By A. M. Howatson (Auth.)
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Convex research is the calculus of inequalities whereas Convex Optimization is its software. research is inherently the area of the mathematician whereas Optimization belongs to the engineer. In layman's phrases, the mathematical technology of Optimization is the research of ways to make a good selection while faced with conflicting necessities.
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If φ is of the form given by eqn. 4) it may be readily shown that the Stoletow point occurs at E/p = B. 2. EFFECT OF SPACE CHARGE In measuring a, or in verifying eqns. 4), the electric field must be uniform. If the currents passed are too high, the uniformity will be appreciably upset by the presence of space charge. Consider the ions and electrons which are produced in pairs in a gas carrying a Townsend discharge, either as primaries by photoionization or as secondaries by electron collision : evidently, in the steady state, positive ions must reach the cathode in the same numbers as the corresponding electrons reach the anode.
4). Auto-ionization is the name given to a process involving a doubly-excited atom; that is, an atom in which successive collisions have transferred two valency electrons to higher levels. Instead of the atom reverting to the ground state, it is possible for one electron to fall back and the other to be released, provided that the total excitation energy is greater than that for ionization. The balance of internal energy is given to the released electron, and when this difference is small the process is more probable.
Excitation energy can also be exchanged between neutral atoms. In particular, an excited atom can ionize by virtue of its excitation energy, if the latter is larger than the required ionization energy. Such a process is made more probable if the excited atom is in a metastable state and has thus a longer lifetime in which to undergo a collision. 7). 5. Attachment and Recombination We frequently assume charged particles to be either positive ions or electrons, but in certain gases electrons can combine with neutral atoms, or molecules, to form negative ions.