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In this paper the following questions are posed and answered with reference to the relation between the input and output signals of a full wave rectifier : (1) Given the mean input and mean output signals what probability density function of input signals achieves the maximum input entropy ? (2) What is this entropy ? (3) How does it compare with the entropy of standard input distributions which achieve the same mean output ? The answer to (1) is a distribution which generalizes the normal distribution by replacing (x2/2σ2) in the exponent by (xv/vMvv), where Mvv is the mean output signal. It is also confirmed that if one orders given distributions either by their entropies or by their variances, then the two orderings will not in general agree. [ABSTRACT FROM AUTHOR]

Three methods for the determination of the free energy δ F1 of the reaction, (CaCO[sub3])[subsolid] + (MgCO3])[subsolid] = [Ca(CO3])[subsolid]d are discussed the method of two triple points, that of combining solubility products and that of combining dissociation pressure curves. The first method, although thermodynamically well founded, fails by irreversibility, and by the third method data of sufficient accuracy are unlikely. The solubility products (L) necessary for the second method may be derived either from solubility or from pH measurements, the results being in good agreement. For dolomite, L[sub25, supD) = (1.26 &plusmin; 0.24). 10[sup-17] is the average of values from the experiments described in this paper and these of KRAMER (1959). The mean value obtained from the solubility and the pH data is δ F[sub1]° = 1720 &plusmin; 280 cal; for L[sub25, supM] the two values 3.43 . 10[sup-S] and 1.3 . l0[sup-7] have been found in both ways. [ABSTRACT FROM AUTHOR]

Yeast alcohol dehydrogenase is inactivated at different rates by the antipodes of α-iodopropionic acid and its amide; the D (+) antipodes react faster. The influence of coenzyme, substrate and pH on the reaction velocity were investigated. Under all conditions second order kinetics have been observed. Activation parameters for the alkylation of the SH groups with the different antipodes were calculated from the temperature dependence of the reaction rates. Large differences in the activation enthalpies (ΔΔH = 6.8 kcal/mole and 2.3 kcal/mole, respectively) were found for the reaction of yeast alcohol dehydrogenase with the different antipodes of α-iodopropionic acid and α-iodopropionamide. These were compensated for by differences in activation entropy of —18.4 and — 5.6 entropy units, respectively. These results are interpreted by assuming highly dissymmetric surroundings of the reacting SH groups favouring the D (+) antipodes in the transition state of the alkylation reaction. The negative activation entropy indicates that this favourable transition state may be attained only by restriction of the degrees of freedom. The relationship between the stereoselective chemical reactivity and the stereospecificity of the enzyme is discussed. [ABSTRACT FROM AUTHOR]

In this paper we have used the entropy measure of concentration to examine the question whether size disparity among the 500 largest industrial firms has changed during the period 1955-1966. Our results indicate that there has been little or no change in the size disparity and, if anything, size disparity may have declined slightly. [ABSTRACT FROM AUTHOR]

The present study proposes another measure of uncertainty known as entropy or expected information that has been widely used in information theory. It is argued that entropy is more *The Pennsylvania State University, U.S.A. Operations Research, Inc., Leasco Company. The authors are indebted to W. Beranek, J. L. Bicksler, K. Borch, N. Jacobs, and F. Renwick for very constructive comments on earlier drafts of this paper. 1See, for example, LEVY and SARNAT (1970), LEVY and HANOCH (1970), and OSTERGAARD (1971), for surveys on the relative effectiveness of efficiency criteria. 2The basic criticisms about the assumed quadratic utility function have been established in BORCH (1963), PRATT (1964), and ARROW (1965). Similarly the condition that portfolio returns be characterized by a symmetric two-parameter distribution has been analyzed by FELDSTEIN (1968) and HANOCH and LEVY (1969). 3See WHITE (1970) for an excellent review of the measures of collective uncertainty and their limitations. general and better suited for the selection of portfolios than variance. MCGILL (1954) and GARNER and MCGILL (1956), have shown that entropy and analysis of variance are analogous techniques for partitioning variability in metric data. Entropies can be estimated directly from variances when the form of the prior distribution is known. Since entropy can be computed from nonmetric data, entropy analysis is more general.
The construction of mean-entropy efficient portfolios is illustrated by the parallel development of similar portfolios based on the Markowitz full-covariance and the Sharpe single-index algorithms. After a brief review of the rudiments of information theory, a simple illustration of mean-entropy portfolio construction is followed by the comparison of the empirical results from three portfolio selection methods. [ABSTRACT FROM AUTHOR]

Investigates the performance of a combined manual and decision task with discrete uncertainty. Development of a prediction equation for the mean decision component time as a function of the entropy of the choice element; Prediction of the mean total cycle time; Comparison of the experimental mean manual times to a standard derived by the methods-time measurement system of predetermined times.

SHANNON'S measure of uncertainty (entropy) is used to plan a simultaneous search for the extreme of a unimodal function of one variable. A general expression is developed to express the expected uncertainty about the location of the extreme of the function after the N-point function has been evaluated at H points. The optimum locations of these H evaluations are then found by choosing them so as to minimize the expected uncertainty. The method requires that the user assign values to the probability that the extremum lies at each of the N locations. In so doing it enables him to develop a search policy that reflects his prior partial knowledge about the location of the extremum. It is shown that the entropy policy is identical to the min-max policy for the special case of equal initial probabilities. [ABSTRACT FROM AUTHOR]

Using general systems theory it was stated that social groups develop according to the principles of entropy decrease typical of the living organism as an open system. It was assumed that interaction with others and especially with others in an ongoing process such as found in a social group is the expression of energy release on a more complex level. This complexity is possible for the human being, a conceptualizing animal in an environment which is necessarily social due to his long dependency on others. These environmental conditions provide an early learning situation and an enrichment of cues for initiating social activity in future entropy-increasing situations. In order to test these assumptions initially in a laboratory experiment, 38 groups, each consisting of four male college students unknown to each other, were seated in a bare room around a large square table. Each 5 was asked to work on a booklet of problems for 30 minutes while the E left the room and secretly recorded each unit of talking, looking, smiling, and gross unusual behavior or restlessness. One-half of these groups, or 19 control groups, worked on easy-looking problems such as letter cancellation, copying a design, judgment of ads, etc., all of which were workable with an expenditure of constant effort. It was assumed that entropy would not develop in this situation because energy would run smoothly into task solution. Hence there would be fewer attempts at intercommunication. The other half, or the 19 experimental groups, worked on easy-looking problems which were actually difficult or insolvable. Expected entropy increase was here used to predict investment of energy into increased intercommunication and eventually group formation, because this situation was so rigged as to make this form of behavior eminently available, and because it represented a given avenue of entropy decreasing activity on a more complex level. Group formation was measured by sociometric ratings and by analyzing... [ABSTRACT FROM AUTHOR]

Spectral changes on interaction of ribonuclease T1 with a number of substrate analogues have been measured. For guanosine and guanosine monophosphates these changes are the same as those produced by protonation of the guanine chromophore. It is concluded that the guanine ring of the substrate analogues is protonated by ribonuclease T1 in position N-7. Evidence is presented for a similar interaction of the enzyme with the purine ring of adenosine monophosphate. From the magnitude of the spectral changes binding constants have been determined. They decrease in the order guanosine 2'-phosphate guanosine >3'-phosphate> guanosine 5'-phos- phate> guanosine. The temperature dependence of the binding constants has been measured and the changes in enthalpy, free energy and entropy, which occur upon the RNAase T1-ligand interaction, have been calculated. The pH dependencies of the different ligand enzyme complex formations revealed several pKa values (2.5, 3.7, 6.5, 8.5). The pKa values of 2.5 and 6.5 have been assigned to protonations of the ligand. The pKa values of 3.7 and 8.5 have been assigned to specific groups in the active site of ribonuclease T1, which are involved in the recognition of the guanine base. From the pH dependencies of the guanosine monophosphate/enzyme interaction it is concluded that only the monoanionic form of guanosine monophosphate can interact with the enzyme. The nature of binding of guanosine monophosphate to ribonuclease T1 is discussed. It is proposed that the positions N-1 and N-7 of the guanine base are recognized by a basic and an acid group in the active site of ribonuclease T1 and that the monoanionic phosphate moiety interacts with a basic group of the enzyme. [ABSTRACT FROM AUTHOR]

1. The free energy, enthalpy, and entropy of activation of the enzymatically catalyzed mutarotation of glucose have been determined: ΔG* 11.9 kcal/mol, ΔH* 12.8 kcal/mol, ΔS* 3.1 cal × mol-1 × K-1. 2. The pH-dependence of the enzymatic activity has been investigated. The active center of the mutarotase from Escherichia coli contains one functional group (pK 5.5) which in the dissociated form has only a catalytic function, and a second one (pK 7.6) which is responsible for the binding of the substrate. 3. The binding group of the substrate has been determined. By comparing the Michaelis and inhibitor constants of a variety of substrates and inhibitors it is concluded that the substrate is bound to the enzyme over an equatorial hydroxyl group at C-2 of the carbohydrate ring. 4. The products of the enzymatically catalyzed mutarotation have been analyzed by gas chromatography. These experiments show that the mutarotase catalyzes not only the anomerisation but also the ring isomerisation. The result is interpreted as evidence of an acyclic intermediate of the mutarotation of the aldoses. 5. The results are summarized in a reaction mechanism of the enzymatically catalyzed mutarotation. Its characteristic feature is that it describes the action of the mutarotase from E. coli as a base catalysis. [ABSTRACT FROM AUTHOR]

The article focuses on the word association technique to evaluate a psychoanalytically based formulation concerning depression. This formulation indicates that aggression is a major area of conflict for depressed patients. One complex indicator to be investigated will be reaction time (RT) of the word associations. It is generally assumed that an increase in RT indicated disruption of association and is related to focal conflict areas for the individual producing the increased RT. Given these assumptions, RTs may be used to investigate the relations ship between depression and hostility. The covariance analysis was used to control for the effect of response entropy or number of competing responses upon RT. The results of that analysis indicated that RT findings associated with stimulus hostility levels could not be accounted for on the basis of response entropy. It should be noted that the covariance analysis used mean entropy scores for classes of stimulus words since the dependent variable was mean RT scores for classes of stimulus words. An experimental design that would permit a different analysis might have shown entropy to be a more important factor.

Equilibrium adsorption isotherms obtained at 20, 30, 40, and 50°C for dimethylolethyleneurea (DMEU) on cotton fiber from aqueous solutions are characterized by an initial smooth-rising portion, followed by a sharp decrease and nega tive adsorption of DMEU. Data on conductivity and freezing-point depression of water DMEU solutions indicated that the maximum in the adsorption isotherms stem from the associative property of DMEU molecules. The exothermic affinity, enthalpy, entropy, and limiting coarea for the equilibrium adsorption of DMEU are evaluated. From the negative adsorption, the amounts of nonsolvent water preferentially adsorbed at different temperatures are calculated. [ABSTRACT FROM PUBLISHER]

The concepts of a super information source and ensemble averaging are used to estimate the amount of information stored in protein and t-RNA sequences. Specifically applied to cytochrome c and hemoglobins, information measures analogous to those found to be highly significant for DNA pair frequency data ( D vs. R) by Gatlin (1968) prove to be extremely highly correlated with organism complexity. Super source stability and the possible taxonomic utility of the extraordinary clusterings obtained are discussed. A restriction on the construction of ancestral sequences and a possible handle on homology are also detailed. [ABSTRACT FROM AUTHOR]