Discrete Reflection Research Articles

Multiple reflections between rigid curved panels.

If the first reflection from a rigid curved surface hits other panels, or the inside of a concave panel has other specular reflection points, discrete reflections among these multiple reflections change their transfer functions very much. It is already shown that multiple reflections of a geometrical wave and boundary waves are separately calculated between rigid plane panels. An impulse response from a rigid curved panel resembles that of a rigid plane panel. A discrete reflection around the specular reflection point of the first panel is replaced by an equivalent image point source and the second reflection between rigid curved panels is estimated by the first reflection of it. The multiple reflections inside a rigid concave panel with large curvature and the contribution of wide area around the specular reflection point can be also approximately calculated by the equivalent image point source from the strength of the first reflection. These calculated results are compared with measured ones in the time and frequency domains.

Systemic arterial hemodynamics in the diamond python Morelia spilotes.

Studies of pulsatile systemic arterial hemodynamics were conducted in 10 diamond python snakes to test the hypothesis that body shape--through spatial dispersion of peripheral reflecting sites--is an important determinant of impedance patterns and of pulse wave contour. Findings support the hypothesis. Flow patterns in the aortic roots were similar to those in humans, sheep, dogs, rabbits, and guinea pigs, but in contrast to larger animals, little change in flow contour was seen in other arteries. Pressure wave contour was similar in all systemic arteries from which records were taken with no secondary diastolic wave under any circumstances. Impedance patterns at different sites showed none of the fluctuations that in other animals are attributable to discrete wave reflection. Discrete proximal wave reflection at the confluence of aortic arches was minimal. Data are explicable on the basis of widely distributed peripheral reflecting sites--a consequence of the snake's long and tapered body.

VOLUME FORMULA FOR CERTAIN DISCRETE REFLECTION GROUPS IN PU(2,1)

For each discrete reflection group in PU(2,1), found and studied by Picard ([4]), Terada ([8],[9]) and Shiga ([7]), we calculate the volume of fundamental domain in the unit ball in C2.

A FORWARD GENERATED SYNTHETIC SEISMOGRAM FOR EQUAL‐DELAY LAYERED MEDIA MODELS*

AbstractA forward solution for the reflection response of a parallel stratified lossless medium characterized by discrete reflection coefficients and unequal layer delays, for a normally incident pressure source signal, is presented. The notation, which details the reflection history of each wavelet in a response record, facilitates systematic enumeration of all terms in the reflection impulse response model, the determination of compact closed form expressions for amplitudes and delays of multiply reflected wavelets, and the aggregation of dynamic analog groups. An equal delay time constraint on layer thicknesses leads then to the reflection sequence or synthetic seismogram structure as an infinite sum of wavelets by their order of reflection.

Reflection groups and internal-symmetry algebras

It is shown that to discrete Abelian reflection groups in pseudo-Euclidean space there correspond, in spinor index space, non-Abelian groups whose anticommuting elements build up Lie algebras; in particular, two reflections, with respect to orthogonal planes, and their product build up asu2,c algebra. Conditions are given for these «reflection algebras» to beinternal-symmetry algebras (commuting with the Poincare algebras). When covariance with respect to the «extended» conformal group (conformal transformations and reflections) is postulated, the full use of 8-component conformal spinors is necessary. The conformal spinor is either a doublet of canonical Dirac spinors (Dirac basis) or a doublet of conformal Cartan semi-spinors (eigenstates ofΓ7) (semi-spinor basis). The two bases correspond toequivalent representations in index space, but they give rise tophysically nonequivalent spinor equations in Minkowski space: Dirac spinors of the doublet may give rise separately to free particles; semi-spinors do not: they obey coupled spinor equations and they transform into each other for any reversal (including space reversal). The conformal reflection group may generate «internal symmetry algebras»,u2,c for massive spinors,u2,c,L⊕u2,c,R for massless ones. Possible conformal covariant Lagrangians with «internal-symmetry algebras» are discussed. It appears that the simplest conformally covariant interaction Lagrangians may naturally represent weak interactions. Next, the groupO4,4 (orO5,3 orO6,2) containing conformal and Poincare groups as subgroups is studied. Reflection groups inV9 give rise tou4 «internal symmetry algebra», which becomesu4,L⊕u4,R for massless spinors. Theu4 internal symmetry algebra acts onV8 spinors, which may either be quadruplets of Dirac spinors (Dirac basis) or three independent quadruplets of conformal semi-spinors (semi-spinor basis); on these acts au3 algebra orthogonal to theu4 above. It is shown that conformal semi-spinors may not exist as free fields individually in Minkowski space, since they obey coupled equations, but only in systems and precisely an even number (≥2) for bosons and odd (≥3) for fermions. Furthermore, these systems must be singlets of theu3 algebra. The analogy ofV8 spinor properties with leptons, when in the Dirac basis, and with coloured quarks, when in the Cartan semi-spinor basis, is emphasized and discussed.

Subjectively optimal conditions of sound fields for recording and reproducing

Does the high fidelity sound reproduction system itself provides desired hearing conditions in a listening room? That is only a necessary condition, because sound fields in a recording room and/or a listening room affect on subjective preference. Results of subjective preference judgements of the synthesized sound fields reveal following optimal objectives, namely “Principle of Desire” of listeners [Y. Ando, J. Acoust. Soc. Am. 62, 1436–1441 (1977) and Y. Ando, 95th Meeting of Acoust. Soc. Am., Providence, paper JJI]: (1) Sound fields with a smaller value of the interaural crosscorrelation are always judged as preferred (Incoherence at the Two Ears). In order to obtain the small value of interaural cross correlation, the preferred direction of reflections is found in the range centered on ±55° in the azimuth to the listener. (2) The discrete reflection arriving after the direct sound is preferred, so that the initial time delay gap can be determined by the coherence of autocorrelation function of source signals and the level of reflections (Renewal of the Direct Sound). For example, a preferred scale factor for the dimensions of rooms exists for a given music source. Taking these points into consideration, it is possible to design a new sound system from recording to reproducing.

Temperature study of the long period structure of cellulose materials

The low and wide angle X-ray methods have been used to investigate the influence of temperature and pyrolysis time on the supermolecular structure of cellulose tri- and diacetates, nitrocellulose and viscose differing in their thermal prehistory. The study comprised the temperature interval T=180–265° and pyrolysis times of 0·5–20 hr. It is shown that a rise in temperature results in increased intensity of the low angle reflection intensity I 1 although as the time of pyrolysis increases within the interval 200–250°C, the intensity of discrete low angle reflection decreases and disappears. A reversible change in I 1 has been detected in a heating-cooling cycle, whilst at the same time the long period remained constant. The density of amorphous regions has been estimated for different temperatures. It is shown that the increase in I 1 accompanying a rise in temperature is mainly related to density changes in amorphous regions.

The Reduction O(3,1)⊃O(2,1)⊃O(1,1)

We set up a representation of the principal series of the group SL(2, C) in terms of the sequence of noncompact subgroups SL(2,C)⊃SU(1,1)⊃O(1,1). The basis functions are just the cross-basis matrix elements of SU(1, 1) between O(2) and O(1, 1) bases, and we derive much material on these before using them to calculate the representation functions. The latter have two pairs of discrete labels distinguishing between equivalent representations occurring in the reduction, and these are related to two discrete reflection operators that are introduced in order to obtain a maximal Abelian set.

Fibrillar crystals of isotactic polystyrene. I. Morphological aspects

Abstract Fibrillar crystals have been prepared by the crystallization of isotactic polystyrene from stirred solutions in 1,3,5-trimethylben-zene and cyclohexanol. Similar microfibrils have been prepared in the nascent state by the polymerization of styrene in 1,3,5-trimethyl-benzene with a heterogeneous Ziegler-Natta catalyst. The microfibrils varied in width between 140 and 250 A and were characterized by periodic lamellar overgrowths which were believed to give rise to a discrete X-ray reflection having a d-spacing of 90 A. Thermal analysis suggested that high growth temperatures favored greater crystal perfection. During crystallization from stirred cyclohexanol solutions, a fractionation of high molecular weight chains occurred which was more efficient at higher crystallization temperatures. In comparison to crystallizations under quiescent conditions, a marked facility of the crystallization process was observed in the formation of stirrer-crystallized and Ziegler-Natta polystyrene. The ease of cryst...

The Line Absorption Spectrum of Gadolinium Ion in Crystals

With a view to determining the dependence upon crystal symmetry and chemical composition of the energy levels in a solid, the absorption spectrum of Gd+++ in a number of different synthetic crystals has been photographed at temperatures between 300° and 20°K. Using the external crystallographic symmetry as an indication of the probable degree of symmetry about the gadolinium ion in the lattice, it is established that the important factor in determining the splitting of the multiplets or the excited levels is the lattice symmetry and not the negative ion except insofar as the negative ion influences the crystal structure, for the spectra of monoclinic gadolinium chloride, bromide, sulfate and selenate are almost identical, but are very different from the spectra of the hexagonal formate, bromate and ethylsulfate. Gadolinium propionate and butyrate evidently have somewhat different internal symmetry from that of the other monoclinic crystals since their spectra resemble much more the spectrum of triclinic gadolinium acetate. The group of compounds including gadolinium trichloracetate, propionate, butyrate, isobutyrate and trichlorbutyrate is similar in that the spectra of all are weak, diffuse, and little resolved even at the temperature of liquid hydrogen. The presence or absence of water of crystallization affects the spectra only slightly. The positions of the multiplets, and the positions of the lines within the multiplets of anhydrous gadolinium formate are much the same as in the ethylsulfate and bromate enneahydrates. The phenomenon of highly discrete selective reflection in the ultraviolet region by three compounds has been observed. A discussion of the nature of the excited states of the gadolinium ion in crystals is presented.