studiot

I'm sorry, why is the question mark a problem, don't you usually have one at the end of a question? The plus sign between the two terms is because you can have either plus or times as operations. You questioner has chosen plus. If you like the output (boolean variable C) is given by your expression between boolean variables A and B. So C = some function of A as well as B

Try to forget 'true' and false', they can be misleading. OK so we use capital letters for boolean variables, eg A, B, C, D, etc. Any boolean variable can take one of two values 0 or 1. Any boolean constant can take one of two values, 0 or 1. Since they are so simple we do not bother with letters for constants. Just as with ordinary algebra we can form equations or expressions combining (boolean) variable. (boolean) constants, We may use powers and multiples these may be integers as in ordinary algebra. eg 1+A ; B2; C(A+B); 4D and so on. We manipulate these using the rules of boolean algebra I listed So your expression is made up of the sum of two terms and Now = and [math]\left[ {\overline {\left( {\overline A } \right) + \left( {\overline B } \right)} } \right][/math]=[math]AB[/math] So your expression can be simplified to [math]\overline A [/math] + [math]\overline B [/math] + [math]AB[/math] You can simplify this further using more rules from my list. I note you mention gates and it is not clear whether you are studying maths or electronics here. If you like we can look at this suing the simplest electronic implementation, which is actually switches, not gates. For switches, variables A and B represent switches, either off or on (negated). The product AB is represented by switches in series The sum (A+B) is represented by switches in parallel

Courses these days seem to plunge straight in to DeMorgan without spelling out the simple relationships. Here are all you will ever need. The last two between them make up De Morgan's Theorem. [math]0*0 = 0[/math] [math]0 + 0 = 0[/math] [math]1*1 = 1[/math] [math]1 + 1 = 1[/math] [math]1*0 = 0[/math] [math]1 + 0 = 1[/math] [math]\bar 0 = 1[/math] [math]\bar 1 = 0[/math] [math]A + 0 = A[/math] [math]A + 1 = 1[/math] [math]A*0 = 0[/math] [math]A*1 = A[/math] [math]A + A = A[/math] [math]A*A = A[/math] [math]A + \bar A = 1[/math] [math]A*\bar A = 0[/math] [math]\overline{\overline A} [/math] = [math]A[/math] [math]nA = A[/math] [math]{A^n} = A[/math] [math]A + B = B + A[/math] [math]A + B+C = A + (B + C) = (A + B) + C[/math] [math]ABC = A(BC) = (AB)C[/math] [math]A(B + C) = AB + AC[/math] [math]A + AB = A[/math] [math]A(A + B) = A[/math] [math]A\left[ {\left( {\overline A } \right) + \left( B \right)} \right][/math] = [math]AB[/math] [math]A + \overline A B = A + B[/math] [math]A + BC = (A + B)(A + C)[/math] [math]\overline {(AB)} [/math] = [math]\left( {\overline A } \right) + \left( {\overline B } \right)[/math] [math]\left( {\overline A } \right)*\left( {\overline B } \right)[/math] = [math]\overline {(A + B)} [/math]

Thank you all for your responses. Something I hadn't considered, good point! However, today's weather and climate calculations depend upon adding together contributions from all the areas around the globe. I don't know if warming cooling models are capable of doing this into the future, but the results would certainly be of more interest to the local population than an it depends statement. Yes the series discusses this as part of the presentation. Thanks for the references. One further consequence is said to be in the fossil record, particularly the pygmy elephants. There is also some spectacular video of the salt caves.

According to the BBC, (Iain Stewart The Power of the Planet) the rate of evaporation in the Med is greater than the replacement water supply from the incoming rivers. That the sea level in the Med is currently not changing is due to inflow of water from the Atlantic, through the Pillars of Hercules. They also state that this inflow is only just enough to accoplish this at present. So if there is a local average temperature rise due to global warming will the increased rate of evaporation raise or lower sea levels in the Med? I understand that the salt deposits and fossil remains show that the Med has dried, perhaps altogether out in not too distant previous times.

copernicus, I don't know why you have chosen to ignore my posts 13 and 22 since they contain the answer to your question. Maxwell extended Ampere's law, adding an extra term due to the time rate of change of an electric field. It is because of this term that he realised that an electromagnetic wave could be generated. In very simple terms If something causes the electric field to vary in a dielectric, this will generate a varying magentic field, according to Maxwell's equation. This, varying magnetic field will, in turn, generate a varying electric field, according to Faraday's law (restated by Maxwell). This varying electric field, in turn will generate a varying magnetic field, completing the cycle. and so it goes on and the wave propagates. This is all due to Maxwell's displacement current in circumstances when the conduction current (Ampere current) is zero.

John has given you most of the reasoning, but the point is stronger than that. Terrestrial freshwater is constantly being flushed through and replenished with new freshwater. This applies to lakes, rivers and groundwater. So the water 'gets out' as John puts it not just by evaporation but also by simply flushing through. But in the sea or ocean there is nowhere for the water to go to, apart from evaporation.

Glad to be of service. I see there are plenty of others willing to discuss this in as much detail as you like, so I will leave it to their capable hands now I've pushed the boat in the right direction.

Good morning Nicholas. The holes are called vents and the lumps are called (cooling) fins. Yes some computers, particularly laptops have a radiator, similar to car radiators but smaller. They serve the same function. They are also similar to the cooling radiator on the back of fridges and freezers and inside airconditioning units. Unfortunately calling these radiators is inappropriate since they do not transfer much heat by radiation. The correct term is convection. If there is also a fan it is called forced convection. If there is no fan it is called free convection. So think carefully about what comes out of your vents. The whole point if equilibrium is that nothing happens in equilibrium. That is no heat is transferred, buildings do not fall down and so on during equilibrium. Thinking about the properties of your aluminium plate, what can you say about its surface area, compared to a cube of the same amount of metal? Can you test this in a dark room using, say, a hair drier?

It is only reversible when there are no dissipative processes.

You are still missing the point. In the development of Thermodynamics as a self consistent discipline we start with definitions propose laws and deduce theorems, much as with Euclid. Using the second law to define reversibility introduces a circular argument. In classical thermo we start with mechanical quantities such as pressure, volume, work and energy. We propose or deduce (whatever you will) the First Law and the existence of state functions ingeneral and a state function called internal energy. We discover that pressure and volume form a state function pair for many processes, but sometimes this fails, as with one of the most common substances used in practical thermodynamics, water, since specific volume is not a unique function of temperature. This kit is enough calculate most of the practical requirements in classical thermo. Entropy is not mentioned or needed. But reversibility is required to perform the calculations. For instance this quote from Lewitt : Thermodynamics Applied to Heat Engines" "In article 10 eight thermodynamic processes were defined; any of these processes that can be operated in the reverse direction are known as reversible processes" Lewitt goes on to many pages to analyse adiabtic, isothermal and ther other six processes for reversibility. Similar discussion can be found in Robinson and Dickinson : "Applied Thermodynamics" and of course, that old standby for all engineers Rogers and Mayhew "Engineering Thermodynamics, Work and Heat Transfer" Yes, all introduce and discuss and employ entropy at a much later stage. and none offer a mathematical definition of reversibility.

Surely the simple statement "1" is the shortest possible, and considerably shorter than the shortest mathematical algorithm or calculation I can think of to generate a 1. Whilst some would debate the null sequence can be a sequence or random, the sequence with just one term is perfectly admissible.

So let us continue to examine the word 'random'. A random sequence is a sequence that cannot be expressed more compactly than a complete list by any algorithm. (after Chaitin and Solmonoff. What Wikipedia call the Kolmogorov definition if you care to look it up) Let my sequence, drawn from a binary system i.e. 1 or 0 for simplicity, be {A} where A is either 0 or 1. Now the question arises:- Is this sequence random? Well, mathematically it conforms to the above definition so it is random. But a physicist might well wish to distinguish between circumstances as to how I arrive at this sequence. For instance if I always calculate A = 4/4 I will always arrive at the sequence {1} and if I always calculate A = (4-4) I will always arrive at the sequence {0}.. So my result is predeterminate But if I flip a coin and choose A = 1 for heads and A=0 for tails then which sequence I arrive at is indeterminate or at the behest of chance.

Of course Nature has provided a catch, as JC notes. On the face of it, there is an enormous amount of apparently available thermal energy compared to the mechanical/electric sort. The problem comes in trying to use that heat. Iseason you have suggested that heat pumps are efficient. They are not, they are hopelessly inefficient. It is just that there is a large amount of heat energy available so the inefficiency can be tolerated. In fact, efficiency is an inappropriate term to use for heat pumps. This is why I talked about COP. Efficiency in % is defined as output divided by input times 100. But this is predicated upon the input being fixed or set (the independent variable) at a aprticular value and the output being the determined by the system. So if I put 100 watts or Joules into an electric motor at 85% efficiency I will get 85 watts or Joules out. So for efficiency calculations the input is fixed and the output varies. For heat pumps it is the other way round. That is in order to extract a set or fixed quantity of energy you need to input a particular quantity of work energy. The parameter that measures this is called the coefficient of performance (COP). The COP is normally reported as a fraction rather than a % however. So the COP is defined as the output divided by the input work but not including the input heat from the heat source. So, as I said earlier, you can get a good figure of receiving three times as much heat as you put work in. COP = 3. Now you have to output the heat into something by raising its temperature. Ususally this is a working fluid, say for instance the hot water in your central heating radiators. The catch is that the higher the temperature you raise the working fluid to the lower the COP. So yes you can raise the temperature of your central heating water from say 20C to 25 C at a COP of 3. But in order to do any useful heating your central heating water needs to be at least 55C and perhaps more. At this temperature the COP falls to about 1.4 . Worse if you actually want to boil water to create steam, the COP is actually less than 1 so you would have to spend more energy pumping than if you simply used that energy to boil the water. That is why engineers distinguish between high grade energy such as electricity and low grade energy such as heat pumped heat as John Cuthber has pointed out. He also points out that for safety reasons planners try to keep areas downstream of dams (they do burst occasionally) free of housing. I will stop here (for questions) because these are actually difficult concepts but a direct consequence of the laws of Thermodynamics.

The comparison I suggested is interesting because 1) 1kg of water falling 30m at 85% efficiency will net you 250 joules of electrical energy. 2) 1kg of water cooled 3 degrees centigrade will supply 12,600 joules of heat energy, but you would need to expend 4,200 in your heat pump leaving 8,400J. These are extreme because the water head is maximised so the fall is usually greater than 30m and the cooling is normally measured in points of a degree. But the principle is there to discuss.

Beer Huh? Hopefully you will also take in the Roman limestone mine? http://www.beerquarrycaves.co.uk/

It is a good question and you should keep asking such questions. However I also suggest you consider the following comparison. How much energy can you extract from 1kg of water falling 30 metres, assuming your hydrogenerator is 85% efficient in conversion to electricity?. How much energy can you extract from 1kg of water as heat energy, by cooling it 3 degrees centirgrade and assuming you have obtain 3 times as much heat as you have to expend energy to run your heat pump (That is the coefficient of performance is 3 - a good figure for a heat pump)? Furthermore, electricity is readily transmittable to be used elsewhere. What would you do with the heat when you had it?

I have to say that if I was just struggling to puzzle out what was meant by the book, I would find the explanations less than helpful. First is to know what is meant by 'apparent weight'. This is the reading that would be obtained by standing the object on a spring type scale. It is the force that the object exerts on the scale. Now Newton's third law tells us that the floor of the lift or the scale pan exerts an upward force on the object and the object exerts a downward force on the scale pan. Whichever way the lift is moving the object always exerts a downward force, due to gravity. When the lift is accelerating upwards, the lift exerts an additional upwards force on the object due to its acceleration (ie in order to accelerate the object upwards). Consequently the object exerts an additional downward force on the lift by Newton's third law. That is it presses harder on the floor when the lift is accelerating upwards. So for upwards acceleration your book is saying that you add the gravitational force on the object to the reaction force due to the acceleration. Does this help?

Looks like part of a reflux condenser to me. http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0104-66322002000100009

Collecting and focusing solar energy can produce substantial power. See solar furnace. https://www.google.co.uk/search?hl=en-GB&source=hp&q=solar+furnace&gbv=2&oq=solar+furnace&gs_l=heirloom-hp.3..0l10.1469.4860.0.5125.13.10.0.3.3.0.125.1124.1j9.10.0....0...1ac.1.34.heirloom-hp..0.13.1248.VlefBCYx98U

Bignose and Cap'n Refsmmat, with the greatest respect both for yourselves and for your positions, I fear you have completely misunderstood my point or points. I continue to hold that the word ‘chance’ embodies different concepts from the word ‘probability’ for very good reasons, not least because ‘chance’ is a much more general concept. I agree, however, that some use (particularly) the plural (chances) as synonymous with (statistical) probability. It is for this reason that statisticians adopted the word probability for rigorous codification so you (as has already been mentioned by several posters) hardly find the word ‘chance’ used in statistical works. Chance is, however, often mentioned in other sciences where there may be several causative agents at work, some deterministic, some not. Turning now to the adjective ‘random’, it is true that a random variate or variable has a well defined probability distribution function, although to quote Professor Kreyszig “Caution! The terminology is not uniform” This function is founded upon and only deducible in elementary theory if based on the principle of mutual exclusion or statistical independence. This principle is another way of stating my principle point. For Bignose’s example this is embodied in his statement fair dice. This means that the first die has equal 1/6 likelihood of turning up 1,2,3,4,5 or 6, as does the second. So the likelihood of turning up say a 12 is given by the product of these equal probabilities ie 1/6 x 1/6 = 1/36. Similarly for a fair draw from a pack of cards the probability of drawing the king of diamonds is 1/52 and the probability of drawing any king is the sum of the individual probabilities, .ie 1/52 + 1/52 +1/52 +1/52 = 4/52. More complicated combinations are also available to form full distributions. All of this is entirely consistent with what I have said before and also with the new material introduced by yourselves.

Only 12 years? You will still be a young man when you finish then.

Again the insulting condescension. I note your quote is identical in substance to mine, but your whole persepective is too narrow. Did you not read my post 15? The word 'random' is an adjective. When applied to one particular noun (as you and I have both agreed) it has a particular meaning. When, in the full gamut of Science and Engineering it is applied to other nouns it has other meanings. Do you actually disagree with any of the reasoning or statements in the example I developed?

And I, in turn, don't understand your difficulty with the question. How can I make it any plainer? Note that I introduced the word 'random', not any of several phrases incorporating theat word, all of which have special meanings. Your phrase random variable is one such and I have already acknowledged that. So I see nothing wrong with what I said. Nor do I see how it is not the common usage. I also said that Science has more than one definition for the word random. I was trying to avoid confusion by not including that second usage but are you familiar with the phrase 'random access'? I would venture a guess that there are more computer engineers using this than statisticians in our modern world, but would not claim that this entitles their definition to override all others. I am very open to the idea of cooperation for the benefit of the Op and his thread. So if you have better definitions and/or explanations please state them. Your expanded detail about random variables takes things on beyond what I said, but in no way detracts from the validy of my statements, so why present them as an argument?

Not even analagous. They embody different concepts. People often (wrongly say) say "what are the chances of....?", when they should say "what is the probability of...?" This is both bad Science and bad English because there is only one probability value per outcome. Asking in the plural makes no sense in either English or Science. To continue my example further suppose we change the rules again, and remove chance entirely. Now, instead of being the nice big brother you are the nasty big brother and you tie your little sister's right hand behind her back. There is no longer a chance that she will catch the ball with the right hand so chance no longer enters into this game. The probability still exists for a catch with either hand, however. 1.0 for the left hand and 0.0 for the right. Edit I am describing single events, not combinations of events. But you are correct that for compound events the probabilities need not be evenly distributed. Would you say that a probability of 1.0 is not deterministic? How does your statement above fit with the statistics of a random walk and diffusion?