Absolute Expressions Research Articles

Reactions at the corroding nickel electrode in molten sodium carbonate under CO/CO 2 atmosphere

Anodic reactions at the CO, CO 2|Ni electrode in molten sodium carbonate at 1000°C are examined in detail. Experimental polarization curves are fitted via a computer graphics procedure to a model employing five anodic reactions with activation, concentration and resistance polarization, and passivation. The resultant empirical parameters are interpreted in terms of absolute rate expressions describing possible anodic reactions. Three of the anodic reactions are found to be in accord with the findings at inert electrodes by previous investigators, i.e. oxidation of CO by two mechanisms and oxidation of carbonate, while the cathodic reaction is consistent with reduction of CO 2. The remaining two anodic reactions were associated with the oxidation of nickel to Ni 2+ with formation of a NiO film above a passivation potential, and, at higher anodic overpotentials, oxidation of NiO to a higher oxide, e.g. Ni 2O 3. There is an indication of the formation of a third oxide at still higher anodic overpotentials.

Reactions at the CO, CO 2/Ni electrode in molten sodium carbonate

Reactions at the nickel electrode in molten sodium carbonate at 1000°C under CO/CO 2 atmospheres were studied by electrode polarization. The polarization curves were analysed by means of a previously described computer model, which in turn was interpreted in terms of the absolute rate expressions for postulated reactions. In agreement with previous workers' observations for inert electrodes, the dominant anodic reactions were found to be oxidation of CO at low and intermediate anodic overpotentials, and oxidation of CO 3 2− at high anodic overpotentials. The cathodic reaction was found to be reduction of CO 3 2−. The form of the polarization curves was described by activation, concentration, and resistance polarization of these reactions; however, anomalous anodic behaviour was observed which was attributed to corrosion reactions at the electrode and accurately described through the use of additional anodic reactions displaying passivity.

Minimal Third-order Expressions of Boolean Unate Functions

ABSTRACT A simple and straightforward procedure for finding absolute minimal third-order expressions (in the ‘ sum-of-product-of-sum’ forms) of a special class of Boolean functions called unate functions is suggested in the paper. The central idea developed through the procedure involves a decomposition of the assigned Boolean function first into a group of sub-functions called maximal uniliteral sub-functions (MTJL's) each of which is realizable in a minimal second-order ‘ product-of-sum ’ form and then a selection of an appropriate sub-set of these maximal uniliteral sub-functions or MUL's (or their sub-functions) in order to cover all the prime implicants of the function minimally.

Shreeram Abhyankar. Absolute minimal expressions of Boolean functions. IRE transactions on electronic computers, vol. EC-8 (1959), pp. 3–8.

Shreeram Abhyankar. Absolute minimal expressions of Boolean functions. IRE transactions on electronic computers, vol. EC-8 (1959), pp. 3–8.

Absolute Minimal Expressions of Boolean Functions

In this paper we make a beginning in the hitherto unexplored problem of finding absolute minimal expressions of Boolean functions. We shall adhere to the notations and terminology introduced in our previous paper,1 which will be referred to as S. In the present paper, we shall find absolute minimals for Boolean functions whose point set complex consists of either one or two points. The case of one point is in Theorem 1, Section I. The case when the two points form a 1-cell is covered by Theorem 4, Section I which discusses an arbitrary dimensional cell. The case when the cell complex consists of two isolated points, the main theme of this paper, is dealt with in Section II.

Radiotherapy for Bone Tumors

ALTHOUGH the classification of bone tumors is still difficult and unsatisfactory, a definite improvement in this respect has occurred during the past few years. Moreover, it is gratifying to know that radiology has played a valuable part in this improvement. The roentgenographic features of such abnormal growths are often distinctive, but sometimes they are not and an absolute diagnosis cannot be made. When tissue from such a tumor can be removed for microscopic examination, the growth can usually be identified. In certain cases, unfortunately, different pathologists cannot agree on the essential character of the tumor. As the experience of radiologists has increased, their attention has been attracted by the fact that certain tumors of bone are sensitive to radium or roentgen rays, while others are much less sensitive. By radiotherapeutic tests alone, or by correlating such tests with the pathologic data, it is now possible to distinguish certain tumors from others with which they had previously been confounded. Thus, one of the features which influenced Ewing in recognizing diffuse endothelioma of bone from osteogenic sarcoma was the peculiar radiosensitiveness of the former in contrast to the relative resistance of the latter. To one who has had sufficient experience this feature is so striking and, on the whole, so uniform that it constitutes a most valuable point by which these two varieties of tumor can be distinguished. As time goes on, the relative radiosensitiveness of different varieties of tumor bids fair to assume an increasingly important rôle in the diagnosis and, perhaps, in the classification of tumors arising in the human skeleton. Physicians who are not well versed in radiology often mistake radiosensitiveness and radioresistance as absolute expressions. To them a tumor is either sensitive or resistant to irradiation, and intermediate gradations are not recognized because of lack of experience with this phase of medicine. Experienced radiologists, on the contrary, use these terms-only in a relative sense because they know that, just as different varieties of normal cells vary greatly in sensitiveness to roentgen rays or radium, tumors vary equally in this respect. Moreover, it has been established that the radiosensitiveness of any tumor corresponds to that of the cells of which it is chiefly composed. In the case of a mixed tumor, its sensitiveness to irradiation represents a composite of its cellular elements; when sensitive cells predominate, the degree of sensitiveness is greater than when the proportion of sensitive cells is small. It is clear that the scale of radiosensitiveness of different varieties of neoplasms must, and in fact does, correspond to the degree of sensitiveness of its essential cellular constituents.