By Katz N.M.

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**Extra resources for A conjecture in arithmetic theory of differential equations (Bull. Soc. Math. Fr. 1982)**

**Sample text**

6) An application of this law is the fact that gas bottles which are often used in laboratories must not be left in exposed hot environments. The increase in temperature of the gas inside the gas bottles could become critical were they to reach a high enough temperature for the gas bottle to explode! THE MOVEMENT OF A GAS FROM AIR INTO A SOLUTION Air flow is very similar to blood flow, as discussed in Chapter 3. The gas from the air must be transported through the respiratory tracts to the alveoli of the lungs whereby a small fraction of the gas will move into a solution: blood.

This chapter will, however, refer to fluids only in the context of liquids (see Chapter 2 for discussion of gases), although there will be times when the laws/principles apply equally to gases. To appreciate the laws and principles as applied to gases it is advisable to read this chapter in conjunction with Chapter 2. In instances whereby laws/principles apply not only to a liquid but also a gas, the text will refer to the dual application. The majority of the earth’s surface is covered by water.

Gases do not occupy a fixed shape or volume unless enclosed and are easily expandable because of the weak attraction of the bonds between gas molecules. Gases are less dense than solids or liquids. The low density allows gas molecules to travel at high speeds, which does not enable calculation of individual gas molecule speeds; rather an average velocity is considered, according to the kinetic theory of gases. Three gas laws, 26 physical states known as Charles’, Boyle’s and the pressure law, are particularly applicable to physiology.

### A conjecture in arithmetic theory of differential equations (Bull. Soc. Math. Fr. 1982) by Katz N.M.

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