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Journal articles on the topic 'Regular projections'

Author: Grafiati

Published: 1 September 2023

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1

Takimura, Yusuke. "Regular projections of the knot 62." Journal of Knot Theory and Its Ramifications 27, no. 14 (December 2018): 1850081. http://dx.doi.org/10.1142/s0218216518500815.

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A knot [Formula: see text] is a minor of a knot [Formula: see text] if any regular projection of [Formula: see text] is also a regular projection of [Formula: see text]. This defines a pre-ordering on the set of all knots. For each knot of five or less crossings, the set of all regular projections of it is determined by Taniyama [A partial order of knots, Tokyo J. Math. 12(1) (1989) 205–229]. Thus, the pre-ordering is determined up to five crossing knots. In this paper, we determine the set of all regular projections of the knot [Formula: see text].

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2

Wang, Xingchang, Tao Yu, Kwokwai Chung, Krzysztof Gdawiec, and Peichang Ouyang. "Stereographic Visualization of 5-Dimensional Regular Polytopes." Symmetry 11, no. 3 (March 18, 2019): 391. http://dx.doi.org/10.3390/sym11030391.

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Regular polytopes (RPs) are an extension of 2D (two-dimensional) regular polygons and 3D regular polyhedra in n-dimensional ( n ≥ 4 ) space. The high abstraction and perfect symmetry are their most prominent features. The traditional projections only show vertex and edge information. Although such projections can preserve the highest degree of symmetry of the RPs, they can not transmit their metric or topological information. Based on the generalized stereographic projection, this paper establishes visualization methods for 5D RPs, which can preserve symmetries and convey general metric and topological data. It is a general strategy that can be extended to visualize n-dimensional RPs ( n > 5 ).

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3

Chalmers, Bruce L., and Boris Shekhtman. "Minimal projections and absolute projection constants for regular polyhedral spaces." Proceedings of the American Mathematical Society 95, no. 3 (March 1, 1985): 449. http://dx.doi.org/10.1090/s0002-9939-1985-0806085-4.

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4

Hept, Kerstin, and Thorsten Theobald. "Tropical bases by regular projections." Proceedings of the American Mathematical Society 137, no. 07 (February 18, 2009): 2233–41. http://dx.doi.org/10.1090/s0002-9939-09-09843-8.

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5

Affentranger, Fernando, and Rolf Schneider. "Random projections of regular simplices." Discrete & Computational Geometry 7, no. 3 (March 1992): 219–26. http://dx.doi.org/10.1007/bf02187839.

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6

B�r�czky, Jr., K., and M. Henk. "Random projections of regular polytopes." Archiv der Mathematik 73, no. 6 (December 1, 1999): 465–73. http://dx.doi.org/10.1007/s000130050424.

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7

TANIYAMA, KOUKI, and CHIZU YOSHIOKA. "REGULAR PROJECTIONS OF KNOTTED HANDCUFF GRAPHS." Journal of Knot Theory and Its Ramifications 07, no. 04 (June 1998): 509–17. http://dx.doi.org/10.1142/s0218216598000279.

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We construct an infinite set of knotted handcuff graphs such that the set of the regular projections of the handcuff graphs in the set equals the set of the regular projections of all knotted handcuff graphs. We also show that no finite set of knotted handcuff graphs have this property.

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8

Filliman, P. "The largest projections of regular polytopes." Israel Journal of Mathematics 64, no. 2 (June 1988): 207–28. http://dx.doi.org/10.1007/bf02787224.

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9

Hofmeister, M. "Enumeration of Concrete Regular Covering Projections." SIAM Journal on Discrete Mathematics 8, no. 1 (February 1995): 51–61. http://dx.doi.org/10.1137/s0895480193248186.

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10

Pędzich, Paweł. "Image of the World on polyhedral maps and globes." Polish Cartographical Review 48, no. 4 (December 1, 2016): 197–210. http://dx.doi.org/10.1515/pcr-2016-0014.

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Abstract Application of polyhedrons as image surface in cartographic projections has a tradition of more than 200 years. The first maps relying on polyhedrons appeared in the 19th century. One of the first maps which based on an original polyhedral projection using a regular octahedron was constructed by the Californian architect Bernard Cahill in 1909. Other well known polyhedral projections and maps included Buckminster Fuller’s projection and map into icosahedron from 1954 and S. Waterman’s projection into truncated octahedron from 1996, which resulted in the “butterfly” map. Polyhedrons as image surface have the advantage of allowing a continuous image of continents of the Earth with low projection distortion. Such maps can be used for many purposes, such as presentation of tectonic plates or geographic discoveries. The article presents most well known polyhedral maps, describes cartographic projections applied in their preparation, as well as contemporary examples of polyhedral maps. The method of preparation of a polyhedral map and a virtual polyhedral globe is also presented.

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11

Filliman, P. "The extreme projections of the regular simplex." Transactions of the American Mathematical Society 317, no. 2 (February 1, 1990): 611–29. http://dx.doi.org/10.1090/s0002-9947-1990-0989573-6.

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12

HANAKI, RYO. "REGULAR PROJECTIONS OF KNOTTED DOUBLE-HANDCUFF GRAPHS." Journal of Knot Theory and Its Ramifications 18, no. 11 (November 2009): 1475–92. http://dx.doi.org/10.1142/s0218216509007567.

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A finite set of specific knotted double-handcuff graphs is shown to be minimal among those which produce all projections of knotted double-handcuff graphs. In addition, we show that a double-handcuff graph has no strongly almost trivial spatial embeddings.

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13

Nyrtsov, M. V., and A. A. Domatieva. "Calculation and visualization of distortions in morphographic projections." Geodesy and Cartography 945, no. 3 (April 20, 2019): 26–36. http://dx.doi.org/10.22389/0016-7126-2019-945-3-26-36.

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There are different ways of estimating the distortions that help us find the best cartographic projections and recommend them for a specific range of tasks from mapping the Earth to extraterrestrial mapping. Besides the planets and their satellites there are small bodies in the Solar System. For mapping these bodies it is advisable to use morphographic projections to show their non-spherical shape. These projections were developed by Philip Stooke. He also proposed replacement of a regular reference surface with a phoboid and methods for estimating distortions but practically implemented them on the example of a body with a regular shape approximated by test triaxial ellipsoid with a ratio of axes 4:3:2. In this regard we set the task of developing and implementing the method for determining distortions in morphographic projections for a body with an irregular shape. We used the algorithm of comparison cartographic cell on projection and on phoboid in order to estimate distortion. The object of mapping is Phobos, a satellite of Mars. Phobos is a non-spherical celestial body for which morphographic projections were first applied. Comparing our results by the values of distortions with the results obtained by Philip Stooke we can conclude that using morphographic projections makes less distortion at portraying a phoboid than a test triaxial ellipsoid.

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14

Saitô, Kazuyuki. "The regular completion of a C*-algebra with large projections." Quarterly Journal of Mathematics 70, no. 3 (May 15, 2019): 999–1007. http://dx.doi.org/10.1093/qmath/haz014.

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Abstract When a unital C*-algebra A is prime and has very large projections, it is shown that the regular completion A^ of the algebra A is a simple, wild type III AW*-factor that has no non-zero σ-finite projections. For example, the Weaver algebra, the Crabb algebra and the Katsura algebra are prime C*-algebras that have very large projections. As a corollary, such algebras have no non-zero abelian elements, that is, they are not of type I.

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15

Xu, Xiao-Ming, and Yile Zhao. "J-Self-Adjoint Projections in Krein Spaces." Journal of Function Spaces 2020 (March 16, 2020): 1–7. http://dx.doi.org/10.1155/2020/6725969.

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Let ℋ be a Krein space with fundamental symmetry J. Starting with a canonical block-operator matrix representation of J, we study the regular subspaces of ℋ. We also present block-operator matrix representations of the J-self-adjoint projections for the regular subspaces of ℋ, as well as for the regular complements of the isotropic part in a pseudo-regular subspace of ℋ.

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16

Nyrtsov, M. V. "Mathematical cartography today." Geodesy and Cartography 943, no. 1 (February 20, 2019): 52–57. http://dx.doi.org/10.22389/0016-7126-2019-943-1-52-57.

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For most small bodies of the Solar System shapes the International Astronomical Union recommends to use a triaxial ellipsoid. Today almost all major classes of cartographic projections for the triaxial ellipsoid have been developed. They require systematization, classification and additional research. The archives of libraries accumulated a significant list of paper maps of the Soviet times which are compiled in projections developed in our country. It is necessary to implement those projections in the PROJ.4 library used by GIS. Distortions in map projections can be defined as deformation of a cell. If we imagine that the sphere is covered with a net of regular hexagons then it is possible to estimate distortions in the projection by their deformation on the plane. Now the majority of cartographers use online calculators to define the values required for mathematical cartography. Programs are usually written in JavaScript and require the user to only enter the initial data. These are only some of the problems facing modern mathematical cartography.

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17

TANIYAMA, KOUKI, and TATSUYA TSUKAMOTO. "KNOT-INEVITABLE PROJECTIONS OF PLANAR GRAPHS." Journal of Knot Theory and Its Ramifications 05, no. 06 (December 1996): 877–83. http://dx.doi.org/10.1142/s0218216596000485.

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For each odd number n, we describe a regular projection of a planar graph such that every spatial graph obtained by giving it over/under information of crossing points contains a (2, n)-torus knot. We also show that for any spatial graph H, there is a regular projection of a (possibly nonplanar) graph such that every spatial graph obtained from it contains a subgraph that is ambient isotopic to H.

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18

Lapon, Lieselot, Kristien Ooms, and Philippe De Maeyer. "The Influence of Map Projections on People’s Global-Scale Cognitive Map: A Worldwide Study." ISPRS International Journal of Geo-Information 9, no. 4 (March 26, 2020): 196. http://dx.doi.org/10.3390/ijgi9040196.

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Map projections are required to represent the globe on a flat surface, which always results in distorted representations of the globe. Accordingly, the world maps we observe in daily life contexts, such as on news sites, in news bulletins, on social media, in educational textbooks or atlases, are distorted images of the world. The question raises if regular contact with those representations of the world deforms people’s global-scale cognitive map. To analyze people’s global-scale cognitive map and if it is influenced by map projections, a short playful test was developed that allowed participants to estimate the real land area of certain regions, countries, and continents. More than 130,000 people worldwide participated. This worldwide dataset was used to perform statistical analyses in order to obtain information on the extent that map projections influence the accuracy of people’s global-scale cognitive map. The results indicate that the accuracy differs with the map projection but not to the extent that one’s global-scale cognitive map is a reflection of a particular map projection.

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19

Placidi, G., M. Alecci, and A. Sotgiu. "Angular Space-Domain Interpolation for Filtered Back Projection Applied to Regular and Adaptively Measured Projections." Journal of Magnetic Resonance, Series B 110, no. 1 (January 1996): 75–79. http://dx.doi.org/10.1006/jmrb.1996.0010.

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20

Herrmann, Christian, and Niklas Niemann. "Representations of $*$-regular rings and their ortholattices of projections." Acta Scientiarum Mathematicarum 86, no. 12 (2020): 105–15. http://dx.doi.org/10.14232/actasm-019-837-x.

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21

Ruiz, L. M. Sanchez, and J. R. Ferrer Villanueva. "Note on pointwise contractive projections." International Journal of Mathematics and Mathematical Sciences 16, no. 4 (1993): 817–18. http://dx.doi.org/10.1155/s0161171293001024.

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LetC(X)be the space of real-valued continuous functions on a Hausdorff completely regular topological spaceX. endowed with the compact-open topology. In this paper necessary and sufficient conditions are given for a subspace ofC(X)to be the range of a pointwise contractive projection inC(X).

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22

Sadkane, Miloud, and Roger B. Sidje. "Efficient computation of the spectral projections of regular matrix pairs." Journal of Computational and Applied Mathematics 298 (May 2016): 72–81. http://dx.doi.org/10.1016/j.cam.2015.11.035.

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23

HUH, YOUNGSIK, and RYO NIKKUNI. "REGULAR PROJECTIONS OF GRAPHS WITH AT MOST THREE DOUBLE POINTS." Journal of Knot Theory and Its Ramifications 19, no. 07 (July 2010): 917–33. http://dx.doi.org/10.1142/s0218216510008261.

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A generic immersion of a planar graph into the 2-space is said to be knotted if there does not exist a trivial embedding of the graph into the 3-space obtained by lifting the immersion with respect to the natural projection from the 3-space to the 2-space. In this paper, we show that if a generic immersion of a planar graph is knotted then the number of double points of the immersion is more than or equal to three. To prove this, we also show that an embedding of a graph obtained from a generic immersion of the graph (does not need to be planar) with at most three double points is totally free if it contains neither a Hopf link nor a trefoil knot.

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24

Kabluchko, Zakhar, and Christoph Thäle. "Monotonicity of expected $f$-vectors for projections of regular polytopes." Proceedings of the American Mathematical Society 146, no. 3 (October 6, 2017): 1295–303. http://dx.doi.org/10.1090/proc/13827.

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25

Maehara, Hiroshi. "Orthogonal projections of cubes and regular simplices into a plane." Journal of Geometry 107, no. 3 (August 15, 2015): 567–77. http://dx.doi.org/10.1007/s00022-015-0289-8.

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26

Lalvani, Haresh. "Non-periodic Space Structures." International Journal of Space Structures 2, no. 2 (June 1987): 93–108. http://dx.doi.org/10.1177/026635118700200204.

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An interesting class of two- and three-dimensional space structures can be derived from projections of higher-dimensional structures. Regular polygons and regular-faced polyhedra provide the geometry of families of n-stars from which two- and three-dimensional projections of n-dimensional grids can be derived. These projections are rhombic space grids composed of all-space filling rhombi and rhombohedra with edges parallel to n directions. An infinite class of single-, double- and multi-layered grids can be derived from n-sided polygons and prisms, and a finite class of multi-directional grids from the polyhedral symmetry groups. The grids can be periodic, centrally symmetric or non-periodic, and act as skeletons to generate corresponding classes of space-filling, packings and labyrinths.

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27

Dzhusoeva, N. A., S. Yu Itarova, and M. A. Pliev. "Order Projection in OAr(E,F)." Contemporary Mathematics. Fundamental Directions 68, no. 3 (September 8, 2022): 407–23. http://dx.doi.org/10.22363/2413-3639-2022-68-3-407-423.

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We investigate order projections onto different bands in the space of all regular orthogonally additive operators. In particular, we obtain formulas for calculation of the order projections onto the band generated by a directed set of positive orthogonally additive operators and onto the band of all laterally continuous operators.

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28

Knox, Hugh W. "Emerging Trends in Agricultural-Based Industries in the Northeast." Northeastern Journal of Agricultural and Resource Economics 20, no. 2 (October 1991): 171–73. http://dx.doi.org/10.1017/s0899367x00002993.

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The Bureau of Economic Analysis (BEA) at the U.S. Department of Commerce produces long-term regional projections of income, population, per capita income and earnings, and employment by industry for regions, states, Metropolitan Statistical Areas, and BEA Economic Areas on a regular basis. The projections are prepared every five years and were last published in 1990.

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29

Boas, Harold P., and Emil J. Straube. "Complete Hartogs domains in C2 have regular Bergman and Szeg? projections." Mathematische Zeitschrift 201, no. 3 (September 1989): 441–54. http://dx.doi.org/10.1007/bf01214907.

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30

Sawollek, Jörg. "Embeddings of 4-Regular Graphs into 3-Space." Journal of Knot Theory and Its Ramifications 06, no. 05 (October 1997): 727–49. http://dx.doi.org/10.1142/s0218216597000406.

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Embeddings of 4-regular graphs into 3-space are examined by studying graph diagrams, i.e. projections of embedded graphs to an appropriate plane. New diagrams can be constructed from the old ones by replacing graph vertices with rational tangles, and these diagrams lead to topological invariants of embedded graphs. The new invariants are calculated for some examples, in particular for classes of alternating diagrams of the figure-eight graph. As an application, it is shown that these diagrams have minimal crossing number, which gives generalizations to some of the so-called Tait conjectures.

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31

Hjouj, Fawaz. "Linear Transformation Recognition Using Radon Transform." Journal of Mathematical Sciences & Computer Applications 1, no. 2 (June 10, 2017): 40–47. http://dx.doi.org/10.5147/jmsca.v1i2.90.

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Given two regular functions (images) f and g on R2 where g is formed from f by a general linear transformation, g(x) = f (Ax + b). We present a procedure to determine the transformation ‘parameters’ A and b using Radon projections of f and only two projections of g. We use these projections together with simple facts on matrix vector multiplication to recover the matrix A. The assumptions we have here are: f is nonnegative and A is nonsingular. Commonly used transformations in image processing such as rotation, scaling and others are special cases of our approach.

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32

Bidlingmaier, Scott, and Michael Snyder. "Regulation of polarized growth initiation and termination cycles by the polarisome and Cdc42 regulators." Journal of Cell Biology 164, no. 2 (January 19, 2004): 207–18. http://dx.doi.org/10.1083/jcb.200307065.

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The dynamic regulation of polarized cell growth allows cells to form structures of defined size and shape. We have studied the regulation of polarized growth using mating yeast as a model. Haploid yeast cells treated with high concentration of pheromone form successive mating projections that initiate and terminate growth with regular periodicity. The mechanisms that control the frequency of growth initiation and termination under these conditions are not well understood. We found that the polarisome components Spa2, Pea2, and Bni1 and the Cdc42 regulators Cdc24 and Bem3 control the timing and frequency of projection formation. Loss of polarisome components and mutation of Cdc24 decrease the frequency of projection formation, while loss of Bem3 increases the frequency of projection formation. We found that polarisome components and the cell fusion proteins Fus1 and Fus2 are important for the termination of projection growth. Our results define the first molecular regulators that control the timing of growth initiation and termination during eukaryotic cell differentiation.

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33

Hamouda, Mouna Ben, Colandane Belajouza, and Mohamed Denguezli. "Filiform projections of the vestibular mucosa: What’s your diagnosis?" Our Dermatology Online 12, e (August 28, 2021): e20-e20. http://dx.doi.org/10.7241/ourd.2021e.20.

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29-year-old recently married woman was reffered by her gynecologist to our dermatology department for suspected vulvar condyloma acuminatum. She had no history of any extramarital sexual contacts and her partner was free of any clinical features of genital HPV infections. She was anxious about the origin of her lesions and the risk of her husband’s contamination. She reported burning sensation, irritation and vulvar pain. On clinical examination soft digitate mucous colored papules with a smooth surface were noted at the vulvar vestibule. These papillomatous projections were pearly, uniformly arranged and had separate bases (Fig. 1). Dermatoscopy demonstrated regular and linear pinkish projections arranged in a symmetric distribution. Irregular linear vascular channels were observed (Fig. 2). Figure 1: Clinical aspect: multiple skin-colored filiform and soft projections. Figure 2: Dermatoscopy showing regular and linear pinkish projections arranged in a symmetric distribution. WHAT’S YOUR DIAGNOSIS? ANSWER: Vestibular Papillomatosis Vestibular papillomatosis (VP) is a normal variant of the female genital mucosa [1,2]. It is first described in 1981 by Altemeyer and named pseudocondylomata of the vulva [3]. VP is frequently misdiagnosed as condyloma acuminatum and presents a source of anxiety in patients, aggressive investigations and inappropriate treatment [2]. This entity is most often asymptomatic, but it can be accompanied, as our case, by a feeling of burning, pain or dyspareunia. To avoid the misdiagnosis of VP as genital warts, Moyal-Barranco et al. had proposed five clinical parameters [4]. Unlike condyloma acuminatum, VP is formed by regular, soft and pink-colored papillae arising from a separate base. It is also characterized by the lack of circumscribed whitening on 5% acetic acid application. Dermoscopy can help to differentiate these two conditions by allowing a better identification of these clinical parameters. Linear vessels may sometimes be observed in the transparent core of the finger-like projections [5]. On the other hand, dermoscopy of condyloma acuminatum shows irregular whitish projections with tapering end that arise from a common base and comprise conglomerate vessel. Based on these clinical criteria and the dermoscopic aspect, biopsies will be unnecessary to confirm the diagnosis of VP.

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34

Kadriu, Arbana. "Building an annotated corpus for Albanian using bilingual projections and regular expressions." International Journal of Knowledge Engineering and Data Mining 6, no. 1 (2019): 1. http://dx.doi.org/10.1504/ijkedm.2019.10020367.

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35

Hackett, Conrad, Marcin Stonawski, Michaela Potančoková, Phillip Connor, Anne Fengyan Shi, Stephanie Kramer, and Joey Marshall. "Projections of Europe’s Growing Muslim Population Under Three Migration Scenarios." Journal of Religion and Demography 6, no. 1 (May 6, 2019): 87–122. http://dx.doi.org/10.1163/2589742x-00601002.

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We present estimates of how Muslim populations in Europe increased between 2010 and 2016 and projections of how they will continue to grow under three migration scenarios. If all migration were to immediately and permanently stop – a “zero migration” scenario – the Muslim population of Europe still would be expected to rise from the current level of 4.9% to 7.4% by the year 2050 because Muslims are younger (by 13 years, on average) and have higher fertility (one child more per woman, on average) than other Europeans. A second, “medium” migration scenario assumes all refugee flows stopped as of mid-2016 but that recent levels of “regular” migration to Europe will continue. Under these conditions, Muslims could reach 11.2% of Europe’s population in 2050. Finally, a “high” migration scenario projects the record flow of refugees into Europe between 2014 and 2016 to continue indefinitely into the future with the same religious composition (i.e., mostly made up of Muslims) in addition to the typical annual flow of regular migrants. In this scenario, Muslims could make up 14% of Europe’s population by 2050. Refugee flows around 2015, however, were extremely high and already have begun to decline as the European Union and many of its member states have made refugee policy changes.

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GUANELLA, ALEXIS, DANIEL KIPER, and PAUL VERSCHURE. "A MODEL OF GRID CELLS BASED ON A TWISTED TORUS TOPOLOGY." International Journal of Neural Systems 17, no. 04 (August 2007): 231–40. http://dx.doi.org/10.1142/s0129065707001093.

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The grid cells of the rat medial entorhinal cortex (MEC) show an increased firing frequency when the position of the animal correlates with multiple regions of the environment that are arranged in regular triangular grids. Here, we describe an artificial neural network based on a twisted torus topology, which allows for the generation of regular triangular grids. The association of the activity of pre-defined hippocampal place cells with entorhinal grid cells allows for a highly robust-to-noise calibration mechanism, suggesting a role for the hippocampal back-projections to the entorhinal cortex.

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37

Bauschke, Heinz H. "The composition of projections onto closed convex sets in Hilbert space is asymptotically regular." Proceedings of the American Mathematical Society 131, no. 1 (May 9, 2002): 141–46. http://dx.doi.org/10.1090/s0002-9939-02-06528-0.

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38

Anusha, Tanneru, Nedunuri Sushma, M. B. Sai Rohit, and A. Akhil. "Creating Financial Statements For Start-Ups." Shanlax International Journal of Arts, Science and Humanities 8, no. 1 (July 2, 2020): 104–14. http://dx.doi.org/10.34293/sijash.v8i1.2391.

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This paper represents the sample of entrepreneurs who are in the process of starting a business. At investigates the determinants of financial projections and statements in start-ups. The predictions information in economics is consistent. There is a positive association frequency of financial statement preparation concerning the use of outside funding, level competition, and venture scale. There are alternative influences and suggestions that benefit in reducing competition and uncertainty in fundamental variations to prepare financial statements. For instance, cash statements are more important for start-ups, and frequency varies among different financial statements with products in earlier stages of development and with greater competition. In contrast to this financial statements projections and regular forecasts of sales by start-ups are positively associated with the importance of intangible investments such as parents, research, and development. The start-ups in high –tech industries are used for projections.

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39

Djukic, Mirko, Jelena Momcilovic, and Ljubica Trajcev. "Structure and use of the medium term projection model in the National Bank of Serbia." Ekonomski anali 56, no. 188 (2011): 32–61. http://dx.doi.org/10.2298/eka1188032d.

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Medium-term projections are an important element of the decision making process in the inflation-targeting regime that the National Bank of Serbia has been implementing for the past several years. The main goal of medium-term projections is to project the policy rate path that will ensure that inflation in the coming period moves close to the targeted inflation rate. The most important tool for medium term projections is a new Keynesian macroeconomic model, which is a set of equations aiming to describe the price formation mechanism in Serbia and the transmission channel of monetary policy to prices. The model is comprised of four main behavioral equations for inflation, exchange rate, output gap, and policy rate, and of a number of side behavioral equations and identities. The model in the current form has been used since the end of 2008 and is subject to regular adjustments and improvements.

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40

Nanayakkara, Asiri, and Chula Abayaratne. "Identification of semiclassical chaos in two-dimensional PT-symmetric systems." Canadian Journal of Physics 81, no. 6 (June 1, 2003): 835–46. http://dx.doi.org/10.1139/p03-052.

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Identification of regular and chaotic motions of two-dimensional PT-symmetric complex systems was investigated. New definitions have been introduced to study properties of trajectories in complex phase space. Projections of these trajectories on complex x- and y-planes, Lyapunov exponents, and surfaces of section have been used for identifying regular and irregular (chaotic) motions in complex phase space. Quantum level spacing distributions of these systems have also been calculated for finding out the connection between regular and irregular states with standard distributions such as Poisson and Wigner distributions. It has been found that the PT-symmetric complex systems behave in the same way as the real systems. PACS No.: 05.45.Ac

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Hassan, Boulchahoub, Rachiq Amina, Labriji Amine, Labriji Elhoussin, and Mohamed Azouazi. "A regexcriteria API to complete the power of regular expressions engine." International Journal of Electrical and Computer Engineering (IJECE) 9, no. 4 (August 1, 2019): 3185. http://dx.doi.org/10.11591/ijece.v9i4.pp3185-3193.

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Regular expressions are heavily used in the field of computer programming. They are known by their strength to search or replace parts of strings according to a given structure (mails, phone, numbers, etc.). Currently regular expressions are only used to search for some patterns or to make some substitutions in strings. However, the need may be wider than that when it comes to order the results of a regular expression or to group them according to some criteria. Developers are always called to analyze the results of a regular expression by doing some restrictions such as (equal, not equal, between) or some projections like (maximum, average, grouping by ..) or sorts. Unfortunately, to do these treatments, the developer must implement his own algorithms which cost him a remarkable effort and a waste of time. We propose in this paper an API called RegexCriteria inspired from Hibernate Criteria to support developer while analysing the results of a regular expression.

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42

DOMERGUE, MICHEL, and PAUL DONATO. "Integrating a weight system of order n to an invariant of (n−1)-singular knots." Journal of Knot Theory and Its Ramifications 05, no. 01 (February 1996): 23–35. http://dx.doi.org/10.1142/s0218216596000035.

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Starting from a Weight-System denoted by P and defined on the n-Chord-Diagrams with values in an arbitrary Q–module, we give an explicit combinatorial formula for an invariant of (n–1)-singular knots which has P as its derivative. The formula is defined for regular knot projections. Its invariance under singular Reidemeister moves is then proved.

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MARNELIUS, ROBERT, and NICLAS SANDSTRÖM. "PHYSICAL PROJECTIONS IN BRST TREATMENTS OF REPARAMETRIZATION INVARIANT THEORIES." International Journal of Modern Physics A 16, no. 17 (July 10, 2001): 2909–44. http://dx.doi.org/10.1142/s0217751x01004177.

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Any regular quantum mechanical system may be cast into an Abelian gauge theory by simply reformulating it as a reparametrization invariant theory. We present a detailed study of the BRST quantization of such reparametrization invariant theories within a precise operator version of BRST which is related to the conventional BFV path integral formulation. Our treatments lead us to propose general rules for how physical wave functions and physical propagators are to be projected from the BRST singlets and propagators in the ghost extended BRST theory. These projections are performed by boundary conditions which are specified by the ingredients of BRST charge and precisely determined by the operator BRST. We demonstrate explicitly the validity of these rules for the considered class of models.

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44

Kiderlen, Markus, and Daniel Meschenmoser. "ERROR BOUNDS FOR SURFACE AREA ESTIMATORS BASED ON CROFTON’S FORMULA." Image Analysis & Stereology 28, no. 3 (May 3, 2011): 165. http://dx.doi.org/10.5566/ias.v28.p165-177.

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According to Crofton's formula, the surface area S(A) of a sufficiently regular compact set A in Rd is proportional to the mean of all total projections pA (u) on a linear hyperplane with normal u, uniformly averaged over all unit vectors u. In applications, pA (u) is only measured in k directions and the mean is approximated by a finite weighted sum bS(A) of the total projections in these directions. The choice of the weights depends on the selected quadrature rule. We define an associated zonotope Z (depending only on the projection directions and the quadrature rule), and show that the relative error bS (A)/S (A) is bounded from below by the inradius of Z and from above by the circumradius of Z. Applying a strengthened isoperimetric inequality due to Bonnesen, we show that the rectangular quadrature rule does not give the best possible error bounds for d =2. In addition, we derive asymptotic behavior of the error (with increasing k) in the planar case. The paper concludes with applications to surface area estimation in design-based digital stereology where we show that the weights due to Bonnesen's inequality are better than the usual weights based on the rectangular rule and almost optimal in the sense that the relative error of the surface area estimator is very close to the minimal error.

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45

Ljeskovac, M., D. C. M. Dickson, S. Kilpatrick, A. S. Macdonald, K. A. Miller, and I. M. Paterson. "A Model Office Investigation of the Potential Impact of AIDS on Non-linked Life Assurance Business." Transactions of the Faculty of Actuaries 42 (1990): 187–276. http://dx.doi.org/10.1017/s0071368600009976.

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The aim of this paper is to use a model office to examine the potential impact of AIDS on non-linked life assurance business in the UK.The subject of AIDS continues to stimulate a large amount of research. The UK actuarial profession has been kept informed by the regular Bulletins [1-5] from the Institute of Actuaries AIDS Working Party (the “IAWP”). Using a model developed by A. D. Wilkie [6], the IAWP examined the possible spread of the infection amongst male homosexuals and produced tables of additional mortality. The most recent Bulletin (No. 4), published in March 1989, updated these projections in the light of new data, and we have based our investigations principally upon these more recent projections.

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Rauschning, Jan, and Peter Slodowy. "An Aspect of Icosahedral Symmetry." Canadian Mathematical Bulletin 45, no. 4 (December 1, 2002): 686–96. http://dx.doi.org/10.4153/cmb-2002-061-6.

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AbstractWe embed the moduli space Q of 5 points on the projective line S5-equivariantly into (V), where V is the 6-dimensional irreducible module of the symmetric group S5. This module splits with respect to the icosahedral group A5 into the two standard 3-dimensional representations. The resulting linear projections of Q relate the action of A5 on Q to those on the regular icosahedron.

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47

Cassar, Gavin. "Financial Statement and Projection Preparation in Start-Up Ventures." Accounting Review 84, no. 1 (January 1, 2009): 27–51. http://dx.doi.org/10.2308/accr.2009.84.1.27.

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ABSTRACT: Using a representative sample of entrepreneurs who are in the process of starting a business, this study investigates the determinants of the preparation of financial statements and projections in start-up ventures. Consistent with predictions from information economics and contracting, I find that the use of outside funding, level of competition, and venture scale are positively associated with the intended frequency of financial statement preparation. However, comparing the economic significance of alternative influences suggests that the benefit of reducing competitive and fundamental uncertainty is more influential in explaining variations in intentions to prepare financial statements. Further, I find the determinants of preparation frequency vary among different financial statements; for instance, cash statements are more important for start-ups with products in earlier stages of development and with greater competition. In contrast to financial statements, the preparation of projections such as formal financial projections and regular sales forecasts by start-ups is positively associated with the importance of intangible investments such as patents, research and development, and with start-ups in high-tech industries.

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Ryabinkov, Andrei I., and Alexander D. Kaminker. "Traces of Anisotropic Quasi-Regular Structure in the SDSS Data." Universe 7, no. 8 (August 6, 2021): 289. http://dx.doi.org/10.3390/universe7080289.

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The aim of this study is to search for quasi-periodical structures at moderate cosmological redshifts z ≲ 0.5. We mainly use the SDSS DR7 data on the luminous red galaxies (LRGs)with redshifts 0.16 ≤ z ≤ 0.47. At first, we analyze features (peaks) in the power spectra of radial (shell-like) distributions using separate angular sectors in the sky and calculate the power spectra within each sector. As a result, we found some signs of a large-scale anisotropic quasi-periodic structure detectable through 6 sectors out of a total of 144 sectors. These sectors are distinguished by large amplitudes of dominant peaks in their radial power spectra at wavenumbers k within a narrow interval of 0.05 < k < 0.07 h Mpc−1. Then, passing from a spherical coordinate system to a Cartesian one, we found a special direction such that the total distribution of LRG projections on it contains a significant (≳5σ) quasi-periodical component. We assume that we are dealing with a signature of a quasi-regular structure with a characteristic scale 116 ± 10 h−1 Mpc. Our assumption is confirmed by a preliminary analysis of the SDSS DR12 data.

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49

Bez, Nicolas. "Global fish abundance estimation from regular sampling: the geostatistical transitive method." Canadian Journal of Fisheries and Aquatic Sciences 59, no. 12 (December 1, 2002): 1921–31. http://dx.doi.org/10.1139/f02-155.

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This article deals with the estimation of fish biomass based on regular samplings. The geostatistical transitive method is a design-based spatially explicit method based on few and falsifiable assumptions concerning the sampling strategy. The falsifiability of a hypothesis corresponds to our capacity to control its adequacy to field data in practice. We first describe the basics of the method, mention the questions relative to the covariogram estimation, the units, and the projections of the coordinates, and explain how to fit the model to the experimental covariogram. We then apply the method to an ICES (International Council for the Exploration of the Sea) triennial mackerel egg survey, with regular sampling, and to a Moroccan octopus survey, with regular stratified sampling. To compare the present technique with existing methods, the number and the falsifiability of their respective hypotheses are considered in addition to the bias, the convergence, and the estimation variance. As is often the case, data are assumed to be synoptic, and we discuss two examples of spatiotemporal methods.

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HAWORTH, P. A. "LOCAL CHARACTERIZATION OF APPROXIMATELY FINITE OPERATOR ALGEBRAS." International Journal of Mathematics 12, no. 07 (September 2001): 751–67. http://dx.doi.org/10.1142/s0129167x01000976.

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We show that the family of nest algebras with r non-zero nest projections is stable, in the sense that an approximate containment of one such algebra within another is close to an exact containment. We use this result to give a local characterization of limits formed from this family. We then consider quite general regular limit algebras and characterize these algebras using a local condition which reflects the assumed regularity of the system.

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