simple Pure Mathematics proofs: left and right inverse of composite functions help?

March 1st, 2010

Let f : A -> B and g : B -> C be two functions.
a) Prove that if g ○ f has a left inverse, then f has a left inverse.
b) Prove that if g ○ f has a right inverse, then g has a right inverse.

I have spent about 4 total hours just manipulating the properties of these functions, and I can not come to a conclusion. I realize that these are probably very simple, but I am effectively stumped. Can anyone help?

consider that if w is the left inverse of [ g o f] then w o [ g o f ] = [w o g ] o f = identity

What web signts can I use to find stock quotes and information?

February 27th, 2010

I have a homework assignment in my business class. I have to track one stock each from, DJIA (Dow Jones Industrial Average), DJU (Dow Jones Utility Average), and Nasdaq AQ composite. The only signts I can find give the average of the whole company, not individual stocks, where can I look to find these?

First of all, a "whole company" generally has just one common stock. I think you are trying to differentiate the *index* (such as the DJIA) from the companies (General Electric, Intel) that comprise the index.

next, the term is "site", not "signt".

I get my information from http://finance.yahoo.com, which lets you enter stock symbols, look up symbols for particular companies, etc.

What is the point of knowing whether the entire DOW or NASDAQ is up or down?

February 25th, 2010

Why is it important to know if the entire composite is up or down rather than only the stocks one invests in?

You have your thinking backwards and that will cost you money.

The most important aspect of successful investing is learning to read market trends so you can maximize your individual stock investments’ entry points.

First, determine market direction to a high probability, putting odds in yoru favor for a successful investment.

Second, invest in individual stocks when the market index is positioning to move with an upward bias, putting the advantage in your favor. Stocks respond to market up movements with a corresponding upward trend bias. In fact, the best stocks will typicallyoutrun the pace of the index upward movement rate. The trend of an index such as S&P’s 500 stocks is far more powerful than the trend of an individual stock. Aligning with it is far more profitable than randomly investing in individual stocks based on their trend profile alone.

Third, be sure to select those stocks with the best opportunity for accelerated growth. Tools like Investors Business Daily do an outstanding job of helping you discern the above critical points, and provide excellent education for when to enter, and when to stand aside from the markets. Their pre-screened high potential stock lists have annihilated the S&P 500 averages since IBD 100’s inception.

If fillers are added to Teflon, does it mean that it becomes composite material?

February 25th, 2010


I would have to say yes to your question based on the link I read.

can you suggest me a topic for paper presentation?

February 23rd, 2010

I have to go through a paper presentation shortly but i am totally confused with the topics…. could you suggest me a topic which can win me the prize. These are the topics given to us. suggest me one and tell me where could i get the whole information regarding that topic

THERMAL
1. Cryogenics
2. Computational fluid dynamics
3. Micro scale heat transfer
4. Nano scale heat transfer
5. Energy transfer
6. Non conventional energy sources

DESIGN
1. Vibrations
2. Aero dynamics/ rotor dynamics
3. Fractured diagnostics
4. Analysis in FEM
5. CAD/CAM
6. Neural networks

MANUFACTURING
1.Agile manufacturing
2.Micro machining
3.Special materials (meta materials, smart materials, share memory alloys, composites)
4.Bench marking techniques
5.Explosive forming
6.Reverse engineering

INDUSTRIAL ENGINEERING
1. Capacity planning
2. Work study
3. Principles of Industrial organization
4. Operations research
5. Engineering optimization
6. Inventory control

LATEST DEVELOPMENTS IN THE FIELD OF MECHANICAL ENGINEERING
1. Robotics
2. Nano technology
3. Rapid prototyping
4. Mechatronics
5. Advances in Automobile engineering
6. Alternative fuels

http://www.youtube.com/watch?v=3q7MH1aPTEQ

Is it better to buy funds and spiders than individual stocks?

February 23rd, 2010

I was watching a finance show over the weekend and Ben Stein said unless your name is Buffet it’s hard to pick individual stocks well. A safer way is to buy funds. I am thinking of getting spy which is a composite of the S & P index. Are these safer bets than individual stocks?

Yes, investments in ETF and funds, especially index funds, are a safer investment than investing in individual stocks. The reason: when you buy SPY, for example, you are buying into 500 shares, some of which go up and and some of which go down. Some of the moves of these 500 individual stocks cancel one another out. When you only own a handful of stocks, it is much likelier that all of them go up or down at the same time, which makes them riskier. The returns of a combination of 500 stocks is normally much more stable than the return of a combination of 5 stocks.

My pc has composite cable inputs but when i want to capture a video it doesn’t show them?

February 23rd, 2010

For example on cyberlink powercinema when i put capture device it doesn’t show my composite cable inputs. How can I make my computer recognize my inputs?
Its the red yellow and white inputs that my pc doesnt show when i want to cature a video.

Ive had that problem as well.

Graphs or tables of composite material and metallic alloy developments?

February 23rd, 2010

Hi there, I am in need of tables and/or graphs of the developments of metallic alloys and composites used in aircraft’s . Developments in corrosion resistance, strength, stiffness, service life from fatigue ect. I tried all over the net but couldn’t find any thing helpful. please fill me in. easy 10 points

Cheers!

Search for any machine design book by Shigley. There are many on the internet, it may be hard to locate all the tables and charts you are looking for but they are in there. I finished the class machine design last semester and some of our problems asked for the same properties you are talking about, with graphs showing the relationship of composites and common materials. Also any library should have some of his books as well.

Numbers p^q or p^q ±r, where p,q are distinct primes?

February 21st, 2010

What properties do the numbers p^q
or the numbers p^q ±r, where p,q are distinct primes, have?
Do these things have a name?
(r could be prime or composite.)
p^q is obviously composite; p^q ±r might or might not be prime

The subcase p=2 is pretty well studied, and in particular
the subcase p=2, q=some prime, r=-1 is Mersenne (at least, for the definition which requires the exponent q to be prime)
Folks don’t be afraid of it, it won’t bite, it’s just an idle question, I don’t even know whether there is an answer, let alone one anyone cares about.

p^q is composite and probably boring, unless it has some unlikely properties I’m not aware of other than:
- it obeys Fermat’s little theorem (see also: Carmichael numbers)
- it has (q+1) distinct factors (boring)
- it is a ‘Powerful number’, since q≥2
- it is a divisor of some Achilles number (Any interesting conjectures about p^q and Achilles numbers?)

The numbers p^q ±r are maybe more interesting, and might throw up some prime-generating or other formulas (not necessarily good ones, but hey), other than Mersenne’s formula. I’ve only ever seen p=2 or rarely p=3 used, are there any formulas involving higher primes?
- see e.g. the formulas for even and odd perfect numbers.
- see also Wieferich prime
- related but different: Pierpont primes; Wagstaff primes;
Ramanujan-Nagell equation (
p=2, q not required to be prime, r=-7)
For more inspiration, see "Lists of the first prime numbers of various types"
http://en.wikipedia.org/wiki/List_of_special_classes_of_prime_numbers
David – there’s no "right answer", it’s just an amateur question, I’m disappointed people didn’t just have a go at it.

For example, are 5^q ±r, 7^q ±r …
(for r even)
any use as prime-generating formulae?
If not, why is 2 special?

And so on.

Seems to me you would be more likely to get an answer if you ask on sci.math (Usenet or Google Groups).

Some jet aircraft eg MD use depleted uranium as counterweights.Is this an acceptable risk for passengers?

February 21st, 2010

In the recent Madrid MD 80 crash & fire there is a risk of ingestion of DU if this aircraft had DU on board. Some people survived the crash & fire, as is often the case, even in severe crashes. Less toxic substances are available. Should they be retro fitted to all aircraft?
Source Term
"DU counterweights have been used primarily in wide-body aircraft on rudders, outboard ailerons (wing assembly), and outboard elevators (tail assembly). Counterweights come in a variety of weights and shapes, and numerous weights and shapes are used in some aircraft. The DU counterweight can range in weight from 0.23 to 77 kg."
"Some aircraft used for military and cargo also use DU counterweights; these include the Lockheed C-130 and C-141, Jetstar, and S-3A. The Boeing Company produced helicopters utilizing DU as a rotor tip weight prior to 1979. These weights consisted of small 0.22-kg triangular weights. One to three weights were installed per blade. Virtually all of the Boeing helicopters manufactured prior to 1979 have had their blades replaced with composite blades that do not contain DU weights." [NUREG-1717]
Use of DU Counterweights in U.S. Domestic Aircraft Aircraft Type Manufacturer Aircraft Number Owned by Domestic Carriers a,b Total Weight of Counterweights per Aircraft (kg)
DC–10 McDonnell-Douglas 168 ~ 1,000 c
L–1011 Lockheed 60 ~ 680 c
B–747 Boeing 202 ~ 850 d
a Number of aircraft owned by domestic carriers that are members of the Air Transport Association (ATA, 1999).
b A reasonable estimate is that 50% of these aircraft still contain DU counterweights. Phone call J. Taylor, Starmet CMI, Barnwell, SC, August 1999.
c Phone call, E. Lanchester, Quality Assurance Department, Nuclear Metals, Inc., Concord, MA, August 1996.
d Phone call, D. Barbour, Project Manager, Depleted Uranium Programs, Philotechnics, Oak Ridge, TN, October 1999.
Source: [NUREG-1717] Table 3.17.1

"In many cases, tungsten alloy counterweights have replaced DU counterweights in aircraft. Since 1981, The Boeing Company has provided customers with tungsten replacement counterweights, and tungsten counterweights have been installed in new Boeing 747 aircraft. Tungsten equivalents have been sent as spares since 1981 (Gallacher, 1994). In 1988, McDonnell-Douglas discontinued using DU counterweights and began using tungsten. Tungsten counterweights are used on the MD–11, MD–80, and MD–90 (Ford, 1994).
It is unknown how many DU counterweights are currently installed in aircraft. It is estimated that approximately 15,000 weights may be associated with the Boeing 747 fleet (based on 550, Boeing 747 aircraft produced between 1968 and 1981 and spare parts) (Gallagher, 1994). However, the number of aircraft that contain DU counterweights is decreasing. Rather than refurbishing the DU (during maintenance operations), tungsten counterweights are used as a replacement." [NUREG-1717]

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Aircraft Workers
Exposure of Aircraft Workers
External radiation during installation of DU counterweights
"The annual dose equivalent to workers responsible for installation, storage, and transport of DU counterweights was 0.9 mSv/yr (90 mrem/yr). The estimated collective EDE (Effective Dose Equivalent) to airline maintenance workers is 0.01 person-Sv (1 person-rem)." [NUREG-1717. Caution: the source mistakenly states 0.09 instead of 0.9 mSv/yr on p. 3-259]

Inhalation of DU dust after aircraft accident involving fire
"For the fireman, the EDE is estimated to be 0.3 mSv (30 mrem) and for the clean-up worker, the EDE is estimated to be 4 mSv (400 mrem)." [NUREG-1717]
The amount of material involved is 850 kg of DU, which is that on a typical Boeing 747 aircraft.

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Aircraft Crews and Passengers
Exposure of Aircraft Crews and Passengers

External radiation from DU counterweights during flight
"Annual estimated individual EDEs (Effective Dose Equivalent) to flight crews, attendants, and passengers were 0.001 mSv (0.1 mrem), 0.01 mSv (1 mrem), and 1×10-4 mSv (0

For many years, aircraft manufacturers have used "depleted" uranium to balance ailerons, rudders, and elevators on certain jet aircraft and rotor blades on certain helicopters. Uranium is 1 1/2 times as dense as lead and is the heaviest naturally occurring metal. According to a 1983 McDonnell Douglas Customer Service First Quarter publication, only "depleted" uranium is used, which means it has been processed to remove most of its uranium 235, the most highly radioactive form used in nuclear powerplants. The remaining uranium 238 emits only low-level alpha radiation. While the depleted uranium normally poses no danger, it is to be handled with caution. The main hazard associated with depleted uranium is the harmful effect the material could have if it enters the body. If particles are inhaled or digested, they can be chemically toxic and cause a significant and long-lasting irradiation of internal tissue. Depleted uranium is slightly radioactive. To minimize radiation hazards, depleted uranium balance weights are 100 percent cadmium plated during the manufacturing process. If the cadmium plating is intact, normal handling of the parts is considered to be non-hazardous and no special precautions are recommended. The use of radioactive materials in many every day applications is not at all unusual. For example, tritium, a radioactive form of hydrogen, is used in self-luminous signs, such as exit signs, and watches. Thorium, which has a radiation activity level comparable to depleted uranium, is used in making gas mantels for lanterns, electronic equipment, and high-quality optical lenses for cameras and overhead projectors. Also, smoke detectors contain americium 241, a radioactive material.

On arrival at accident scenes of aircraft suspected of containing balance weights made of depleted uranium, determine if balance weights have been damaged or lost their cadmium plating coating. Request specialized assistance if balance weights have been damaged or lost their cadmium plating. No penetration of the plating is allowed.