Binary system and Cantor (Cantor) set of _4679

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Binary system and Cantor (Cantor) set of

Corresponding proof,[link widoczny dla zalogowanych], we can construct measure for the £ (0 <£ <1) of the complete Lichtung set. Another example: the Cantor set can be defined on the binary decimal representation of the Cantor singular function ⑩ (x) has the following important properties: 1) ⑩ (x) is [0,1】 nondecreasing function on: 2) ⑩ ( X) is continuous and ⑩ '(X) = 0, a · e · 0,1】 in 【very valued function; (Note: ① (x) makes the classical mathematical theory of a, b, respectively, right, left continuous, f (X) = 0 in (a, b) hold, then f (X); c in [a, b] set up a ) 』⑩ (X) dX = 0 <@ (1) a ⑩ (0) = 1 (Note: it makes the classical theory of mathematical analysis known and commonly used Newton-leibniz formula ff (x) dx = f (b) a f (a) does not hold), and so on. Due to space limitations, this article not going to start. (Continued on page 116) * 109.2008 Coke Southwest Guizhou Teachers College 1 features, we will be able to reflect the beginning of the irreversible process, the final process of the two states in influence on the direction and extent of non-equivalence , will certainly be able to determine the process by it to find out the direction and extent of the state function entropy and the principle of entropy increase. Sixth, the principle of entropy increase and the mathematical formulation of second law of thermodynamics can be defined by the equation of Clausius entropy state function, then by the Clausius equality and inequality, and the second law of thermodynamics can be obtained entropy defined mathematical expression ds ≥ half of the second law of thermodynamics is given restrictions on the process, in violation of the inequality of the process is impossible. Adiabatic conditions on the system, Q: 0, then there is sB-sA ≥ 0 which is the principle of entropy increase. Principle that: The adiabatic process, the system will never decrease the entropy of the system entropy by reversible adiabatic process is the same, by the adiabatic process is irreversible entropy increase, decrease in the adiabatic process the entropy can not be realized. The principle of entropy increase is an important application of isolated lines to analyze the process of occurring. Isolation system with other objects do not matter and energy exchange, which occurred during the process must be adiabatic. This can be and, the entropy of an isolated system will never decrease. Isolated system in the irreversible process occurs always towards the direction of entropy increase. Students often can not be correctly applied the principle of entropy increase, to enable students to grasp the process of using it to determine the direction and extent of this core issue, it should be noted: the process can be involved in all the objects all together constitute an isolated system, then the principle of entropy increase direct determine the nature of macro process of Spontaneous direction and limits. Because the process of isolating lines must be spontaneous and natural processes are irreversible thermodynamics of macro. Therefore, we can see by the principle of entropy increase: the process of nature should be toward Spontaneous macroscopic direction of entropy increase, until the maximum entropy state (steady state) so far. VII, thermodynamic probability of the statistical significance of the second law of thermodynamics, the entropy of the physical meaning of each state can contain multiple micro-macro-state probability of the other principles, the isolated system is such that all micro-motion state probability, then a macroscopic state which contains more than the number of micro-motion state, the macroscopic state of the opportunities to large. Microscopic theory of entropy increase in real terms is: the process occurs within the isolated system is always a small chance of the state from the thermodynamic probability of the thermodynamic state of a large transition. Principle of entropy increase reflects the thermal motion of microscopic particles increase in clutter, so the physical meaning of entropy should be: the system of microscopic particles constitute clutter thermal motion (disorder) of the measure. Editor: Liu Zhi (Continued from page 109)