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Journal articles on the topic 'Projections2'

Author: Grafiati

Published: 9 March 2023

Last updated: 31 July 2025

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1

Cecconello, Moiseis S., Jefferson Leite, Rodney C. Bassanezi, and Joao de Deus M. Silva. "About Projections of Solutions for Fuzzy Differential Equations." Journal of Applied Mathematics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/184950.

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In this paper we propose the concept offuzzy projectionson subspaces of , obtained from Zadeh's extension of canonical projections in , and we study some of the main properties of such projections. Furthermore, we will review some properties of fuzzy projection solution of fuzzy differential equations. As we will see, the concept of fuzzy projection can be interesting for the graphical representation of fuzzy solutions.

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2

Nyrtsov, Maxim V., Maria E. Fleis, Michael M. Borisov, and Philip J. Stooke. "Conic projections of the triaxial ellipsoid: the projections for regional mapping of celestial bodies." Proceedings of the ICA 1 (May 16, 2018): 1–3. http://dx.doi.org/10.5194/ica-proc-1-84-2018.

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Different distortion classes of the azimuthal and cylindrical projections of the triaxial ellipsoid have been considered in our previous works. These projections make it possible to construct maps of the celestial bodies in planetary scale. However, for regions in the middle latitudes it is advisable to use a conic projection which was not developed until now. In this investigation we describe the development of three conic projections of a triaxial ellipsoid: a conic projection with true scale along meridians, an equal-area conic projection and a quasi-conformal conic projection. In derivatio

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KhaIiI Ibrahim Kadhim. "Principal Components Analysis as enhancement Operator and Compression factor." journal of the college of basic education 17, no. 72 (2019): 25–33. http://dx.doi.org/10.35950/cbej.v17i72.4495.

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Principal components analysis (PCA) is effective at compressing information in multivariate data sets by computing orthogonal projections that maximize the amount of data variance. Unfortunately, information content in hyper spectral images does not always coincide with such projections. We propose an application of projection pursuit (pp), which seeks to find a set of projections that are "interesting" in the sense that they deviate from the Gaussian distribution assumption. Once these projections are obtained, they can be used for image compression, segmentation, or enhancement for vis

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Lapaine, Miljenko. "Cylindrical Projections as a Limiting Case of Conic Projections." Kartografija i geoinformacije 22, no. 39 (2023): 62–75. http://dx.doi.org/10.32909/kg.22.39.4.

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Lambert (1772) derived the equation of the Mercator projection as a limiting case of a conformal conic projection. In this paper, we give a derivation for equidistant, equal-area, conformal and perspective cylindrical projections as limiting cases of equidistant, equal-area, conformal and perspective conic projections. In this article the conic and cylindrical projections are not projections on a cone or a cylinder whose surfaces are cut and developed into a plane, but rather mappings of the sphere directly into the plane. Exceptions are projections that are defined as mappings on the surface

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Lapaine, Miljenko. "From Conic to Cylindrical Map Projections." Geodetski vestnik 67, no. 03 (2023): 363–73. http://dx.doi.org/10.15292/geodetski-vestnik.2023.03.363-373.

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In books and textbooks on map projections, cylindrical, conic and azimuthal projections are usually considered separately. It is sometimes mentioned that cylindrical and azimuthal projections can be interpreted as limiting cases of conic, but this is rarely proven. The goal of this article is to show in a rigorous and systematic way how to generally approach solving the problem of transition from a conic to a corresponding cylindrical projection. This article points to the fact that J. H. Lambert showed as early as 1772 that a conformal cylindrical projection is created from a conformal conic

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Barrenechea, Ana Lucía, and Carlos Peña. "Invariance and normality of projections in the dual of Banach algebras." New Zealand Journal of Mathematics 51 (December 14, 2021): 115–18. http://dx.doi.org/10.53733/132.

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We study the classes of invariant and natural projections in the dual of a Banach algebra $A$. These type of projections are relevant by their connections with the existence problem of bounded approximate identities in closed ideals of Banach algebras. It is known that any invariant projection is a natural projection. In this article we consider the issue of when a natural projection is an invariant projection.

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7

Wilson, Tom, and Philip Rees. "A brief guide to producing a national population projection." Australian Population Studies 5, no. 1 (2021): 77–100. http://dx.doi.org/10.37970/aps.v5i1.84.

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Background There are surprisingly few resources available which offer an introductory guide to preparing a national population projection using a cohort-component model. Many demography textbooks cover projections quite briefly, and many academic papers on projections focus on advanced technical issues. Aims The aim of this paper is to provide a short and accessible guide to producing a national-scale population projection using the cohort-component model. Data and methods The paper describes the cohort-component model from a population accounting perspective, presents all the nece

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Lapaine, Miljenko, and Nedjeljko Frančula. "Polar and Equatorial Aspects of Map Projections?" Proceedings of the ICA 2 (July 10, 2019): 1–6. http://dx.doi.org/10.5194/ica-proc-2-71-2019.

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<p><strong>Abstract.</strong> There is no standard or generally accepted terminology of aspect in the theory of map projections. The term is probably derived from the concept that a graticule is produced by perspective projection of the meridians and parallels on a sphere onto a developable surface. Developable surfaces are widely accepted, and it is almost impossible to find a publication that deals with map projections in general and without developable surfaces story. If found, it usually classifies projections as cylindrical, conical and azimuthal, and applies developable

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9

Krikštolaitis, R. "Statistical Estimation of Discriminant Space using Various Projection Indices." Nonlinear Analysis: Modelling and Control 6, no. 1 (2001): 67–77. https://doi.org/10.15388/na.2001.6.1.15226.

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Projection pursuit is a method for finding interesting projections of high-dimensional multivariate data. Typically interesting projections are found by numerical maximizing some measure of non-normality of projected data (so-called projection index) over projection direction. The problem is to select the index for projection pursuit. In this article we compare performance of five projection indices: projection indices based on omega2, Omega2, Kolmogorov-Smirnov goodness-of-fit measures, entropy index and Friedman's index. It is supposed that observed random variable satisfies a multidimension

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10

Lee, Jimmy, Ka Lun Leung, and Yi Wu. "Polynomially Decomposable Global Cost Functions in Weighted Constraint Satisfaction." Proceedings of the AAAI Conference on Artificial Intelligence 26, no. 1 (2021): 507–13. http://dx.doi.org/10.1609/aaai.v26i1.8130.

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In maintaining consistencies, such as GAC*, FDGAC* and weak EDGAC*, for global cost functions, Weighted CSP (WCSP) solvers rely on the projection and extension operations, which entail the computation of the cost functions' minima. Tractability of this minimum computation is essential for efficient execution. Since projections/extensions modify the cost functions, an important issue is tractable projection-safety, concerning whether minimum cost computation remains tractable after projections/extensions. In this paper, we prove that tractable projection-safety is always possible for projection

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11

Salsabila, Husniati, Wahyu Hidayat, Nurbaiti Nurbaiti, and Gando Sari. "PERBEDAAN PROYEKSI PEMERIKSAAN RADIOGRAFI SINUS PARANASAL PADA KLINIS SINUSITIS DI RUMAH SAKIT MAYAPADA LEBAK BULUS." Healthy Tadulako Journal (Jurnal Kesehatan Tadulako) 9, no. 1 (2023): 36–42. http://dx.doi.org/10.22487/htj.v9i1.538.

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Radiographic examination of the paranasal sinuses using an X-ray machine can be performed with various projections. Selection of the right projection will provide imaging results that support the diagnosis process. This study aims to analyze the management of the radiographic examination of the paranasal sinuses and to analyze the use of X-ray projections for the examination of the paranasal sinuses in patients with clinical sinusitis at Mayapada Hospital Lebak Bulus. This research method is descriptive qualitative with secondary data analysis approach in January 2022. The study sample consist

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Wosar, Marc A., Daniel D. Lewis, Lisa Neuwirth, et al. "Radiographic evaluation of elbow joints before and after surgery in dogs with possible fragmented medial coronoid process." Journal of the American Veterinary Medical Association 214, no. 1 (1999): 52–58. http://dx.doi.org/10.2460/javma.1999.214.01.52.

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Objective To determine the usefulness of 5 radiographic projections of the elbow joint for identification of fragmented coronoid process (FCP) and associated secondary degenerative changes in dogs. Design Longitudinal clinical study. Animals 19 dogs suspected of having FCP (7 dogs, 1 elbow joint; 12 dogs, both elbow joints). Procedure 5 radiographic projections were obtained before and after surgery for all elbow joints on which exploratory arthrotomy was performed because of suspected FCP. Radiographs obtained before surgery were compared with radiographs obtained after surgery and radiograph

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Borisov, Mirko, Miro Govedarica, and Vladimir Petrovic. "Cartographic conic projections and their appliance in national cartography." Glasnik Srpskog geografskog drustva 91, no. 4 (2011): 183–204. http://dx.doi.org/10.2298/gsgd1104183b.

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This paper is dedicated to the mapping of conic projections and their appliance in producing maps of our state cartography. So far they were often applied, and will be used precisely coned, polyconed and modified polyconed projections for the official mapping (1:500 000, 1:750 000, 1:1000 000 and 1:1500 000). In particular, they cartographic conical projection at a scale of 1:1000 000 were taken into consideration. Those are the Lambert conformal conical projection with two standard parallels and the Modified polyconic projections. In addition to these cartographic conical projections, is desc

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Horiguchi, Kirara, Ayaka Shimizu, Ryohei Watanabe, and Yoshiro Yaguchi. "Axis systems of link projections." Journal of Knot Theory and Its Ramifications 26, no. 08 (2017): 1750043. http://dx.doi.org/10.1142/s0218216517500432.

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An axis of a link projection is a closed curve which lies symmetrically on each region of the link projection. In this paper we define axis systems of link projections and characterize axis systems of the standard projections of twist knots.

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Gibbs, Andrew, E. James Pearse, Jennifer A. Sheehan, Kathleen T. Meleady, Hirani Jayasinha, and Neill Jones. "Estimating and projecting subacute care demand: findings from a review of international methods." Australian Health Review 32, no. 4 (2008): 778. http://dx.doi.org/10.1071/ah080778.

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A review of projection methodologies used to project sub-acute inpatient activity in various international health care jurisdictions was undertaken as part of a project to develop subacute inpatient activity projections for the state with the largest population in Australia. The literature search identified nearly 200 articles and found three main groups of projection methodologies: projections with a focus on subacute care; projections with a focus on acute care, but which often included subacute activity in the overall projections; and projections of specific diseases/conditions influencing

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HELEODORO, RAPHAEL AQUINO. "A new species of Mecomera Audinet-Serville earwig (Dermaptera: Spongiphoridae) from the Brazilian Atlantic Rainforest." Zootaxa 5047, no. 4 (2021): 477–83. http://dx.doi.org/10.11646/zootaxa.5047.4.7.

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A new earwig species, Mecomera ze sp. nov. (Spongiphoridae: Sparattinae: Sparattini) from the Brazilian Atlantic Rainforest is described based on males and females from Piracicaba, São Paulo, Brazil. Mecomera ze sp. nov. has a pygidium shape similar to that of M. chacoensis (Borelli), and can be differentiated by the flattened projections of M. ze sp. nov., with emarginations between each projection, whilst in M. chacoensis the pygidium has cylindrical projections, with a single emargination between apical projections. Mecomera ze sp. nov. is also similar to M. reichardti in that both have cer

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Arablouei, Reza, and Kutluyıl Doğançay. "Affine projection algorithm with selective projections." Signal Processing 92, no. 9 (2012): 2253–63. http://dx.doi.org/10.1016/j.sigpro.2012.02.018.

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18

Ni, Chengcai, and Chunmei Liu. "Evaluating behaviors of factors affecting the site index estimate on the basis of a single stand using simulation approach." Canadian Journal of Forest Research 38, no. 11 (2008): 2762–70. http://dx.doi.org/10.1139/x08-095.

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Height observations H1and H2present on the right- and left-hand sides of site index models, respectively. The error terms associated with H1and H2, along with parameter estimate errors, affect the estimate of the site index. Projection error variance (PEV), in a projection from A1to A2, consisted of four components associated with H1, H2, the covariance of H1and H2, and the parameter estimate errors. In this study, behaviors of these components were investigated via simulations on the basis of six equations derived from the Lundqvist–Kerf and the Hossfeld IV functions. Simulation results showe

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19

Fleis, M. E., M. V. Nyrtsov, and A. I. Sokolov. "Cylindrical projections of triaxial ellipsoid: precise formulae and elliptical integrals." Geodesy and Cartography 982, no. 4 (2022): 26–38. http://dx.doi.org/10.22389/0016-7126-2022-982-4-26-38.

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Cylindrical projections of a triaxial ellipsoid are used for global mapping the surfaces of celestial bodies, the figures of which the International Astronomical Union recommends to approximate by the mathematical surface of the mentioned geometric body. Its reference surface and projections are not available in GIS packages. In this regard, we are facing the problem of representing projection formulae in finite elementary functions or reducing the integrals included in them to elliptic ones. This will simplify direct and inverse transformations of such map projections for inclusion in GIS sof

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20

Kerkovits, Krisztián. "Polyazimuthal Map Projections." Kartografija i geoinformacije 18, no. 32 (2019): 18–32. http://dx.doi.org/10.32909/kg.18.32.2.

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A polyazimuthal map projection is a mapping that represents parallels as non-concentric full circles on the plane. Polyazimuthal mappings are almost never mentioned in the literature dealing with map projections. However, these projections are flexible; their distortion characteristics are highly mutable. This paper expands the theory of polyazimuthal map projections. Furthermore, this study also shows the derivation for variants of this projection family (e. g. equal-area, orthogonal). The article concludes with some practical applications in the field of low-distortion map projections to dem

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Kessler, Fritz. "Map Projection Education in General Cartography Textbooks: A Content Analysis." Cartographic Perspectives, no. 90 (August 16, 2018): 6–30. http://dx.doi.org/10.14714/cp90.1449.

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As developments in the field of map projections occur (e.g., the deriving of a new map projection), it would be reasonable to expect that those developments that are important from a teaching standpoint would be included in cartography textbooks. However, researchers have not examined whether map projection material presented in cartography textbooks is keeping pace with developments in the field and whether that material is important for cartography students to learn. To provide such an assessment, I present the results of a content analysis of projection material discussed in 24 cartography

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Lapaine, М. "Secant Parallels in Azimuthal Projections." Geodesy and Cartography 946, no. 4 (2019): 39–54. http://dx.doi.org/10.22389/0016-7126-2019-946-4-39-54.

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Map projections are commonly approached as mapping onto developable surfaces; cylindrical projections onto the lateral surface of a cylinder, conic projections onto the lateral surface of a cone, and azimuthal projections onto a plane. If an intermediate developable surface intersects the Earth’s sphere or ellipsoid, the projection is referred to as a secant projection. The intersection of a developable surface and the Earth’s sphere or ellipsoid, e.g. secant parallel is considered a standard parallel. In this paper the definitions of secant and standard parallel in azimuthal projections are g

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Werschler, T., and F. Nault. "Projecting Interregional Migration Balances within a Multiregional Cohort—Component Framework." Environment and Planning A: Economy and Space 28, no. 5 (1996): 769–82. http://dx.doi.org/10.1068/a280769.

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An examination of the projection output derived from fixed-rate and variable-rate interregional migration assumptions reveals the difficulty with which an acceptable range of migration scenarios is developed for use in Canadian population projections. The development of acceptable migration assumptions is limited by the choice of projection methodology, the requirements of projections within the present context, and the demographic characteristics of Canada's regions. In order to overcome these limitations, a technique for controlling projected interregional migration balances within a cohort—

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Indrati, Rini, Siti Daryati, Dewi Kartikasari, Sri Mulyati, and Marichatul Jannah. "RADIATION DOSE AND ANATOMICAL INFORMATION IN SACRUM BONE EXAMINATION WITH AP AND AXIAL AP PROJECTIONS." Jurnal Riset Kesehatan 10, no. 1 (2021): 77–83. http://dx.doi.org/10.31983/jrk.v10i1.6777.

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The projections for the sacrum are axial anteroposterior with the beam 15 degrees toward the cephalad, and axial posteroanterior in the direction of the beam 15 degrees caudally. Some practitioners take steps to examine the sacrum with AP projections in a perpendicular beam direction. Around the sacrum are reproductive organs that are sensitive to radiation, so it is necessary to select the right projection to reduce the radiation dose and show clear anatomical information. This study aims to determine the projection of an examination that produces clear anatomical information at a minimal dos

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Ball, Vaughn, Luis Tenorio, Christian Schiøtt, Michelle Thomas, and J. P. Blangy. "Three-term amplitude-variation-with-offset projections." GEOPHYSICS 83, no. 5 (2018): N51—N65. http://dx.doi.org/10.1190/geo2017-0763.1.

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A three-term (3T) amplitude-variation-with-offset projection is a weighted sum of three elastic reflectivities. Parameterization of the weighting coefficients requires two angle parameters, which we denote by the pair [Formula: see text]. Visualization of this pair is accomplished using a globe-like cartographic representation, in which longitude is [Formula: see text], and latitude is [Formula: see text]. Although the formal extension of existing two-term (2T) projection methods to 3T methods is trivial, practical implementation requires a more comprehensive inversion framework than is requir

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Liu, Qiang, Shao Feng Bian, and Zhong Mei Li. "Comparisons and Direct Transformation Formulae between Azimuthal Conformal and Gnomonic Projections." Advanced Materials Research 1065-1069 (December 2014): 2259–64. http://dx.doi.org/10.4028/www.scientific.net/amr.1065-1069.2259.

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Definitions of azimuthal conformal and gnomonic projections were introduced, and contrastive analyses of graticules shapes between these two projections were conducted. Based on theories of perspective azimuthal projection and space geometrical relationships, transformation between azimuthal conformal and gnomonic projections was carried out through series of derivation. Direct transformation formulae between coordinates of the two projections were established with respect to standard parallel. Finally, correctness and reliability of these formulae were tested and verified by numerical example

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DA ROCHA, RONALDO DOS SANTOS. "Definição de um Sistema de Projeção Cartográfica para Mapeamento Urbano no Estado do Rio Grande do Sul." Pesquisas em Geociências 23, no. 1-2 (1996): 25. http://dx.doi.org/10.22456/1807-9806.21223.

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This work studies the use of map projections in large scale mapping to provide support for a Land Information System. For this purpose, evaluations of the map projections commonly used in France, Switzerland, USA and Brazil are presented. The adequate precision to record property lines in a cadastral survey is identified and then compared to the linear distortions inherent to the map projections used in Brazil. Based upon these discrepancies, an optimum projection was developed to be used in large scale cartography in the State of Rio Grande do SuI. The expressions to transform geographic coor

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HE, YUN, XU CAO, FEI LIU, JIANWEN LUO, and JING BAI. "INFLUENCE OF LIMITED-PROJECTION ON FLUORESCENCE MOLECULAR TOMOGRAPHY." Journal of Innovative Optical Health Sciences 05, no. 03 (2012): 1250020. http://dx.doi.org/10.1142/s1793545812500204.

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Challenges remain in imaging fast biological processes in vivo with fluorescence molecular tomography (FMT) due to the long data acquisition time. Data acquisition with limited projections can greatly reduce the time consumption, but the influence of limited-projection on reconstruction quality is currently unclear. Both numerical simulations and a phantom experiment are conducted to analyze this problem. Through a systematic investigation of all the results reconstructed from different numbers of projections, we evaluate the influence of limited-projection data on FMT. A mouse experiment is a

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Nuramdiani, Dian. "Reduction of Organ Absorbed Dose and Cancer Risk through Optimizing the Use of Projection in Diagnostic X-ray Examination." International Journal of Global Operations Research 4, no. 3 (2023): 182–88. http://dx.doi.org/10.47194/ijgor.v4i3.245.

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This study aimed to calculate and compare the estimated organ absorption dose, risk of cancer due to exposure, and dose received by the gonads for women and men in radio diagnostic examinations with different projections. Radiographic examination of the abdomen (with anterior-posterior (AP) and posterior-anterior (PA) projections) and lumbar vertebrae (with anterior-posterior projection (AP), Right posterior-anterior oblique (RPO), and Left posterior-anterior oblique (LPO)), were performed. Software based on the Monte Carlo program has been used to calculate the estimated absorbed dose of the

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Gomi, Tsutomu, and Yukio Koibuchi. "Use of a Total Variation Minimization Iterative Reconstruction Algorithm to Evaluate Reduced Projections during Digital Breast Tomosynthesis." BioMed Research International 2018 (June 19, 2018): 1–14. http://dx.doi.org/10.1155/2018/5239082.

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Purpose. We evaluated the efficacies of the adaptive steepest descent projection onto convex sets (ASD-POCS), simultaneous algebraic reconstruction technique (SART), filtered back projection (FBP), and maximum likelihood expectation maximization (MLEM) total variation minimization iterative algorithms for reducing exposure doses during digital breast tomosynthesis for reduced projections. Methods. Reconstructions were evaluated using normal (15 projections) and half (i.e., thinned-out normal) projections (seven projections). The algorithms were assessed by determining the full width at half-ma

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Read, E. B., H. H. Okamura, and D. G. Drubin. "Actin- and tubulin-dependent functions during Saccharomyces cerevisiae mating projection formation." Molecular Biology of the Cell 3, no. 4 (1992): 429–44. http://dx.doi.org/10.1091/mbc.3.4.429.

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Several conditional-lethal mutant alleles of the single-copy Saccharomyces cerevisiae beta-tubulin and actin genes were used to evaluate the roles of microtubules and actin filaments in the pheromone-induced extension of mating projections. Mutants defective in tubulin assembly form projections indistinguishable in appearance from those formed by wild-type cells. However, the tubulin mutants are unable to move their nuclei into the projections and to orient the spindle pole body associated with each nucleus toward the projection tip. Actin mutants are defective in spatial orientation of cell-s

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Panigrahi, Narayan, and Cyan Subhra Mishra. "A Generic Method for Azimuthal Map Projection." Defence Science Journal 65, no. 5 (2015): 390. http://dx.doi.org/10.14429/dsj.65.8598.

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Map projections are mathematical methods for projecting spherical coordinates in the form of (φ, λ) to the map coordinates in the form of (X,Y) in Cartesian reference frame. Numerous methods for map projection have been derived and are being used for preparation of cartographic products. These map projections take into account specific position of the viewer on the datum surface for derivation of the map projections. A generic method for azimuthal map projection where the position of the viewer can be taken at an arbitrary point on the datum surface is derived. Using this generic method all th

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Raymer, James, Nicholas Biddle, and Qing Guan. "A multiregional sources of growth model for school enrolment projections." Australian Population Studies 1, no. 1 (2017): 26–40. http://dx.doi.org/10.37970/aps.v1i1.10.

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Background: Education planning requires accurate and efficient projection models. Current projection models either do not make use of all available information and are reliant on idiosyncratic expert judgement, or are too complex to be maintained and explained. Aims: To test whether a multiregional projection model performs better than current methodology in explaining and projecting school enrolments in a school system with student mobility. Data and methods: A multiregional cohort model was developed for projecting enrolments for multiple schools or districts simultaneously. For

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Strebe, Daniel. "Given the problem of projection, are heat maps an oxymoron?" Abstracts of the ICA 1 (July 15, 2019): 1–2. http://dx.doi.org/10.5194/ica-abs-1-352-2019.

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<p><strong>Abstract.</strong> With the proliferation of data analysis and visualization tools, we see more and more heat maps. But should we? Are such displays meaningful? At large scales, heat maps need not be controversial (though common tools can blight even simple cases). But what about small-scale maps? Is anyone thinking about the effects of projection on heat maps? How do map projections change the semantics of heat maps? What projections permit meaningful heat maps? How should heat maps be calculated in the presence of a map projection? We explore these problems and q

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Marois, Guillaume, Patrick Sabourin, and Alain Bélanger. "Forecasting human capital of EU member countries accounting for sociocultural determinants." Journal of Demographic Economics 85, no. 3 (2019): 231–69. http://dx.doi.org/10.1017/dem.2019.4.

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AbstractInclusion of additional dimensions to population projections can lead to an improvement in the overall quality of the projections and to an enhanced analytical potential of derived projections such as literacy skills and labor force participation. This paper describes the modeling of educational attainment of a microsimulation projection model of the European Union countries. Using ordered logistic regressions on five waves of the European Social Survey, we estimate the impact of mother's education and other sociocultural characteristics on educational attainment and implement them int

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Lapaine, Miljenko, and Nedjeljko Frančula. "Web Mercator Projection – One of Cylindrical Projections of an Ellipsoid to a Plane." Kartografija i geoinformacije 20, no. 35 (2021): 30–47. http://dx.doi.org/10.32909/kg.20.35.2.

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The Web Mercator projection is a projection of a relatively recent date. There has been a lot of controversy about its application. Some believe that this projection is not a projection of either the sphere or the surface of the ellipsoid. Therefore, in this paper, several projections of the surface of a rotational ellipsoid into a plane are investigated and it is shown that the Web Mercator projection is one of such projections. Namely, although the equations of this projection are identical to the equations for the projection of the sphere, the basic difference is in the choice of the area o

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Li, Yuan, Jiajia Niu, and Xiao-Ming Xu. "The minus order for projections." Filomat 35, no. 8 (2021): 2761–74. http://dx.doi.org/10.2298/fil2108761l.

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Let B(H)Id be the set of all projections on a Hilbert space H. The necessary and sufficient conditions are presented for the existence of the supremum, as well as the infimum, of two arbitrary projections in B(H)Id with respect to the minus order ?. For a projection Q in B(H)Id; the properties of the sets {P : P is an orthogonal projection on H and Q ? P} and {P : P is an orthogonal projection on H and P ? Q} are further explored.

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Bodnarchuk, Iryna, Yuliya Mishura, and Kostiantyn Ralchenko. "Fractional Gaussian Noise: Projections, Prediction, Norms." Fractal and Fractional 9, no. 7 (2025): 428. https://doi.org/10.3390/fractalfract9070428.

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We examine the one-sided and two-sided (bilateral) projections of an element of fractional Gaussian noise onto its neighboring elements. We establish several analytical results and conduct a numerical study to analyze the behavior of the coefficients of these projections as functions of the Hurst index and the number of neighboring elements used for the projection. We derive recurrence relations for the coefficients of the two-sided projection. Additionally, we explore the norms of both types of projections. Certain special cases are investigated in greater detail, both theoretically and numer

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Ningrum, Tia Ayu, Sufyarma Marsidin, and Hadiyanto. "THE DESIGN OF THE SUTI (STUDENT PROJECTION) APPLICATION WITH THE PHP PROGRAM FOR EDUCATION PLANNING." Journal of Law and Sustainable Development 12, no. 5 (2024): e3269. http://dx.doi.org/10.55908/sdgs.v12i5.3269.

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Objective: The research objective is to design a student projection application that is needed in educational planning. Theoretical reference: Student projection is a process of predicting the number of students in the future which is necessary to make plans for the future. Methods: The research methodology is to design the application using PHP (Hypertext Preprocessing) programme. After that, a trial was conducted to see the effectiveness of the application. The results were compared with data processing manually and through the application. Results and Conclusion: The PHP application produce

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Tejada, Eduardo, Rosane Minghim, and Luis Gustavo Nonato. "On Improved Projection Techniques to Support Visual Exploration of Multi-Dimensional Data Sets." Information Visualization 2, no. 4 (2003): 218–31. http://dx.doi.org/10.1057/palgrave.ivs.9500054.

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Projection (or dimensionality reduction) techniques have been used as a means to handling the growing dimensionality of data sets as well as providing a way to visualize information coded into point relationships. Their role is essential in data interpretation and simultaneous use of different projections and their visualizations improve data understanding and increase the level of confidence in the result. For that purpose, projections should be fast to allow multiple views of the same data set. In this work we present a novel fast technique for projecting multi-dimensional data sets into bid

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Qin, Xianhao, Chunsheng Li, Yingyi Liang, et al. "Robust Bi-Orthogonal Projection Learning: An Enhanced Dimensionality Reduction Method and Its Application in Unsupervised Learning." Electronics 13, no. 24 (2024): 4944. https://doi.org/10.3390/electronics13244944.

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This paper introduces a robust bi-orthogonal projection (RBOP) learning method for dimensionality reduction (DR). The proposed RBOP enhances the flexibility, robustness, and sparsity of the embedding framework, extending beyond traditional DR methods such as principal component analysis (PCA), neighborhood preserving embedding (NPE), and locality preserving projection (LPP). Unlike conventional approaches that rely on a single type of projection, RBOP innovates by employing two types of projections: the “true” projection and the “counterfeit” projection. These projections are crafted to be ort

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Jenny, Bernhard, Tom Patterson, and Lorenz Hurni. "Flex Projector–Interactive Software for Designing World Map Projections." Cartographic Perspectives, no. 59 (March 1, 2008): 12–27. http://dx.doi.org/10.14714/cp59.245.

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Flex Projector is a free, open-source, and cross-platform software application that allows cartographers to interactively design custom projections for small-scale world maps. It specializes in cylindrical, and pseudocylindrical projections, as well as polyconical projections with curved parallels. Giving meridians non-uniform spacing is an option for all classes of projections. The interface of Flex Projector enables cartographers to shape the projection graticule, and provides visual and numerical feedback to judge its distortion properties. The intended users of Flex Projector are those wit

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Dunstan, Kim, and Christopher Ball. "Demographic Projections: User and Producer Experiences of Adopting a Stochastic Approach." Journal of Official Statistics 32, no. 4 (2016): 947–62. http://dx.doi.org/10.1515/jos-2016-0050.

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Abstract Statistics New Zealand is one of the few national statistical agencies to have applied a stochastic (probabilistic) approach to official demographic projections. This article discusses the experience and benefits of adopting this new approach, including the perspective of a key user of projections, the New Zealand Treasury. Our experience is that the change is less difficult to make than might be expected. Uncertainty in the different projection inputs (components) can be modelled simply or with more complexity, and progressively applied to different projection types. This means that

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Pędzich, Paweł. "Image of the World on polyhedral maps and globes." Polish Cartographical Review 48, no. 4 (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

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Liu, Weiping, Jennifer Fung, Craig Abbey, John W. Sedat, and David A. Agard. "Automatic/interactive bead alignment in electron tomographic image processing." Proceedings, annual meeting, Electron Microscopy Society of America 52 (1994): 932–33. http://dx.doi.org/10.1017/s0424820100172395.

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In the electron tomographic (EM) reconstruction process the mutual alignment between projections of different view angles is a crucial step. The routinely used alignment method is based on fiducial markers': a single-axis tilt projection series is collected with gold particles distributed on the specimen, the positions of high density gold beads on the projections are found, and the relationship between the specimen and the digital projection coordinate systems is determined from least-square fitting these found bead positions. There are four alignment parameters for each projection: two in sh

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Ene, Alina, Huy L. Nguyen, and Adrian Vladu. "Projection-Free Bandit Optimization with Privacy Guarantees." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 8 (2021): 7322–30. http://dx.doi.org/10.1609/aaai.v35i8.16899.

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We design differentially private algorithms for the bandit convex optimization problem in the projection-free setting. This setting is important whenever the decision set has a complex geometry, and access to it is done efficiently only through a linear optimization oracle, hence Euclidean projections are unavailable (e.g. matroid polytope, submodular base polytope). This is the first differentially-private algorithm for projection-free bandit optimization, and in fact our bound matches the best known non-private projection-free algorithm and the best known private algorithm, even for the weak

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Rivard, Denis, and Malcolm G. Foy. "An Analysis of Errors in Catch Projections for Canadian Atlantic Fish Stocks." Canadian Journal of Fisheries and Aquatic Sciences 44, no. 5 (1987): 967–81. http://dx.doi.org/10.1139/f87-115.

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Two techniques were used to identify and evaluate the components of error inherent in the catch projection method used in the assessment of Canadian Atlantic fish stocks. Firstly, a retrospective analysis was used to evaluate, for the projections made in 1979 and 1981, the impact of the actual error made in input variables such as catch-at-age, mean weight-at-age, recruitment, and stock size. Secondly, the variance of projections was estimated from the variance of input variables. From the retrospective analysis, the principal causes of error in catch projections were identified as the estimat

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Ledermann, Florian. "Classifying Cartographic Projections Based on Dynamic Analysis of Program Code." Abstracts of the ICA 2 (October 9, 2020): 1. http://dx.doi.org/10.5194/ica-abs-2-38-2020.

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Abstract. Analyzing a given map to identify its projection and other geometrical properties has long been an important aspect of cartographic analysis. If explicit information about the projection used in a particular map is not available, the properties of the cartographic transformation can sometimes be reconstructed from the map image. However, such a process of projection analysis requires significant manual labor and oversight.For digital maps, we usually expect the projection from geographic space to map space to have been calculated by a computer program. Such a program can be expected

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Arroyo Ohori, Ken, Hugo Ledoux та Jantien Stoter. "Visualising higher-dimensional space-time and space-scale objects as projections to ℝ3". PeerJ Computer Science 3 (3 липня 2017): e123. http://dx.doi.org/10.7717/peerj-cs.123.

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Objects of more than three dimensions can be used to model geographic phenomena that occur in space, time and scale. For instance, a single 4D object can be used to represent the changes in a 3D object’s shape across time or all its optimal representations at various levels of detail. In this paper, we look at how such higher-dimensional space-time and space-scale objects can be visualised as projections from ℝ4to ℝ3. We present three projections that we believe are particularly intuitive for this purpose: (i) a simple ‘long axis’ projection that puts 3D objects side by side; (ii) the well-kno

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Heitzler, Magnus, Hans-Rudolf Bär, Roland Schenkel, and Lorenz Hurni. "The Light Source Metaphor Revisited—Bringing an Old Concept for Teaching Map Projections to the Modern Web." ISPRS International Journal of Geo-Information 8, no. 4 (2019): 162. http://dx.doi.org/10.3390/ijgi8040162.

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Map projections are one of the foundations of geographic information science and cartography. An understanding of the different projection variants and properties is critical when creating maps or carrying out geospatial analyses. The common way of teaching map projections in text books makes use of the light source (or light bulb) metaphor, which draws a comparison between the construction of a map projection and the way light rays travel from the light source to the projection surface. Although conceptually plausible, such explanations were created for the static instructions in textbooks. M

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