals (Woolf's method), obtained by multiple logistic regression. Results of the analysis on health care use are presented stratified by place of residence (urban or rural) since the availability of and access to services differ between the two areas.

RESULTS

A total of 12 757 men and 16 186 women aged 60 years and above participated in the study. Table 1 shows the distribution of older people according to sociodemographic characteristics. The proportion of women was significantly greater than that of men in age groups 7074 and 80+ years, and more women lived in urban areas, independently of age. After adjusting for age and place of residence, women remained significantly different from men in the following aspects: lower schooling, less often being the family head, smaller personal income, higher household income per capita, higher proportion living alone, living in lower density residences, and better living conditions (sanitation, electricity, and color television).

In relation to indicators of independence and physical mobility, women presented worse conditions for all indicators, independently of age and urban/rural condition (Table 2). With the reported health conditions shown in Table 2, all illnesses were more common among elderly women except cancer and cirrhosis, which were more frequent among older men, and bronchitis/asthma and renal diseases, which did not show significant gender differences.

Table 3 shows that, after adjustment for age, older women in urban and rural areas sought health services more often than men did, reported more medical visits in the previous year, and were more likely to be covered by private health plans. However, older women in urban areasbut not in rural areashad lower age-adjusted hospitalization rates in the previous year than did older men.

DISCUSSION

We found that older men and older women differed in terms of their socioeconomic conditions. The women had worse indicators of schooling and personal income, but seemed better off than the men regarding housing conditions and household income per capita. In relation to health, our results are consistent with data from developed countries showing that women have worse health indicators, seek medical attention more often than men do, and report more medical visits, while men report higher hospitalizations rates (9, 10).

The apparent contradiction in socioeconomic indicators, such as personal and household income per capita, may be explained by current as well as past differences in the working lives that men and women have experienced. The usual sources of income for older Brazilians are pensions, paid employment, and financial support from other family members. In our study the total income received by the elderly Brazilian women was on average around half of that of the elderly men (US$110 vs. US$ 203 per month). This disparity, of around 50%, was close to the country's overall gender gap in income in 1998 (11). In addition, the percentage of men who were economically active in later life as of 1998 was three times as high as the percentage for women (26.8% vs. 8.9%), thus contributing to men's higher average personal income in older age (8). Moreover, income during retirement reflects social and working conditions that prevailed in a person's life before retirement. Empirical evidence shows that the effects of socioeconomic disadvantages are cumulative over the course of an individual's life (10). Most of the older women in the cohorts in our study were housewives and had depended on a husband's income during most of their lives. In 1950, for instance, only 13% of women in Brazil were economically active, so the gender gap in income was probably even larger than it is today.

However, work histories cannot explain women's higher household income per capita and better housing conditions in later life. Part of the explanation may be survival bias, since there are more women living alone and thus not sharing their income with other persons in the house. But it is also possible that these indicators reflect women's positions in family and society (Figure 2). There seems to be no doubt of women's differential role in family care, from childhood up through older ages (12). Data from Brazil from 1970, 1995, and 1999 indicate that elderly women who were widowed, single, or divorced tend to live with close relatives more often than do equivalent older men (13). Women's traditional roles and the type of family ties and other social connections that they make over the course of their lives may result in greater family and social links in later life. One cannot assume, however, that women's greater ability to form strong family bonds compensates for economic and social disadvantages in old age. That is because these family connections also generate responsibilities, tensions, and demands that might negatively affect older women's health and quality of life (12). Despite reporting more illnesses, older women continue to have important roles as caregivers for both younger and older family members (14). Furthermore, we do not know how important personal income is, as opposed to household income per capita, for the well-being and health of elderly men and women. The impact of personal income on health may vary across generations and is likely to be mediated by factors such as schooling and the access to and the quality of health and social care available in the country. Other studies are needed to understand these relationships in order to clarify the effect of socioeconomic inequalities in men and women's needs in older age.

This study's findings on the poorer health conditions of elderly women are in line with the results of other studies (9, 10, 15) that indicate women's greater disadvantages and dependency in later life. Health is central to quality of life in older age, and it is the utmost determinant of remaining socially active and independent. Many persons regard dependency as a threat to self- respect, dignity, and satisfaction in life (10). The higher number of medical visits reported by elderly women is probably associated with their poorer health conditions, which are especially due to higher prevalences of chronic diseases that are rarely fatal.

Various factors are likely to explain this gender gap in health condition and health care use (Figure 3). For instance, it is possible that men who survive to old age are healthier than women in the same age group, reflecting men's higher premature mortality. For instance, black men in the United States who reach the age of 75 are apparently healthier than their white counterparts (10). Nevertheless, we found in Brazil that despite their lower consultation rates and apparent better health conditions, urban men are hospitalized more often than are urban women, independently of age. This finding is consistent with men's higher mortality rates but inconsistent with their better health indicators and lower number of medical visits. This apparent gender paradox seems to be related to differences in the prevalence of some illnesses that differ in their risk of causing premature death. For instance, diseases of the musculoskeletal system, which are hardly associated with increased mortality but increase disability and medical visits, are much more common among aged women than among aged men. The differences may also be explained by the fact that men perceive their health differently and seem to have more difficulties in reporting illnesses than do women (5, 6, 16). A review article on the United Kingdom (17) reported that men, independently of income and ethnicity, had more difficulties in talking about their health problems and tended to seek medical care in more advanced and life-threatening stages of disease, explaining in part their higher hospitalizations rates (17). As health care practices are established early during one's life, it is possible that primary health services are more friendly to women than they are to men. For example, most health services are open mainly during daytime hours, when more men than women are at work. Women's reproductive life and motherhood may also make women more apt to make use of health care than is true for men (5). Moreover, discrimination against females by doctors and other health service providers likely contributes to men's higher hospitalization rates, especially from cardiovascular diseases (18) and medical interventions such as coronary bypass graft (19).

In conclusion, as men and women live and age in different ways, inequalities observed in later life express social and biological advantages and disadvantages accumulated over one's life. The older people included in this study in Brazil belong to cohorts with sizable families. Between 1940 and 1970, when they were in their 20s, 30s, and 40s, total fertility rates in the country were around 6.0 children per woman, and few women were engaged in paid work. Such conditions may help impoverish women, leading to their need for family and social support in old age (10, 20) and negatively influencing their quality of life and health (12). On the other hand, elderly men in this study belong to generations that experienced very unsafe working conditions and drastic changes in the labor market and working processes. These circumstances and the speed at which they occurred in Brazil are likely to have affected men's health and the way that they perceive and take care of themselves. Between 1990 and 1994, male life expectancy in Russia fell by 6 years, resulting in a gender longevity gap of 13.5 years. This dramatic change has been attributed to men's greater difficulties in coping with socioeconomic uncertainties and turmoil (7).

Our results show that there are gender inequalities in health that cannot be explained by age and place of residence. These findings raise questions regarding how gender interacts with socioeconomic background, health conditions, and health care use in Brazil. In planning for the future, one cannot forget the past. Gender inequalities have to be confronted in all ages, spheres, and social groups if we want to build a future of healthy aged men and women. As pressures on social security and health care provision increase in developing countries as a result of population aging, new policies are needed that take gender perspectives into account.

REFERENCES

1. Mathers CD, Sadana R, Salomon JA, Mur- ray CJ, Lopez AD. Healthy life expectancy in 191 countries, 1999. Lancet. 2001;357(9269): 168591.

2. Hemstrom O. Biological and social conditions: hypothesis regarding mortality differentials between men and women. In: Ostlin P, Danielsson M, Diderichsen F, Harenstam A, Lindberg G, eds. Gender inequalities in health. Boston: Harvard University Press; 1998. Pp. 195223.

3. Diaz MD. Socio-economic health inequalities in Brazil: gender and age effects. Health Econ. 2002;11:14154.

4. Hammarstrom A, Harenstam PO. Gender and health: concepts and explanatory models. In: Ostlin P, Danielsson M, Diderichsen F, Harenstam A, Lindberg G, eds. Gender inequalities in health. Boston: Harvard University Press; 1998. Pp. 221.

5. Kalache A. Gender-specific health care in the 21st century: a focus in developing countries. Aging male. 2002;5:12938.

6. World Health Organization. Men, ageing and health. Achieving health across the life span. Geneva: WHO; 2002.

7. Notzon FC, Komarov YM, Ermakov SP, Sempos CT, Marks JS, Sempos EV. Causes of declining life expectancy in Russia. JAMA:1998; 279:793800.

8. Giatti L, Barreto MS. Trabalho feminino e saúde na terceira idade. Cienc Saude Coletiva. 2002;7(4):82539.

9. Sen K. Gender. In: Ebrahim E, Kalache A. Epidemiology in old age. London: BMJ Publishing Group; 1996. Pp. 21020.

10. Arber S, Ginn J. Gender and inequalities in health in later life. Soc Sci Med. 1993;36(1): 3346.

11. Barros RP, Machado AF, Mendonça RSP. A desigualdade da pobreza: estratégias ocupacionais e diferenciais por gênero. Rio de Janeiro: IPEA; 1997. (Texto para Discussão no. 453).

12. Marks NF, Ashleman K. Life course influences on women's social relationships at midlife. In: Kuh D, Hardy R, eds. A life course approach to women's health. New York: Oxford University Press; 2002. Pp. 25368.

13. Camarano AA, El Ghaouri SK. Familias com idosos: ninhos vazios? Rio de Janeiro: IPEA; 2003. (Texto para Discussão no. 950).

14. Hoskins I, ed. Combining work and elder care. A challenge for now and the future. Geneva: International Labour Office; 1996.

15. Lima-Costa MFF, Barreto SM, Uchôa E, Firmo JOA, Vidigal PG, Guerra HL. The Bambuí Health and Aging study (BHAS): prevalence of risk factors and use of preventive health care services. Rev Panam Salud Publica. 2001; 9(4):21927.

16. Hunt K, Ford G, Harkins L, Wyke S. Are women more ready to consult than men? Gender differences in family practitioner consultation for common chronic conditions. J Health Serv Res Rolicy. 1999;4:96100.

17. Banks I. No man's land: men, illness, and the NHS. BMJ. 2001;323:105861.

18. Foster S, Mallik M. A comparative study of differences in the referral behaviour patterns of men and women who have experienced cardiac-related chest pain. Intensive Crit Care Nurs. 1998;14:192202.

19. Crawford BM, Meana M, Stewart D, Cheung AM. Treatment decision making in mature adults: gender differences. Health Care Women Int. 2000;21:91104.

20. Camarano AA, Pasinato MT. Envelhecimento, condições de vida e política previdenciária: como ficam as mulheres? Rio de Janeiro: IPEA; 2002. (Texto para Discussão no. 883).

Manuscript received 22 July 2003. Accepted for publication 15 June 2004

Suggested citation: Barreto SM, Giatti L, Kalache A. Gender inequalities in health among older Brazilian adults. Rev Panam Salud Publica. 2004;16(2):1107.
* Send correspondence to: Sandhi Maria Barreto, Av. Prof. Alfredo Balena 190, 10° andar. CEP 30 130 100, Belo Horizonte, MG, Brasil; e-mail: sbarreto@medicina.ufmg.br

Organización Panamericana de la Salud Washington - Washington - United States
E-mail: contacto_rpsp@paho.org


text:
DISCLAIMER: Let me say this first. Google’s regular expression implementations are known for not implementing features that make them, well, not regular. Both re2 and Golang’s regexp do not support backreferences. Otherwise, the things done here would be hard, or impossible.

I may not be Golang’s biggest fan in general (lack of generics, verbose syntax, simplistic type system, etc), but I’ve written a bunch of it in the last couple of years and found an unexpectedly useful feature. Golang provides a package called regexp/syntax that proves to be as useful as its documentation is sparse.

In essence, this package exposes the user to the finite state machines built by the regexp compiler. This can be used to do analyses on regular expressions such as “does this regexp ever match a particular character after matching n characters?” or “does this regexp match any strings starting with a particular prefix?”. These might sound like constructed examples, but both of them actually popped up in my dayjob.

# Toy Example: Loop detection

For sake of simplicity, let’s explore a constructed example first in this post: does a regexp match strings of arbitrary length? Or, in more technical terms: is there a loop in the finite state machine? Let’s get right started with the boilerplate of compiling a regular expression into something called a Prog.

This actually produces a nice and readable representation of the generated finite state machine. Note the * next to 2 which tells us that this is the initial state.

What we see here is the textual representation of the Prog object. It’s a struct containing

• Inst: list of instructions
• Start: initial instruction

Inst is the type used to represent an instruction. It’s a struct containing:

• Op: type of instruction
• Out: next instruction (except for InstMatch and InstFail, which are terminal instructions)
• Arg: additional argument to some instructions

For the purposes of this toy example, all we care about is which instructions can follow from a given instruction. For most instructions, that is the instruction referred to in Out. Let’s introduce the odd ones here:

• InstMatch: successfully match input string. Does not have successor instruction.
• InstFail: reject input string. Does not have successor instruction.
• InstAlt / InstAltMatch: either Out or Arg are the successor instruction. A string matches if either of the branches arrives at InstMatch.

If you are curious about the difference between InstAlt and InstAltMatch: From all I could determine, InstAltMatch is an optimisation where it is known that one branch leads to a match while the other branch consumes characters. I do not see the compiler or any rewriting actually using this instruction, so it does not seem to be in use. Most of the implementation treats them interchangeably, while backtrack.go in the regex evaluator appears to use it to determine which branch to take.

This information allows us to implement a helper function to determining the successor instructions, given an instruction.

Now we can implement loop-detection by a simple breadth-first search, keeping track of already visited nodes in a set (i.e. a map[uint32]bool, because Golang does not have a set type).

# A regex engine

Now let’s try to build a very inefficient regex engine based on this. To do so, let us first introduce the various rune instructions (rune is Golang for Unicode codepoint). There is InstRune, InstRune1, InstRuneAny and InstRuneAnyNotNL. Most of them (except InstRune and InstRune1) should be self-explanatory, but here’s the whole list:

• InstRuneAny matches any rune.
• InstRuneAnyNotNL matches any rune except newlines.
• InstRune has a MatchRune method to determine whether it matches a rune.
• InstRune1 matches the rune provided in i.Rune[0] (obviously.)

This leaves us with two remaining useful instructions:

• InstCapture: capture a match into a capture group. We won’t bother with this here.
• InstEmptyWidth: match constrains on the current position in the string. This has a MatchEmptyWidth to determine whether it matches.

There’s also InstNop which, well, does nothing.

Of course, the easiest way to do this is a recursive evaluator. We pass in a program, the current instruction, and input, and the current position in the input.

Let’s first determine the previous and current rune at the current position, and use -1 for the borders of the string (to be consistent with MatchEmptyWidth).

And now all that’s left is one fairly large switch (if you look at actual implementations of regex engines, there are also often giant switches, so it’s legit).

InstAlt and InstAltMatch are the same, so let’s use the fallthrough statement for go switch statements (this is much more sane than C-style fallthrough by default).

We don’t care about InstCapture or InstNop here.

For InstEmptyWidth we use the method that was given to us for this.

(I could get used to this). InstMatch and InstFail are obvious.

Then there come the various ways of matching runes. Note that this is the only time we have to increment the index into our input, as this is the only time we actually consume any runes.

That’s it. Now some due diligence against us being bad programmers, and we’re done.

Well, that was fun. But not terribly exciting. But what this gives is as good mental model of what exactly the different instructions mean, which can be used to build more exciting things.

# Do we only match even-length strings?

Now that we can proudly proclaim we have written a regular expression engine (well, maybe we were slightly cheating and someone else helped a bit), let’s take up a bigger challenge. Given a regular expression that possibly matches arbitrarily length strings, determine whether all strings matched have an even size. Sounds like an interview question? A bit, but I also hope I’ll never get this as an actual interview question.

Let’s start with a similar prototype as for our Match function, but instead of our input let’s have something that flips around whether we are at an even or odd step. For reasons that will make sense later, let’s encode this as an integer that flips between 0 and 1 (so it’s idx % 2). We also need to keep track of which nodes we have seen before, or we will wait for a long time. But if you think about it a bit, we need to keep track of this for even and odd steps, an even visit and an odd visit are not the same. That results in the beautiful type of map[int]map[uint32]bool, or a map from an integer to a set of uint32.

Now let’s start with the easy part. I literally copy & pasted the Match code, removed all the stuff that actually does any … matching, plumbed through the visited map and made idx mod 2. That gives us all the rune instructions and InstCapture, InstNop and InstEmptyWidth (which are all, for all intents and purposes, noop).

InstMatch is straightforward, as we just have to check whether we are at an even step. InstFail confusingly returns true, as we do not care about branches that do not lead to matches.

Now to one of my least favourite parts of Golang, copying nested maps. But here we go. Let’s introduce a helper method, as when we branch for InstAlt we will need a separate ropy of the visited map for both branches.

OK, with that out of the way, we can tackle the InstAlt instructions.

This one is different, as we want to make sure we can only match even length strings, so we need to && the conditions, rather than || them.

Due diligence again.

If we stop for a second to see what we’ve built, it’s obvious we’ve built a potential infinite loop. Let’s rectify this. If we arrive back at an instruction that we’ve been before with the same idx % 2, we can just prune this branch and return true as it is exactly the same.

So let’s prepend our switch statement with the following.

And then, of course, we need to keep track of what we’ve seen before, which again involves one of my least favourite parts of Golang, nested maps.

And that’s done! To see the whole code used in this post head of to this Github Gist.

If you have made it this far, it is probably also worth noting that the Z3 SMT solver has a Regex Theory. The last time I’ve played with it it was giving obviously incorrect answers, but that seems to have been rectified since. The nice thing about regexp/syntax is that it uses the same library your application uses if you write it in Golang, and can be used in programs with more predictable performance and fewer dependencies than Z3.