jian

The energy conversion in the fan is : electric power-----> mechanical energy of the fan itself+ mechanical energy of the moving air+heat loss due to resistance of the coil. The enerfy is always conserved. The moving of the blade makes the nearby air to move. Then there is a pressure difference betwwen the staionary air and the moving air. Then the air starts to flow and blow. Overall, the electric energy are converted many kinds of energy, however, the total amount of energy is always a constant. If you consider the mass energy equality, the energy conservation and mass conservation are combined together. That is the generlized conservation law.

It should be 1 Firstly take the logarithm of original expression. ln([sin(x)]^x)=xln(sinx)=(ln(sinx))/(1/x) take the derivative of both the denominator and numerator got lim(-xcosx)*(x/sinx)=lim(-xcosx)=0 when x approaches to 0. so the original limit will be 1. limits.doc

That is right, and the absorption is not only happen in the matter consist of molecules,also in the atomic and ionic substances. In another way, lights are also particles which are called photons. They contains energy determined by the frequency(which determines the color of light) of the light. In a matter, electrons have many discrete energy levers. When the energy of the photon is just equal to the energy difference of two energy levels or higher than the ionization energy, the photon will be absorded and the electron will be excited to higher state. This is the process of absorption of light. There is also a re-emission process which refers to that the excited state jump back to lower energy state and give off the energy in the form of photons. Macroscopically, it is lookes as reflection. The unabsorbed photons just travel though the materials and form the transmitted light. These are the qualitative description of the interaction between matter snd light.

I vote for that maths is a discovery rather than the invention. Every species has own unique languages. Maths is the language of the nature. Like R.P.Feynman said" If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in."

how about make a real dragon ?

Why don't do a simulation first and attach the results with your proposal. Simulation will be much cheaper snd facts speaks louder than words. If your idea is applicable, you will change the whole world.

Color is the wavelength of electromagnetic waves that recieved by our eyes and brain. Normally only refers to the visible light range. The color of the object is dependent on the optical properties of the object. When the object does not emit light, its color depents the light it absorbed, refected and transmitted through it. For transpant objects, its color is determined by the color of light that pass through the object. An example is that the blue glass only let the blue light go through. The color of an opaque object is determined by the color of that it reflects. A yellow paper absorbs all the light except the yellow light. When the reflected yellow light is detected by our eyes, it appears yellow. However, color is always subjective in terms of senses, it is qualitative. Also it is not really a property of a system.

It is an old question, it says: In a gambling game, there are three door numbered #1,#2 and #3. There are a car behind one of the doors. If you guess the right door number, you can get the car. Then you made a guess, say door #1, then the host opened the door3, it turned out to be empty. Then he offered you a change to guess again. The question is " should you change your choice to #2?"

The logic gates are not that abstract that they consist of electronic elements. The most basic ones are made of diodes. Unlike resistors, diodes only allow the current go through the positive direction provied that the voltage across it is not high eough to damage them. Because of this property, they are used to control the current in a circuit. Logic values are assigned on the output depends whether there is current or not. When we are not concern about the circuit, we can simply call them logic gates. They give us cirtain output when the input is injected. They are the ancestor of the computer chips.

what is the angle theta refer to? Can anyone give me a graphic representation for the angle theta? Thanks in advance.

For a given optical system, there always a term called resolution power. It is called limitaion caused by diffraction. I have known the equation sin(theta)=1.22lambda/ampture. But not really understanding the meanings. Can anyone give a comprehensive explanlation about the resolution power or diffraction limitaion?