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Ordinary electromagnetic (em) fields do not couple significantly with those that underlie gravitation and give rise to inertia, and it is suggested that this is because they are of different field essence and form. It is also suggested that a much stronger electro-gravitic coupling might be accomplished for effective propulsion by conditioning ordinary em fields into configurations that are similar to those which underlie gravitation and give rise to inertia. This paper summarizes theoretical and experimental em field conditioning work.

Cytokine production by peripheral blood mononuclear cells (PBMC) is a sensitive indicator of cytokine-inducing substances which may cross from contaminated dialysate into the blood compartment. The objective of this study was to compare the transfer of cytokine-inducing substances from dialysate contaminated with a culture filtrate from Pseudomonas aeruginosa across dialyzers with low (hemophan) or intermediate ultrafiltration coefficients (modified cellulose triacetate, CTA), under conditions where either 10% plasma or whole blood was circulated in the blood compartment. Eight paired experiments of in vitro dialysis were carried out at 37 degrees C using a countercurrent recirculating loop dialysis circuit with either a new CTA or hemophan dialyzer. 10% plasma in standard tissue culture medium was circulated through the blood compartment and bicarbonate dialysate was circulated in the dialysate compartment. The dialysate was challenged sequentially by log-fold dilutions (10(2), 10(3) or 10(4)) of a Ps. aeruginosa culture filtrate. Samples were drawn from the blood compartment 5 and 15 minutes after each challenge and incubated with suspensions of PBMC in the absence or presence of polymyxin B, in order to block endotoxin. After 24 h at 37 degrees C, total interleukin-1 alpha (IL-1 alpha) was measured by RIA. Although the dialysate contained potent cytokine-inducing substances, there was no significant IL-1 alpha production by PBMC incubated with the plasma mixture from the blood compartment in the majority of experiments with both dialyzers and with each of the three dilutions of the bacterial challenge. Eight experiments were also performed with CTA dialzyers using heparinized whole blood in the blood compartment. Samples of whole blood and dialysate were drawn at baseline, after one hour of dialysis with uncontaminated dialysate and 15 minutes and three hours after dialysis with dialysate contaminated with Ps. aeruginosa filtrate. There was no significant IL-1 alpha production by PBMC isolated from the whole blood 1 h after dialysis with uncontaminated dialysate, and 15 min and 2 h after adding the Ps. aeruginosa filtrate to the dialysate side. In contrast, production of IL-1 alpha by PBMC from the same donors incubated with samples from the dialysate were 263 +/- 50, 1074 +/- 306, 2333 +/- 774 and 2602 +/- 702 pg/2.5 x 10(6) PBMC, respectively at the same four time points. These data suggest that although the Ps. aeruginosa culture filtrate present in the dialysate was a potent inducer of IL-1 alpha, neither dialyzer permitted transfer of cytokine inducing substances from the dialysate into the blood compartment.

The lack of consensus regarding the significance of transmembrane passage of bacterial products across hemodialysis membranes can be related to several methodological differences in the various studies, including the choice of circulating fluid in the blood compartment of the model, nature and concentration of the bacterial products employed to challenge the dialysate compartment and whether cytokine production by PMBC or the limulus amebocyte lysate (LAL) assay was used as the index of transfer and the cytokine used as the read-out. In this study, we examined the production of interleukin-1 alpha (IL-1 alpha), interleukin-1 receptor antagonist (IL-1Ra) and interleukin-8 (IL-8) by peripheral blood mononuclear cells (PBMC) incubated with a Pseudomonas aeruginosa culture filtrate. Further, the effects of 10% autologous human plasma and Polymyxin B sulfate (PmB) on cytokine production by PBMC were also characterized. The results of our study indicate that the Ps. aeruginosa culture filtrate had both PmB suppressible and PmB non-suppressible components and that the addition of 10% human plasma significantly enhanced cytokine production by both PmB suppressible and PmB non-suppressible components. The enhancing effect of plasma was most evident at low concentrations of the filtrate. The inhibitory effect of PmB was most evident in samples cultured in the presence of 10% plasma. There was a direct correlation between the production of IL-1 alpha and IL-1Ra suggesting that both pro-inflammatory cytokines and cytokine-specific inhibitory proteins are concurrently produced. There results have direct relevance to selection of study conditions for in vitro models used to study the transmembrane passage of bacterial products across hemodialysis membranes.

This study compared bereavement experiences of suicide survivors with those of other survivors. The primary focus of investigation was upon grief reactions suggested to be unique to suicide bereavement and upon quality of grief resolution 2-4 years after death. Fifty-seven women and men, between the ages of 24 and 48, who had experienced the death of a marital partner were interviewed. Subjects were assigned to one of four groups by mode of death (suicide, accident, unanticipated natural, and expected natural). Analyses of variance and Scheffe procedures indicated no significant differences among survivors on frequencies of grief reactions considered common to all bereavements. The suicide survivors were significantly different from all others on certain grief measures, including rejection and unique grief reactions. On various other grief measures, significant differences were indicated among the groups of survivors. Four primary conclusions, implications of the findings, and limitations of the study are discussed.

The Wiener functional expansion method for the analysis of nonlinear systems is applied to identify and analyze both nonlinear and linear molecular systems by spectroscopic methods. As the sampling filter (monochromator) of any spectroscopic apparatus may be defined by a Weber-Hermite polynomial, an analysis of the refracted or scattered light by orthogonal polynomials is easily achieved. Time averaging obtains the Weber-Hermite coefficients which permit the characterization of the molecular system with respect to the polarization of the incident and scattered light. In the case of two series of measurements made with incident and emerging light polarized in different directions: the identification of the JonesM matrices for the molecular system irradiated is possible. In the case of three series of measurements made, for example, with incident and emerging light (a) circularly polarized corotating, (b) circularly polarized contrarotating, and (c) plane polarized perpendicular: the identification of the molecular system's McClain invariants related to the vibrational symmetry group for Raman inelastic light scattering is possible. The analysis presents a unified picture of elastic and inelastic light scattering and one-photon and two-photon processes. The apparatus described would detect those instances in molecular systems for which Beer's law does not apply.

We postulate that only linear systems are basic,i.e. irreducible. Any nonlinear system may be resolved into constituent systems such that ultimately only basic interacting linear systems are obtained. TheS-matrix analysis of quantum electrodynamics is formally equivalent to special instances of Duffing's equation. These special instances describe interacting systems of the three-body kind. Three-body interaction is a parametric excitation, in which each of the interacting systems is describle by a wave amplitude equation. Each wave amplitude equation can be related deterministically to quantum theory. The coupling of linear systems may be either continuous or discontinuous. The Klauder phenomenon is an example of discontinuous coupling. Nonrenormalizable field phenomena may be explained as due to the existence of a singularity in the relation of the wave amplitude equation and the exponential peerturbation. The two types of system coupling-continuous and discontinuous-give rise to two separate types of nonlinear transduction. The first is based on the activity of the harmonic oscillator and its theoretically identical to the white-noise analysis. The second is based on the activity of the harmonie oscillator parametrically excited to anharmonicity and is theoretically identical to the shot noise analysis. Together, the two types of system analysis provide a general theory of nonlinear phenomena.

The linear dischroism in the radial direction of solution flow over a velocity gradient of approximately 10–850 sec−1 has been obtained for human umbilical cord hyaluronic acid at concentrations of 0.1, 0.0666, and 0.0333%, and pHs 6.0, 6.5, 7.0, 7.5, 8.0, and 8.5, at constant ionic strength 0.1. The redial flow briefingenece has also been obtained for these solutions by a Kroing-Kramers transformation. The data indicate a change in linear dichroism and optical anisotrophy as a function of pH, with most of the transition across the physiological range: 7.0–7.5. Previously reported axial flow birefringence and extinction angles indicating a similar pH-dependent structural change in hyaluronate solutions across the same pH range are thus confirmed with other instrumentation. The radial birefringence measurements reported here, together with the axial measurements previously reported, permit a complete description of the refractive index tensor for each of the six solutions. The interpretation of these tensors in terms of the Peterlin modification of the Rouse-Zimm Gaussian subchain theory results in a description of entropy production induced by changes in system pH.

The addition of ammonium hydroxide to a weakly acidic oxazine perchlorate dye produces a color change by means of a deprotonation mechanism in which the hydroxyl radical abstracts a loosely bound proton, leaving the positively charged ammonium cation to counter balance the perchlorate anion. This reaction produces significant absorption and fluorescence band shifts which can be accounted for by a semi-classical oscillator model predicting two dichroic electronic band systems associated with this dye. Peculiar wavelength excitation dependent fluorescence band shifts are attributed to overlapping triplet states simultaneously excited.

The dynamics underlying quantum theory for macroscopic physics is based on the topology of flows on a cusp catastrophe obtained by the minimization of a potential function. By this relation at a known potential energy, a causal explanation of the quantum effect is provided.

In a previous paper, a deterministic account of the dynamics underlying the quantum-mechanical wave amplitude equation (Schrodinger’s equation) was given. In the present paper, that topological analysis is extended to a deterministic interpretation of the commutation relations of quantum theory and Planck’s constant is redefined as a resonance coupling condition for linearly progressing and circularly orbiting particles. In the case of parametric excitation coupling of two linearly progressing particles, a temporal coupling condition is required, not Planck’s constant. It is demonstrated that, when described in four-parameter form, quantum-mechanical systems behave in a way identical to the hypercomplex systems called, by Hamilton, quaternions. The analysis provides a physical picture of quantum mechanics and quantum electrodynamics.

Analysis of the Raman spectra of NAD and NADH indicates that the intensity characteristic of a band at ˜ 1400 cm−1, assigned to the nicotinamide ring vibrations, demonstrates interactive effects correlated with conformational changes of NAD in basic phosphate solutions and NADH in acid phosphate solutions. The Raman lines of these dinucleotides are discussed with respect to the spectra of the individual bases and previous Raman studies of nucleotides. The data reported provide the groundwork for future application of the Raman technique to NAD and NADH reactions.

A new method is presented for studying the tertiary and possibly the secondary structure of a biopolymer, which is applied to the pH-dependent structural transition of potassium hyaluronate solutions. The method involves a new application of Dirac dispersion theory polarization dependence measures to isotropic and anisotropic components of the refractive index ellipsoid. Changes in the dipole moment may also be observed by this method. The pH-induced changes in viscosity and optical properties of hyaluronic acid previously reported appear to be dependent on changes in secondary and tertiary structure.

The solvent-subtracted Raman spectrum of hyaluronic acid is reported. The spectrum is unchanged by (i) variations in the pH of the solution 6.0–8.5, when buffered at constant ionic strength 0.1, and (ii) changes in temperature 10–50°C. As rheological, flow birefringence, and linear dichroism studies of hyaluronate solutions indicate a large and abrupt structural transition across the physiological pH range 7.0–7.5, the negative finding reported here is of considerable interest in contrast with those previous studies. When considering the polysaccharides in general, as precise rheological, flow birefringence and linear dichroism data are only available for hyaluronic acid, the present finding is of interest for hyaluronic acid considered as a model polysaccharide system exhibiting elasticity. The result reported here is discussed within the context of, on the one hand, the possible limitations of the Raman technique which is a probe of g-state vibrational modes and, on the other hand, the possible extension of the Raman technique to probing oriented (stressed) samples. As a previous study demonstrated a small limiting birefringence but a large limiting extinction angle with minimum change in monomer anisotropy for these solutions, the suggestion is favored that the abrupt structural transition across the physiological pH range previously reported is due to long-range Van der Waals interactions.

A method of defining structural information in Hilbert space is described. Instead of commencing an information theory analysis with a simple signal and progressing to an n‐dimensional information space, the reverse procedure can be followed: the signal is defined completely in both real and imaginary spaces, and is then represented as a dimensionless number in Hilbert space. Thus, a signal can be analyzed into a Hilbert space measure of information. This measure has similarities to the relativity of states of Everett's (1957) reformulation of quantum mechanics involving observer‐observed interaction. Whereas Everett's theory deals with the totality of all possible ways in which a state function can be decomposed into the sum of products of state functions for subsystems of the overall system, the theory presented here deals with the totality of possible ways in which a Hilbert space measure of signal state can be decomposed by signal definition into reciprocally related measures of the state for subsyste...

This report describes differences in the polarization of the resonance Raman lines at 1317, 1142 and 1012 cm−1 with respect to an exciting wavelength (5730 A), which is within the long wavelength absorption region, for human normal hemoglobin AA versus sickle cell hemoglobin AS. The evidence indicates that the NCa band region differs in the two hemoglobins. These differences may be related to the differences in dipole moment between normal and sickle cell hemoglobin originally reported by Pauling.1 The usefulness of the resonance Raman technique in providing additional microscopic information in a study of abnormal hemoglobins is discussed.

The purpose of this article is to develop the concept of Legendre's differential operators, which are constructed from both ascending and descending operators. These operators are anticommutative except for the lowest eigen‐value l = 0. The application of Legendre's differential operators to linear differential equations is also discussed.

X-ray small-angle scattering of human normal and sickle cell deoxyhemoglobin in aqueous solution was measured at various concentrations, including those approximating the intracellular. The calculated radius of gyration, determination of the overall shape, and Soule-Porod plots all indicate a concentration-dependent difference in strength of interparticle forces between normal and sickle cell samples at high concentration.

The generalization of Bessel's equation to functions of order zero was investigated by Sharpe and applied in the theory of the reflection of sound by a paraboloid. Here, a modification of Sharpe's differential equation to express both the spherical Bessel's equation and Bessel's (cylindrical) equation for functions of order zero is introduced. The generalization of the modified spherical Bessel's. equation to functions of order zero is also discussed.

The density matrix approach to the constitutive relation between electric fields and the current density in organic polymers is compatible with a nonlinear transport equation. The derivation of such an equation is fundamental to any understanding of conduction in submicron devices, in organic polymers and in multiple quantum well structures—which may be considered the ultimate submicron devices—and also to understanding the nonlinear optical properties of those same polymers and materials. As a theoretical platform for such a derivation, physical models are introduced based on the long Josephson junction and the nonlinear line of pendula. A nonlinear transport equation is presented based on a density matrix formalism and a nonlinear Hamiltonian for charge transport in organic conductors. The equation can describe both local and displacive transitions and gives a physically intuitive picture of the concept of off-diagonal long-range order and Bose-Einstein condensation.

Hyaluronic acid transduces a very gentle pressure into an electrical potential. Such pressure, depending on its direction, changes the optical rotary dispersion properties of the salt, either increasing the rotation in the direction already shown by the unpressured salt or changing and increasing the rotation in the opposite direction. These findings have implications for understanding the funtion of the cochlear and vestibular fluids, renal function, and the approximation to frictionless motion of normal joints.

A possible explanation for the necessary and sufficient irradiation to produce the controversial Comorosan effect is discussed. Using a modified quantum theory requiring a definition of the relation of four parameters of a light signal instead of the usual two, the lack of superposition of irradiating sources is accounted for as well as the ineffectiveness of all parts of the total visible spectrum. The most effective average wavelength for obtaining the effect is unique merely because of the appropriateness of the bandwidth of the filter. Changing the filter bandwidth in a way related to a change in the average wavelength should produce the effect at other average wavelengths. The storage of energy within the irradiated substance is considered to be due to either a resonance effect with photon annihilation or a Raman effect with photon scattering.

The anharmonic oscillator theory is applied to the nonuniformly doped, electrically conducting, trans-polyacetylene (CH)x chain, as well as the long Josephson junction with varying bias current. The variations in bias current determine the number of fluxons on the Josephson junction. As the soliton is the equivalent of the fluxon in trans-(CH)x, the average voltage on the (CH)x chain is demonstrated to be a function of propagation velocity and the number of solitons contained on it.

An electrical potential develops between the ends of a column of hyaluronic salt solution displaced from a resting position by gentle pressure. A previous study demonstrated that such displacement changes the optical rotary dispersion properties of the salt, either increasing the rotation in the direction already shown by the salt before displacement or changing and increasing the rotation in the opposite direction, depending on the direction of the displacement. The present investigation demonstrates that the loss of bound water component across a membrane separating the solution and water is corelated with the extent of the column displacement. In addition, a return of the column to the position before displacement is correlated with a return of the water component across the membrane-but not at the same rate as the exodus. The data seem consistent with the hypothesis that the hyaluronic acid salt, when strained, adopts a less entropic configuration, releasing bound water and thus increasing the entropy of water component. This change in the distribution of entropy is reversible; i.e., Eddington's "time's arrow" is reversible with respect to the water component of the solution.

The topic of this paper is how different forms of acoustical information may be measured. The specific problem addressed is how information is transferred from a three-dimensional source of longitudinal waves to a one-dimensional vibrating membrane. In previous papers1,12, the author has demonstrated through the derivation of different forms on informational 'quanta' that the modulating envelopes for the wave packets representing these quanta are functional solutions to the Weber equation (the Helmholtz equation in parabolic cylinder coordinates). The geometrical structure described by the Weber equation suggests a resonance effect existing between an 'angular momentum' involving an 'azimuthal quantum number' and one involving a 'magnetic quantum number' in analogy with structural chemistry formulations12. In the present paper, the geometrical formulation is carried further. A sound source is commonly spherical, therefore solutions are found for the wave equation in spherical coordinates, giving a precise meaning to the 'azimuthal' and 'magnetic quantum number' analogy. These informational wave packets are then translated into a one-dimensional representation because of the nature of the receiver (the tympanic membrane). The difference between descriptions of electromagnetic and acoustical forms of energy is presented as consisting in the number of variables remaining constant in the acoustical formulation (as compared with the electromagnetic) but not in the basic geometrical formulations, which are primary.

Chemical parametric excitation is presented as the fundamental mechanism of energy transfer. Together with the Franck-Condon principle, it provides a mechanically sound explanation for enzymatic reaction, nerve excitation, muscle contraction, and electron transfer at a basic level. Intermediate between macroscopic models of membrane asymmetry and molecular models, the new model rests on a systematic approach, proposed here, to organizational aspects of the energy transfer processes. In support, a derivation is given of the chemical analog of the Manley-Rowe power conservation relations for parametrically excited electrical networks. This extension to chemical systems indicates for the first time an explanation of power flow directionality and delegates a pumping role to the enzyme. The generalized Manley-Rowe relations are suggested to be a universal law of nature. In such case, nonlinearity could be attributable to the coupling of three systems by these generalized Manley-Rowe conditions relating flows/reactions/oscillations--even though separately each system might be described by linear (Onsager) relations.

Molecular control is the efficient transfer of energy to a molecular system for purposes of useful work, whether the energy originates from electromagnetic field or photon, electron, or phonon. The transferred energy may be used in any purposeful way and may serve, for example, in increasing biocatalysis in reactors dedicated to bulk chemical production, in the formation of proton gradients across membranes, or in radiation-induced reactions. It is thus evident that, given this goal, one requirement is an understanding of the periodic and quasiperiodic behavior of molecular systems to ensure that the transferred energy is not dissipated. In contrast, the molecular system should not be of the kind that treats the energy stochastically by intramolecular randomization (Noid et al., 1981), because the transferred energy is then lost for useful work purposes.

A complete polarization study of human oxy- and carbonmonoxyhemoglobin A and S is reported for backscattered light in the resonance Raman light scattering situation with excitations in the long wavelength region, wavelength = 4579 A and 5815 A, and excitation in the short wavelength region, wavelength = 4579 A and 4880 A, as comparison. All four polarization components of the scattered light with respect to the two polarization conditions of linearly and circularly polarization of the incident light were measured. These were: (1) parallel; (2) perpendicular; (3) corotating; and (4) contrarotating. Keywords: Hemoglobin; Porphyrin; Magnetic resonance; Resonance raman light scattering; Polarization measurement.

A sinusoidal signal is generally considered the simplest auditory signal. It is, indeed, a simple signal. However, it does not follow that a complex analysing device, like the cochlea, should treat a simple signal in a simple way. Indeed, a simple signal may appear to be complex when viewed from the standpoint of the device considered. Such an observation becomes cogent when one is attempting to discover the analysing capabilities of a device such as the cochlea, which appears designed to handle signals more complex than a sinusoid or multiple sinusoids.

The flow birefringence and extinction angle over a velocity gradient range of approximately 5–100 sec−1, and the zero shear-viscosity have been obtained from human umbilical cord hyaluronic acid at concentrations of 0.25, 0.125 and 0.0625%, and pHs 6.0, 6.5, 7.0, 7.5, 8.0, and 8.5 and constant ionic strength 0.1. The data indicate a large change in optical anisotropy as a function of pH, with most of the transition in the pH range 7.0–7.5, i.e., across the physiological range. The sign of the anisotropy changes between pH 8.0 and 8.5. These results, together with changes in the extinction angle and intrinsic viscosity as a function of pH, suggest a pH-dependent structural change in the system. Due to the abruptness of the transition, as evidenced by the intrinsic viscosity and flow birefringence, it is probable that the structural transition is cooperative. If the data are interpreted in terms of the Rouse-Zimm Gaussian subchain theory, a modification of the model in terms of the Haller-Cerf concept of internal viscosity is required. Thus, the demonstrated properties of hyaluronate solutions indicate a system with memory of stress. Due to the presence of large concentration effects discernible in the extinction angle measurements, hyaluronic acid probably exists as a network in solution. The results are discussed with respect to the mechanoelectrical transducing properties of hyaluronates and stress-dependent changes in ORD already reported.

The theory of cancer induction of ultimate carcinogens by parametric excitation is presented. Attention is drawn to the requirement of an energy transfer in perturbing DNA. The concept of energy transfer by resonance is rejected in favor of energy transfer by parametric excitation of which resonance is a special case. The result, reported here, is a remarkable agreement between the Raman vibrational bands of these ultimate carcinogens, various hypochromic bands of DNA and the predictions of parametric excitation theory. This result suggests that the peculiar relation of an ultimate carcinogen and DNA results in parametrically induced energy transfer in the vibrational mode. The problem, then, of cancer induction becomes one of analytical mechanics.

The phthalocyanines, both metal-free and metal-substituted (Fig. 1), are well known as gas absorbers and useful as ambient vapour sensors1–5. The increase in conductivity which occurs on irradiating phthalocyanine films with light (the photovoltaic effect) is a relatively slow diffusion-controlled process6–9. We report here the modulation of electrical conductance by circularly, as opposed to linearly, polarized light of phthalocyanine films sublimed onto an interdigital electrode surface [metal-semiconductor-metal (MSM) structure]. The influence of an adsorbed electron acceptor, the oxygen molecule, in creating the p-type semiconductor has been investigated. The underlying mechanism of the conductance change involves change of the Fermi level of the phthalocyanine electrode system by circularly polarized light acting as an effective magnetic field in an inverse Faraday effect.

Es wurden die mikrophonische Potentiale und Summierungspotentiale der Ohrschnecke mit elementar-akustischen Signalen (Wellenpaketen) untersucht. Offenbar wird zu einem Gesamtbild der Ohrschneckenpotentiale eine Vier-Parameter-Analyse der akustischen Signale benotigt.

The boundary conditions for the minimum elementary signal defined: f0 t0 = ΔfΔt= 1/2 (where f0 is signal midfrequency, t0 is signal midperiod. Δf is signal bandwidth, and Δt is signal duration) also describe the topologically defined condition known as either (i) a critical point, (ii) a singularity in mapping one manifold into another, (iii) a local potential fluctuation, or (iv) a flow on a cusp catastrophe. An elementary signal, or any quantum, is a limit cycle or oscillation hysteresis defined within an area of instability of a precisely defined mapping plane. The collection of unstable maps of the potential function, from which the elementary signal is derived, defines those instances in which quantum theory is applicable. Thus, a wave event cannot become infinitely small and still be meaningful, i.e., informationally relevant. This result provides an explanation for parametric excitation, as well as a tool for the study of cochlear fluid mechanics.

Circularly polarized light in the long-Wavelength absorption region for ferrocytochrome c (5500A) produces increased scattering which is present neither with linearly polarized radiation nor with radiation in the short wavelength region (ca.5100 A).

The neural response of neurons in the medial superior olive was recorded to electrical stimulation of nervous processes in the osseous spiral laminae and also to antidromic stimulation from the inferior colliculi. The osseous spiral laminae were stimulated at the first, second, and third turns. Time of signal arrival differences (Δτ) at the two spiral laminae and also intensity differences (Δi) were varied. It was found that (1) electrical stimulation gives a regular neural response; (2) the neural response to changes in Δτ and Δi is nonlinear; (3) fine latency changes in the neural response can signal changes in Δr and Δi; (4) stimulations of different turns of the osseous spiral laminae (i.e., with different current flows) give different neural responses reflecting the anatomical tonotopic arrangement of the medial superior olive; and (5) changes in Δτ and Δimay be registered by the ratio of the spike count in a short period following the stimulus to the spike count in a longer total period.

The topic of this paper is how different forms of acoustical information may be measured. The specific problem addressed is how information is transferred from a three‐dimensional source of longitudinal waves to a one‐dimensional vibrating membrane. In previous papers [Barrett, TIT J. Life Sciences 1, 129–135 (1971); Acustica (1973), in press], the author has demonstrated through the derivation of different forms of informational “quanta” that the modulating envelopes for the wave packets representing these quanta are functional solutions to the Weber equation (the Helmholtz equation in parabolic cylinder coordinates). The geometrical structure described by the Weber equation suggests a resonance effect existing between an “angular momentum” involving an “azimuthal quantum number” and one involving a “magnetic quantum number” in analogy with structural chemistry formulations [Barrett, Acustica (1973), in press]. In the present paper the geometrical formulation is carried further. A sound source is commonl...

Using elementary signals defined Δf⋅Δt = 12 and f0⋅t0 = 12 (Δf = bandwidth, Δt = duration, f0 = center frequency, t0 = center period), dichotic stimuli were delivered at cats' ears and varied interaurally by differences in intensity (Δi), time of signal arrival (Δτ), and both Δi and Δτ in an attempt to at least approximate a parametric study of neurons in the inferior colliculus in the time available for recording. Changes of Δτ and Δi with either right or left ear leading in some units had noticeable effects on the profile of post‐stimulus time (PST) histograms with increased effects at some delays than at others. The registration of Δτ and Δi is either by a PST histogram profile or by a change in maximum spike count. Changes in the f0 of the Δf⋅Δt signal and of Δt influenced the PST profile indicating not merely a Δi⋅Δτ trade but a Δf⋅Δt⋅Δi⋅Δτ = a constant function. For some units of the inferior colliculus, therefore, a constant response is elicited by a constant product of four stimulus parameters tha...