Double Symmetry Research Articles

Measurement of axially nonsymmetrical refractive-index distribution of-a single-mode fiber by a multidirectional scattering-pattern method

A high spatial resolution, typically 0.2 \sim 0.3 \mu m, has previously been achieved by the proposed by one of the authors for measuring refractive-index profiles of optical fibers. This method, therefore, is especially suitable for measuring the index profiles of single-mode fibers. Described in this paper is the modification of this technique for measuring nonsymmetrical index distributions in single-mode fibers. In the modified method, a two-dimensional index distribution in an axially nonsymmetrical fiber is computed from a set of its forward scattering patterns for different directions of incident light. The distribution to be measured is somewhat restricted, i.e., it must have point symmetry. However, the point symmetry includes double symmetry which holds in most of polarization-maintaining fibers. The spatial resolution is as high as the scattering-pattern method for the axially symmetrical case; in the present experiment the resolution limit is 0.28 μm. Results of computer simulation and measurement are shown.

Microstrip-Slot Coupler Design-Part I: S-Parameters of Uncompensated and Compensated Couplers

Using the even-odd mode analysis of four-port networks with double symmetry, the scattering parameters of the microstrip-slot coupler are derived from the even- and odd-mode parameters of the coupler cross section. The uncompensated coupler and the coupler compensated by extending the slot fines are treated and design specifications are given covering the compensation slot lines. A comparison with experimental data will be given in Part II.

Delta sequences and double symmetry in a yeast chromosomal replicator region

A specific autonomously replicating sequence ( ars2) occurring near the ARG4 locus on chromosome VIII of yeast ( Saccharomyces cerevisiae) has been localized on a 100 base-pair region of DNA. The nucleotide sequence of a 1517 bp † † Abbreviations used: bp, base-pair; kb, 10 3 base-pairs. fragment spanning the ars2 region has been determined. The 100 bp ars2 region contains an 18 bp A + T sequence of perfect double symmetry (alphabetic symmetry superimposed on dyad symmetry). A 0.3 kb repetitive sequence (solo delta sequence) and a tRNA Gln gene are located within the 1517 bp fragment along with ars2. The 100 bp ars2 region may be located within a divergent delta sequence that is oriented in an inverted and nearly tandem position with respect to the solo delta sequence.

Influence of six types of visual structure on complexity judgments in children and adults.

Individuals at five grade levels (kindergarten, Grade 2, Grade 4, Grade 6, and college) made pair-comparison judgments of visual complexity. The influence of the presence or absence of six types of visual structure (double symmetry, vertical symmetry, horizontal symmetry, diagonal symmetry, checkerboard organization, and rotational organization) and of amount of contour were examined. Two general developmental trends were revealed: First, the age at which visual structure initially affected complexity judgments varied with the type of structure, independent of amount of contour, within the range of contour values used. Second, there was a uniform increase in the effect of structure on complexity judgments between the fourth and sixth grades. These results are discussed in relation to possible mechanisms of visual pattern encoding and complexity judgment.

Orientation and symmetry: effects of multiple, rotational, and near symmetries.

Time to detect bilateral symmetry in different orientations was studied for closed polygons with single, double, quadruple, rotational, and near symmetry. In Experiment 1, the orientation of the axis of symmetry was varied. Detection was fastest for vertical symmetry, next fastest for horizontal, and slowest for left- and right-diagonal symmetries. For corresponding orientations, responses were faster to quadruple than double symmetries, and faster to double than single symmetries. Negative responses to nearly symmetric figures produced an orientation effect similar to that for single symmetries. Rotational symmetries showed no orientation effect and took longer to reject than near symmetries. In Experiment 2, subjects looked only for vertical symmetry. Responses were twice as fast as in comparable conditions of Experiment 1. The effect of multiple symmetries was still present, but rotational symmetries were rejected faster than near symmetries. The results are interpreted as supporting a dual process model for detecting symmetry in multiple orientation channels: Observers first select potential axes of symmetry defined by mirror-similar parts and then evaluate specific axes sequentially in a detailed comparison for mirror-identity.

Surface fitting of three-dimensional closed solutions of the restricted three-body problem

The orbits of a family of three-dimensional periodic orbits in the restricted problem of three bodies form a surface. In this paper we determine the equation of this surface in the case of the orbits of double symmetry of the family which emanates from the equilibrium pointL1. This equation is obtained numerically by a least squares approximation method.

Derivation of higher approximations in the problem of special flows in plane laval nozzles: PMM vol. 42, n≗2, 1978, pp. 289–295

The method of expansion in series in self-similar components is used for deriving solutions of gasdynamic equations for some off-design modes of flow in a plane nozzle, particularly in the case when local supersonic zones interlock at the nozzle axis (the Taylor limit flow). Analysis of expansions in self-similar solutions is carried out simultaneously in the stream and the hodograph planes. The first three terms of expansion are determined for the Taylor limit flow in a plane Laval nozzle. In that case the correction terms retain the property of double symmetry about the horizontal and vertical axes that pass through the nozzle center.

Young children's processing of asymmetrical and symmetrical patterns

Dot patterns varying in type of symmetry (double symmetry, vertical symmetry, horizontal symmetry, and asymmetry) were presented tachistoscopically for 200 msec, followed by a patterned mask, to kindergarten, second-grade, and fourthgrade children. All subjects reported symmetrical patterns more accurately than asymmetrical patterns. Double symmetry patterns were reproduced more accurately than vertical symmetry patterns, and vertical symmetry patterns were reproduced more accurately than horizontal symmetry patterns. These results stand in marked contrast to previous research by demonstrating that the ability to process symmetrical relationships evolves early in perceptual development. There was a suggestion that subjects of all ages perceived information about the type of symmetry presented in the display, but there were agerelated differences in subjects' abilities to use this knowledge in constructing their responses. Additionally, analyses revealed no age-related biases toward imposing symmetrical responses on asymmetrical patterns.

Double perturbation theory and symmetry

A formulation of double perturbation theory is described which allows symmetry to be included in those cases where the zero-order hamiltonian does not contain the full symmetry of the problem. As an example we apply the theory to the Epstein-Johnson spin model.

Vibration Anaylysis of Clamped Square Orthotropic Plate

An approximate method is presented for the determination of the natural frequencies and mode shapes of a square orthotropic plate with all sides clamped. The presentation of the clamped plate's frequency in a form analogous to the corresponding frequency of a simply supported plate is postulated, considering the wave numbers as unknown quantities. These are determined from a system of two transcendental equations, obtained from the solution of two auxiliary Levy's type problems. It is shown, that our method reduces to Bolotin's asymptotic method for large wave numbers. The solution is given for the case of equal coefficients of orthotropy and mode shapes with double symmetry. The results are compared with those known from the literature.

The Center Frequency ω<inf>0</inf>and Normalized Curves of Z<inf>0</inf>,<tex>θ_{Z_0}</tex>, γ, θ<inf>γ</inf>, α, β, and Velocity of Propagation for Electrical Transmission Lines

Transmission lines exhibit a center frequency \omega_{0} = \sqrt{(R/L)(G/C)} about which several interesting phenomena can be observed when plotted on log paper. The magnitude of the characteristic impedance manifests double symmetry, with the impedance being greater below this frequency than above, when R/L > G/C , and less if the converse is true. The impedance angle has a mirror symmetry about ω 0 , and is constrained to values between \pm45\deg , with negative values when R/L > G/C . Further, the angle of the propagation functions, α and β, and the velocity of propagation all possess mirror symmetry. γ is asymmetrical. The behavior of all of these parameters is such that each can be presented in a normalized plot of the form ( P(m\omega_{0})/P(\omega_{0}) ) and centered upon ω 0 .

Symmetry, recall, and preference in relation to chronological age

The effects of double, bilateral, horizontal symmetry, and asymmetry on recall and preference were investigated. The Ss were 76 elementary school children. Dot patterns were projected, each for 1.5 seconds; Ss reproduced the patterns. The errors in reproduction were analyzed by a CA × Pattern Mode design. Significant differences ( p < .001) were found between: (a) mean errors for the four modes, averaged over all CA levels; (b) mean errors for CA levels, averaged over modes; and (c) CA × Mode interaction. Multiple comparisons within each age level revealed: (a) double symmetry was decoded at the sixth year of age; (b) bilateral symmetry at the seventh year of age; and (c) horizontal symmetry at the eleventh year of age. A paired-comparisons design revealed similar developmental trends in expressed preference for the four modes.

Magnetic Space Groups and their Irreducible Representations

AbstractIn this paper magnetic space groups are defined. Their irreducible representations are given in terms of the irreducible representations of the group of the k‐vector. The irreducible representations of the double groups and time inversion symmetry are discussed.

Coleoptile of Zea mays and Other Grasses

Whether the coleoptile in grasses is to be interpreted as a single leaf, or as the result of the union of two organs, is still a matter for discussion. SARGANT and ARBER' favor the theory that the coleoptile is the equivalent of a pair of fused stipules. WORSDELL2 substantially agrees, concluding that it is a ligular-like structure formed by the union of stipules. They base their interpretations principally on the presence of the two vascular bundles characteristically present in the coleoptiles of most grasses. These two bundles establish a symmetry in the coleoptile. Recently, however, PERCIVAL3 has shown that in the coleoptiles of an Indo-Abyssinian emmer wheat (Triticum dicoccum Schtibl.) from two to six bundles may be present. He has construed the presence of these several bundles as evidence in favor of the coleoptile being a single leaf, and not in origin. Further evidence in favor of the single leaf theory, as set forth by PERCIVAL in Triticum dicoccum, is supplied by the writer's observations on some I 5,000 seedlings of Zea mays L. The greater number of plants examined represented different strains of the varieties Golden Glow, Ninety-Day Yellow Dent, and Golden Bantam. In addition Dwarf, Liguleless, and Chinese Suckering strains were observed. Certain strains of the Golden Glow variety showed more than two bundles in the coleoptile. Two to five bundles were observed to be present (figs. I-4). These additional bundles destroy the double symmetry of the coleoptile. The position of the bud in the axil of the coleoptile should also be of some significance in determining whether it is a single structure,