Cinder cone distribution described using cluster analysis and two-dimensional Fourier analysis in the central Transmexican Volcanic Belt, Mexico, and in SE Guatemala and NW El Salvador.

We develop Fourier analysis over hyperbolic algebra (the two-dimensional commutative algebra with the basis e1 = 1, e2 = j, where j2 = 1). We demonstrated that classical mechanics has, besides the well-known quantum deformation over complex numbers, another deformation — so-called hyperbolic quantum mechanics. The classical Poisson bracket can be obtained as the limit h → 0 not only of the ordinary Moyal bracket, but also a hyperbolic analogue of the Moyal bracket.

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Tiling Efflorescence of Expanding Kernels in a Fixed Periodic Array

Communications of the Blyth Institute ◽

10.33014/issn.2640-5652.3.1.marks.1 ◽

2021 ◽

Vol 3 (1) ◽

pp. 13-34

Author(s):

Robert J Marks II

Keyword(s):

Fourier Analysis ◽

Fixed Points ◽

Limit Cycles ◽

Circular Cone ◽

Two Dimensional ◽

Periodic Functions ◽

Fundamental Properties ◽

Art And Architecture ◽

The Trinity ◽

Func Tion

Continually expanding periodically translated kernels on the two dimensional grid can yield interesting, beau- tiful and even familiar patterns. For example, expand- ing circular pillbox shaped kernels on a hexagonal grid, adding when there is overlap, yields patterns includ- ing maximally packed circles and a triquetra-type three petal structure used to represent the trinity in Chris- tianity. Continued expansion yields the flower-of-life used extensively in art and architecture. Additional expansion yields an even more interesting emerging ef- florescence of periodic functions. Example images are given for the case of circular pillbox and circular cone shaped kernels. Using Fourier analysis, fundamental properties of these patterns are analyzed. As a func- tion of expansion, some effloresced functions asymp- totically approach fixed points or limit cycles. Most interesting is the case where the efflorescence never repeats. Video links are provided for viewing efflores- cence in real time.

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Two Dimensional Fourier Analysis

Fourier Transforms ◽

10.1007/978-1-4615-2359-8_7 ◽

1995 ◽

pp. 309-332

Author(s):

Robert M. Gray ◽

Joseph W. Goodman

Keyword(s):

Fourier Analysis ◽

Two Dimensional

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Fourier Analysis of Dielectric Constant in Arbitrarily Shaped Two-Dimensional Grating for Coupled-Wave Analysis

Laser & Optoelectronics Progress ◽

10.3788/lop50.090501 ◽

2013 ◽

Vol 50 (9) ◽

pp. 090501

Author(s):

张强 Zhang Qiang ◽

熊伟 Xiong Wei ◽

荣健 Rong Jian

Keyword(s):

Dielectric Constant ◽

Fourier Analysis ◽

Two Dimensional ◽

Wave Analysis ◽

Coupled Wave

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Cluster analysis in the comparison of two-dimensional chromatograms

Journal of Chromatography A ◽

10.1016/s0021-9673(01)84633-1 ◽

1989 ◽

Vol 466 ◽

pp. 371-378 ◽

Cited By ~ 6

Author(s):

Daniela Heimler ◽

Vieri Boddi

Keyword(s):

Cluster Analysis ◽

Two Dimensional

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The Loyal Traveler: Examining a Typology of Service Patronage

Journal of Travel Research ◽

10.1177/004728759703500401 ◽

1997 ◽

Vol 35 (4) ◽

pp. 2-10 ◽

Cited By ~ 136

Author(s):

Mark P. Pritchard ◽

Dennis R. Howard

Keyword(s):

Cluster Analysis ◽

Discriminant Analysis ◽

Service Providers ◽

Two Dimensional ◽

Composite Measure ◽

The Third ◽

Dimensional Matrix ◽

Repeat Purchase ◽

Clear Support

The first goal of this study was to determine whether Day's (1969) measure of loyalty could be extended to better understand travel service patronage. Findings provide clear support that this composite measure, of repeat purchase and loyal attitude, is an effective approach to distinguishing the loyal traveler. A cluster analysis that combined scores on the composite measure from 428 travelers supported a two-dimensional matrix that identified four types of loyalty: true, spurious, latent, and low. This accomplished the study's second purpose by confirming that the four distinct levels of loyalty exist in a variety of service settings. Discriminant analysis was used to achieve the third objective — To identify those characteristics that differentiate the truly loyal patron. The resulting profile found this traveler to be a highly satisfied, symbolically involved consumer drawn to those services that exhibit an empathetic, caring concern for their patrons. These findings generate a much clearer understanding of how service providers can measure and manage their returning patrons.

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Vernier Image Processing: Model and Experiments

Perception ◽

10.1068/v970363 ◽

1997 ◽

Vol 26 (1_suppl) ◽

pp. 110-110

Author(s):

A V Chihman ◽

V N Chihman ◽

Y E Shelepin

Keyword(s):

Fourier Analysis ◽

Visual Processing ◽

Fourier Spectrum ◽

Field Size ◽

Two Dimensional ◽

Frequency Range ◽

Additional Line ◽

Point Spread ◽

Model Predictions ◽

Spread Function

Earlier we proposed a model for visual processing of the optical image of Vernier targets (1996 Perception25 Supplement, 115 – 116) based on Fourier analysis of the image. Our model comprises blurring of the thin Vernier bars by the optical point-spread function followed by calculation of the two-dimensional Fourier spectrum. In our model the processing area for Fourier analysis (the receptive field size) is 5 min arc. For a Vernier target, the contrast energy in the low-spatial-frequency range is different in different orientations, and magnification of the Vernier shift changes the orientation of the oblique Fourier components. To test the model, we carried out experiments in which the stimuli were Vernier lines with additional line distractors orthogonal to the orientation of the oblique Fourier components. Thresholds for detecting Vernier displacements were determined by a 2AFC paradigm and compared with model predictions. The results are consistent with our modelling of Vernier performance as a measurement of oblique components of the 2-D Fourier spectrum.

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Cognitive and Emotional Aspects of Cupping Therapy

Brain Sciences ◽

10.3390/brainsci10030144 ◽

2020 ◽

Vol 10 (3) ◽

pp. 144 ◽

Cited By ~ 1

Author(s):

Minyoung Hong ◽

In-Seon Lee ◽

Yeonhee Ryu ◽

Junsuk Kim ◽

Younbyoung Chae

Keyword(s):

Cluster Analysis ◽

Healthy Volunteers ◽

Cupping Therapy ◽

Emotional States ◽

Two Dimensional ◽

Fear Of Pain ◽

Public Attention ◽

Emotional Aspects ◽

Psychophysical Analysis ◽

Valence And Arousal

Cupping therapy has recently gained public attention and is widely used in many regions. Some patients are resistant to being treated with cupping therapy, as visually unpleasant marks on the skin may elicit negative reactions. This study aimed to identify the cognitive and emotional components of cupping therapy. Twenty-five healthy volunteers were presented with emotionally evocative visual stimuli representing fear, disgust, happiness, neutral emotion, and cupping, along with control images. Participants evaluated the valence and arousal level of each stimulus. Before the experiment, they completed the Fear of Pain Questionnaire-III. In two-dimensional affective space, emotional arousal increases as hedonic valence ratings become increasingly pleasant or unpleasant. Cupping therapy images were more unpleasant and more arousing than the control images. Cluster analysis showed that the response to cupping therapy images had emotional characteristics similar to those for fear images. Individuals with a greater fear of pain rated cupping therapy images as more unpleasant and more arousing. Psychophysical analysis showed that individuals experienced unpleasant and aroused emotional states in response to the cupping therapy images. Our findings suggest that cupping therapy might be associated with unpleasant-defensive motivation and motivational activation. Determining the emotional components of cupping therapy would help clinicians and researchers to understand the intrinsic effects of cupping therapy.

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