Difficulties in Complex Multiplication and Exponentiation

During my study of the iteration of functions of the form $f(z)=z^{\alpha}+c$, where z,c \in \mathbbC, and $\alpha$ is a rational non-integer larger than 2 (\cite{s1}), I encountered a fundamental difficulty in the exponentiation of a complex number. This paper will explore this difficulty and the problems encountered in trying to resolve it using a Riemann surface which is the direct generalization of the polar form of the complex plane. This paper will also answer two questions raised by Robert Corless in his \emph{E.C.C.A.D.} presentation \cite{co}: "Can a Riemann surface variable be coded? What will the operations be on it?" Unfortunately, the addition operation will be incompatible with the Riemann surface structure.Comment: 17 pages, 9 figures (.ps format

Material interactions of the operational SNAP-9A generator

The design of the SNAP-9A generator includes a number of different materials in intimate contact. The possible interactions among the materials and their effect on the postulated re-entry breakup sequence of the generator are discussed. Experimental evidence obtained under static vacuum conditions for all of the interactions possible is presented. (auth

Second Generation of Antisense Oligonucleotides: From Nuclease Resistance to Biological Efficacy in Animals

From efforts to improve the biophysical properties of antisense oligonucleotides by incorporating backbone- or sugar-modified nucleoside analogs, 2'-O-methoxyethyl ribonucleosides 8b were identified as building blocks for a second generation of antisense oligonucleotides. Compounds containing these modifications were demonstrated to combine the benefit of a high binding affinity to the RNA complement with a large increase in nuclease resistance, allowing the use of regular phosphodiester linkages. Chimeric oligonucleotides with 2'-O-methoxyethyl ribonucleosides, 8b, in the wings and a central DNA-phosphorothioate window were shown to efficiently downregulate C-'raf' kinase and PKC-α messenger-RNA in tumor cell lines resulting in a profound inhibition of cell proliferation. The same compounds were able to effectively reduce the growth of tumors in animal models at low concentrations indicating the potential utility of these second generation antisense oligonucleotides for therapeutic applications

The Effect Of Husband Inclusion In Assertiveness Training For Married Women

Purpose. This study examined the effect of husband\u27s inclusion in assertiveness training for married women by comparing groups in which husbands were and were not included. It was predicted that husband inclusion would facilitate assertiveness training and produce a greater increase in the wife\u27s assertion and a greater decrease in her aggression, passivity and passive-aggression. To enhance the generalizability of the assertiveness training program, multiple trainer team effects were investigated.Procedure. Twenty-eight couples were randomly assigned to one of three groups: Couples (husbands and wives trained together); Wives Only (only wives trained); and a No-Treatment Control group. Measures of self-reported assertiveness (Assertiveness Scale for Couples) and behavioral assertiveness (Inventory of Marital Conflict) were obtained from each subject before and after training. Post-Pre treatment difference scores on each of the four scales of each instrument (assertion, aggression, passivity and passive-aggression) were obtained and analyzed using analyses of variance. Pretreatment marital satisfaction was assessed using the Locke-Wallace Marital Adjustment Scale.Review of the Findings. There was no significant difference in pretreatment marital satisfaction between women in any of the three groups. Women in either assertiveness training group showed significant increases in self-reported assertion and significant decreases in self-reported passivity, compared to women in the control group. No training effects were observed on any of the four behavioral measures. There was no significant difference in the increase in self-reported assertion between the two treatment groups. Women in the Wives Only group showed a significantly greater decrease in self-reported passivity compared to women in the Couples group. No trainer team effects were observed. Significant treatment-trainer team interaction effects were found on measures of self-reported assertion and self-reported passive-aggression.Conclusion and Discussion. Inclusion of the husband in the wife\u27s assertiveness training does not produce the increase in effectiveness anticipated. With the husband present, the training is less effective in reducing passivity and equally effective in increasing assertion. One trainer team was significantly more effective in training couples while the other was more effective in training women only, as determined by several measures

Operant conditioning of a small-scale muscle response

Six naive male subjects were reinforced for responses in the 20-30 microvolt range, and two each for those in 10-20 and 30-40 microvolt ranges. Records were taken of 15 min of “settling down,” 15 min of initial operant level responding, 30 min of conditioning, and 45 min of extinction, 30 min with light present and 15 min without. The results were: (1) small-scale muscle potentials from the thenar eminence, in the 10-20, 20-30, and 30-40 microvolt ranges, were conditioned, using pointer movement as the reinforcement; (2) the response rate in adjacent ranges of greater and lesser amplitude also increased during such conditioning and decreased during the subsequent extinction; (3) during conditioning the frequency of response distribution shifted toward the reinforced range; (4) subjects were unaware of the reinforced response; (5) observing a noncontingent moving pointer increased the response rate in the 20-30 microvolt range, but did not lead to conditioning