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    • If we consider the absorption of solar

    2018-10-24

    If we consider the cytoskeleton of solar radiation without the ‘greenhouse glass’ in the range of emission frequencies of the Earth\'s surface, as well as in the frequency band of solar radiation adjacent to it, up to 3000cm (prior to our examination of the problem, it was a boundary above which the ‘greenhouse glass’ transmitted radiation), then the main substrates are the same, i.e., water and carbon dioxide molecules. It is because of these molecules that the atmosphere is opaque below 900cm and in the range from 1200 to 2400cm. Among other gases, the vibrational-rotational band of ozone O at a frequency of 1042cm has the greatest impact on the transparency of the atmosphere. Methane CH (1300cm), nitrous oxide NO (589, 1285 and 2224cm), and carbon monoxide CO (2143cm) have less influence on transparency. The influence of nitrogen dioxide, nitric acid, ammonia, sulfur dioxide and freons is even lesser due to their low content in the atmosphere. The analysis of the factors affecting the absorption of the atmosphere may also take into account a certain difference in the spectra of different isotopic configurations of carbon dioxide compared with the basic modification, and also the collision-induced spectra of nitrogen (about 2350cm) and oxygen (close to 1600cm) absorption. Additionally, the natural and the Doppler broadenings of spectral lines should not be neglected. However, these effects have no influence on the overall conclusions. To summarize, the following conclusions can be drawn from the conducted analysis of the factors affecting the absorption and transmission of solar and terrestrial radiation by the atmosphere, as well as from the above-listed arguments.
    Introduction
    The key definitions Let us examine a disjunctive minimization problem formulated as where , . From now on we shall call it the Disjunctive Program (DP). The expression in the parentheses of the formula is a logical variable that takes a true value if the x point satisfies the system of n+1 inequalities (or a false one if it does not). The subject of inquiry is the admissible set of the disjunctive minimization problem under consideration The S4 set is called disjunctive, and it can be represented in two ways. In the first case its representation is a disjunctive normal form of a logical expression containing linear inequalities (any such expression can be reduced to the disjunctive form). The second way of representing a disjunctive set has the form As a matter of fact, these two representations are equivalent. Notice that the S4 set can be nonconvex.
    Disjunctive cuts and One of them is known to be true, but it is not known which one it is. The question is whether there is at least one inequality which is necessarily true. We assert that such an inequality exists, and in this case it is a third inequality, for example, of the form which is a relaxation of both inequalities (1) and (2), since Thus, inequality (3) holds true in the event that at least one of inequalities (1) and (2) is true. The DC metaprinciple generalizing the idea of obtaining the last inequality (3) from inequalities (1) and (2) can be formulated in the following way. The DC metaprinciple. Let us assume that at least one of the inequalities holds, and that the variables x1, x2,…, are non-negative. Then the inequality and all its relaxations are valid cuts for the set Since the DC principle, which is key for our study, follows from the LP principle and the DC metaprinciple [3,5], let us first formulate the LP principle. The LP principle. If λ is an arbitrary non-negative m-vector, then the inequality and all its relaxations are valid inequalities for a non-empty set So let us now formulate the disjunctive cuts principle. The DC principle[2,3,5]. Let us assume that at least one of the systems of linear inequalities× and all its relaxations are valid cuts for a disjunctive setHere and elsewhere we shall use the concept of a supremum of vectors. In inequality (7), denotes the v vector whose jth component is where λ is a row vector of components, is a ×r matrix, and h is an index.