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This article explores cinematic representations of American military interventions in Iraq and Afghanistan, examining documentary and fiction films from American, Iraqi, and Afghan perspectives. The article argues that these films often fail to communicate meaningfully with domestic and international audiences effectively, instead remaining 'asymptotic' or 'uroboric' in their rhetorical and communicative impact. I highlight the ethical challenge faced by filmmakers, whether situated in the West or in the Middle East, of turning the 'traumatic mirror' back on themselves, and the difficulties in achieving successful communication and self-reflexivity. The post-9/11 era is marked by a complex intersection of realpolitik, public performatives, and moral commitments, with long-standing tensions between West and non-West persisting in new forms. Cinematic representations of these interventions serve as a window into the traumatic legacies of these conflicts and the ongoing struggle for ethical representation, as well as a lens on the rhetorics of cinema. [ABSTRACT FROM AUTHOR]

The twenty-first century came with new concepts for the design process, due to the impact of the digital revolution and the progress of computer applications. Accordingly, the new distinctive features of digital architecture emerged, as the modularity was rejected, merging between interior and exterior and extent to which building adapts to the surrounding environment, The building is no longer just a regular structure, but has become a living body, as the designer found the tool through which he can express his ideas, as important as their complexity. The problem of research lies in the lack of sufficient benefit from the technological development accompanying the digital revolution through the thought of architect Hani Rashid, and the local architecture lack to integrate culture, technology, society and surrounding environment, which resulted in rigid buildings. The research aims to benefit from the technological development accompanying the digital revolution, and improve the design thought by linking local architecture with the surrounding environment, technology and society culture through Hani Rashid thought. The results were applied to the Radio and Television Union building. The results confirmed that the design trends stemming from the digital revolution can produce local architecture that is technologically advanced and linked to the society cultural identity and the surrounding environment. This happens by merging between: environmental standards, society cultural standards, digital technologies, values of superposition, complexity, overlapping studied masses, abstraction, and that the building intangible spatial form is what drives its architectural meaning, defining and achieving the client goals in the building.

This article discusses a universal way to create animation using Asymptote the language for vector graphics. The Asymptote language itself has a built-in library for creating animations, but its practical use is complicated by an extremely brief description in the official documentation and unstable execution of existing examples. The purpose of this article is to eliminate this gap. The method we describe is based on creating a PDF-file with frames using Asymptote, with further converting it into a set of PNG images and merging them into a video using FFmpeg. All stages are described in detail, which allows the reader to use the described method without being familiar with the used utilities.

Proper regulative in earthquake risk reduction, hazard assessment, earthquake resistant design and construction of structures, should be under perpetual improvement. They are mainly the result of earthquake study and analysis of post-seismic effects. In this context, a new frame for seismogram analysis is proposed, based on its decomposition into elementary and single (positive and negative) fluctuations (EF/SF). Decomposition enables rearrangement, both providing the frame for defining new attributes, where several main ones are proposed and elaborated in the paper: fan diagram of EFs structural axes; R- or RQ-envelope, formed over positive and over negative peaks of ordered SFs; two forms of difference functions of positive and negative R/RQ-envelopes, as a measure of seismogram's (a)symmetry, in respect to t-axis; distributions of SFs durations. Several others are in perspective. Analogy between R-envelope and seismogram's spectrum is considered from the aspects of arranged elements, and asymptotic behavior of these two functional attributes. More objective definition of seismogram duration is proposed, determined by linear regression across the scatter plot of SFs peaks. R-envelope showed itself as an invariant in the seismogram population, and the distribution of SFs durations as well. Results are presented through extensive graphics, backed with mathematical description. Thorough discussion of the concept and results is given. [ABSTRACT FROM AUTHOR]

The artwork of sculptor, draftsperson, and installation artist Michael Richards (1963 – 2001) challenges prevalent assumptions about the physical properties, and therefore the aesthetic application, of suspension in Black cultural production. As an African American of Jamaican and Costa Rican descent, Richards grappled with questions of citizenship, racism, and freedom, frequently using motifs of flight and gravity. Although Richards created his work before his untimely death in the September 11 attacks on the World Trade Center, his piece titled Tar and Feather nevertheless anticipates the possibilities, and important limitations, of suspension as a theoretical framework. When placed in conversation with the theoretical discourse that now exists surrounding suspension, Richards's material sculptures and archival sketches posthumously anticipate the limits of conventional strategies for Black possibility. This paper argues that Tar and Feather illustrates the asymptotic imbrication of blackness and freedom, which renders the plot as both a diagram of forces and an abstract aesthetic geography from which to create. [ABSTRACT FROM AUTHOR]

Evoking a heady mix of the Cranbrook campus viewed from his window and the liquid viscerality of Hieronymus Bosch's Garden of Earthly Delights, which he was architecturally deconstructing at the time, architect and teacher Hani Rashid recounts his days as a Cranbrook student and the profound influence across the decades of those experiences on the work of his New York practice Asymptote Architecture. [ABSTRACT FROM AUTHOR]

Gamma ray spectra have interesting information about energy and intensity of gamma photons. Normally, this information is available in the peak area and background region. A full energy peak sits on a background continuum and produced by full energy absorption of high energy photons, while background region is produced by Compton scattering of the photons. The most essential concern of errors is in the method of determining the events in both peak and background areas. The uncertainty is low when the background counts are small relative to the peak counts. However, it becomes high when the counts of the peak area are low with respect to that of background. The detection threshold for the peak is ultimately determined by the uncertainty in the background counts. This depends on the technique used and the form of the produced spectra. This paper reviews different methods of determining peak area and their associated uncertainties in terms of the principle and application of the techniques used.

The formation of waviness on the working surfaces of bearing parts is associated with fluctuations in the size of the cut layer of metal and changes in the components of the cutting force. Laplace operators were used to model the centerless grinding system based on the construction of the transfer function and the characteristic equation. It was found that the formation of waviness depends on the position of the hodograph of the movement of the vector of the center of the part in the complex plane, which in turn depends on the geometric parameters of the rigid supports of the centerless grinder machine. This makes it possible, based on hodographs and the angular orientation of their asymptotes, to determine the geometric stability of the process depending on the angles of adjustment of the rigid supports of the grinder machine. Two methodological approaches were used to confirm the correctness of the hypotheses. The first one is a multiplication of wave’s hodographs. The second one is regeneration displacement and the coincidence of the combined hodograph of regeneration and waviness displacement mechanisms with the hodograph of infinitely rigid machine displacement. The diagrams which allow choosing geometry of adjustment of rigid support that allows to increase or decrease parameters of certain harmonics are developed. The 3D diagram allows setting the local minima, characterized by acceptable geometric adjustment conditions, providing regulated waviness of the working surfaces of bearing parts.

This essay considers an alternative form of reconciliation with my abuelita who passed away unexpectedly from a stroke in 2021. Beginning with her career as a professional singer refuting gender roles in Spain, I consider the trajectory of her life that led to her adulthood as a conservative Jehovah's Witness. Through speculative memory work and queer futurity, this essay queers abuelita in a way that reimagines her life as a musician, performer, and grandmother. I offer this as an example of how queer individuals negotiate and address the contradictions of reconciliation and queerness on their own terms. [ABSTRACT FROM AUTHOR]

In the present paper, we study Busemann functions in a general Finsler setting as well as in asymptotically harmonic Finsler manifolds. In particular, we show that Busemann functions are smooth on asymptotically harmonic Finsler manifolds. [ABSTRACT FROM AUTHOR]

Copyright of Journal of University of Anbar for Pure Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

There is increasing evidence that occasional utilization area (peripheral sites), in addition to typical utilization area (home range), is important for wildlife conservation and management. Here we estimated the maximum utilization area (MUA), including both typical and occasional utilization areas, based on asymptotic curves of utilization area plotted against sample size. In previous studies, these curves have conventionally been plots of cumulative utilization area versus sample size, but this cumulative method is sensitive to stochastic effects. We propose a new method based on simulation studies where outcomes of replicated simulations are averaged to reduce stochastic effects. In this averaged method, possible combinations of sample size with the same number of location data replicated from a dataset were averaged and applied to the curves of utilization area. The cumulative method resulted in a large variation of MUA estimates, depending on the start date as well as total sample size of the dataset. In the averaged method, MUA estimates were robust against changes in the start date and total sample size. The large variation of MUA estimates arose because location data on any day including the start date are affected by unpredictable effects associated with animal activity and environmental conditions. In the averaged method, replicates of sample size resulted in a reduction of temporal stochasticity, suggesting that the method stably provides reliable estimates for MUA. [ABSTRACT FROM AUTHOR]

Abstract There is increasing evidence that occasional utilization area (peripheral sites), in addition to typical utilization area (home range), is important for wildlife conservation and management. Here we estimated the maximum utilization area (MUA), including both typical and occasional utilization areas, based on asymptotic curves of utilization area plotted against sample size. In previous studies, these curves have conventionally been plots of cumulative utilization area versus sample size, but this cumulative method is sensitive to stochastic effects. We propose a new method based on simulation studies where outcomes of replicated simulations are averaged to reduce stochastic effects. In this averaged method, possible combinations of sample size with the same number of location data replicated from a dataset were averaged and applied to the curves of utilization area. The cumulative method resulted in a large variation of MUA estimates, depending on the start date as well as total sample size of the dataset. In the averaged method, MUA estimates were robust against changes in the start date and total sample size. The large variation of MUA estimates arose because location data on any day including the start date are affected by unpredictable effects associated with animal activity and environmental conditions. In the averaged method, replicates of sample size resulted in a reduction of temporal stochasticity, suggesting that the method stably provides reliable estimates for MUA.

The author of this article considers a numerical method that uses high-precision calculations to construct approximations to attractors of dynamical systems of chaotic type with a quadratic right-hand side, as well as to find the vertical asymptotes of solutions of systems of explosive type. A special case of such systems is the population explosion model. A theorem on the existence of asymptotes is proved. The extension of the numerical method for piecewise smooth systems is described using the Chua system as an example, as well as systems with hysteresis. [ABSTRACT FROM AUTHOR]

Abstract When we collect the growth curves of many individuals, orderly variation in the curves is often observed rather than a completely random mixture of various curves. Small individuals may exhibit similar growth curves, but the curves differ from those of large individuals, whereby the curves gradually vary from small to large individuals. It has been recognized that after standardization with the asymptotes, if all the growth curves are the same (anamorphic growth curve set), the growth curve sets can be estimated using nonchronological data; otherwise, that is, if the growth curves are not identical after standardization with the asymptotes (polymorphic growth curve set), this estimation is not feasible. However, because a given set of growth curves determines the variation in the observed data, it may be possible to estimate polymorphic growth curve sets using nonchronological data. In this study, we developed an estimation method by deriving the likelihood function for polymorphic growth curve sets. The method involves simple maximum likelihood estimation. The weighted nonlinear regression and least‐squares method after the log‐transform of the anamorphic growth curve sets were included as special cases. The growth curve sets of the height of cypress (Chamaecyparis obtusa) and larch (Larix kaempferi) trees were estimated. With the model selection process using the AIC and likelihood ratio test, the growth curve set for cypress was found to be polymorphic, whereas that for larch was found to be anamorphic. Improved fitting using the polymorphic model for cypress is due to resolving underdispersion (less dispersion in real data than model prediction). The likelihood function for model estimation depends not only on the distribution type of asymptotes, but the definition of the growth curve set as well. Consideration of these factors may be necessary, even if environmental explanatory variables and random effects are introduced.

A relation connecting stress intensity factors (SIF) with displacement intensity factors (DIF) at the crack front is derived by solving a pseudodifferential equation connecting stress and displacement discontinuity fields for a plane crack in an elastic anisotropic medium with arbitrary anisotropy. It is found that at a particular point on the crack front, the vector valued SIF is uniquely determined by the corresponding DIF evaluated at the same point.

One persistent curiosity in visuomotor adaptation tasks is that participants often do not reach maximal performance. This incomplete asymptote has been explained as a consequence of obligatory computations within the implicit adaptation system, such as an equilibrium between learning and forgetting. A body of recent work has shown that in standard adaptation tasks, cognitive strategies operate alongside implicit learning. We reasoned that incomplete learning in adaptation tasks may primarily reflect a speed-accuracy tradeoff on time-consuming motor planning. Across three experiments, we find evidence supporting this hypothesis, showing that hastened motor planning may primarily lead to under-compensation. When an obligatory waiting period was administered before movement start, participants were able to fully counteract imposed perturbations (Experiment 1). Inserting the same delay between trials – rather than during movement planning – did not induce full compensation, suggesting that the motor planning interval influences the learning asymptote (Experiment 2). In the last experiment (Experiment 3), we asked participants to continuously report their movement intent. We show that emphasizing explicit re-aiming strategies (and concomitantly increasing planning time) also lead to complete asymptotic learning. Findings from all experiments support the hypothesis that incomplete adaptation is, in part, the result of an intrinsic speed-accuracy tradeoff, perhaps related to cognitive strategies that require parametric attentional reorienting from the visual target to the goal. [ABSTRACT FROM AUTHOR]

The author of this article considers a numerical method that uses high-precision calculations to construct approximations to attractors of dynamical systems of chaotic type with a quadratic right-hand side, as well as to find the vertical asymptotes of solutions of systems of explosive type. A special case of such systems is the population explosion model. A theorem on the existence of asymptotes is proved. The extension of the numerical method for piecewise smooth systems is described using the Chua system as an example, as well as systems with hysteresis.

Copyright of KoG is the property of Croatian Society for Geometry & Graphics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

High school students often ask questions about the nature of infinity. When contemplating what the “largest number” is, or discussing the speed of light, students bring their own ideas about infinity and asymptotes into the conversation. These are popular ideas, but formal ideas about the nature of mathematical sets, or “set theory,” are generally unknown to high school students. The authors propose a method for introducing basic ideas in set theory to high school trigonometry students by connecting prior knowledge of the tangent function and the unit circle to Georg Cantor’s ideas about infinity. By doing so, high school teachers have an opportunity to inspire their students with rich mathematics.

When we collect the growth curves of many individuals, orderly variation in the curves is often observed rather than a completely random mixture of various curves. Small individuals may exhibit similar growth curves, but the curves differ from those of large individuals, whereby the curves gradually vary from small to large individuals. It has been recognized that after standardization with the asymptotes, if all the growth curves are the same (anamorphic growth curve set), the growth curve sets can be estimated using nonchronological data; otherwise, that is, if the growth curves are not identical after standardization with the asymptotes (polymorphic growth curve set), this estimation is not feasible. However, because a given set of growth curves determines the variation in the observed data, it may be possible to estimate polymorphic growth curve sets using nonchronological data.In this study, we developed an estimation method by deriving the likelihood function for polymorphic growth curve sets. The method involves simple maximum likelihood estimation. The weighted nonlinear regression and least‐squares method after the log‐transform of the anamorphic growth curve sets were included as special cases.The growth curve sets of the height of cypress (Chamaecyparis obtusa) and larch (Larix kaempferi) trees were estimated. With the model selection process using the AIC and likelihood ratio test, the growth curve set for cypress was found to be polymorphic, whereas that for larch was found to be anamorphic. Improved fitting using the polymorphic model for cypress is due to resolving underdispersion (less dispersion in real data than model prediction).The likelihood function for model estimation depends not only on the distribution type of asymptotes, but the definition of the growth curve set as well. Consideration of these factors may be necessary, even if environmental explanatory variables and random effects are introduced. [ABSTRACT FROM AUTHOR]

This paper reports on a study conducted with Grade 11 learners as participants, in four public high schools in a rural district of the Eastern Cape Province of South Africa. The central objective was to investigate the mathematical discourses of Grade 11 learners related to the word, algebraic and graphic representations of asymptotes of the hyperbola and exponential functions. Commognition and social learning theories were referred to, with particular emphasis on the characteristics of the mathematical discourse, that is, word use, visual mediators, endorsed narratives and routines. The study adopted a qualitative research design, with exploratory, descriptive and interpretive elements complementing both its data collection and analysis processes. A purposive sampling strategy was opted for in the study. Data was collected by means of a test administered to a total of 112 Grade 11 participants from the selected four high schools. Data was thematically analysed by means of a developed Discourse Profile of the Hyperbola and Exponential Function adapted from the Arithmetic Discourse Profile. The study's findings revealed that, while there was evidence of learning functions, for these leareners, the process of de-ritualisation was not yet complete. There were also challenges in linking different representations of a function. Learners could work efficiently on procedure tasks, but struggled on action-oriented tasks. [ABSTRACT FROM AUTHOR]

As Internet of Things (IoT) has boomed in recent years, many security issues have also been exposed. Focusing on physical layer security in wireless Internet of Things network communication, a series of security methods have been widely studied. Nevertheless, cooperative jamming methods in physical layer security to fight against collusive eavesdroppers have not been thoroughly studied yet. In this article, we study a cooperative-jamming-based physical layer secure transmission scheme for Internet of Things wireless networks in the presence of collusive eavesdroppers. We design a cooperative jamming strategy without knowing the channel state information of eavesdroppers. Considering the cooperation of multiple nodes with multiple antennas, this strategy can maximize the signal-to-interference-plus-noise ratio at an actuator (legitimate receiver). Meanwhile, the generated cooperative jamming signals can reduce the signal-to-interference-plus-noise ratio at eavesdroppers. To explore the theoretical security performance of our strategy, we perform a secrecy outage probability analysis and an asymptotic analysis. In the cases of cooperative jamming and without cooperative jamming, the closed-form expressions of the secrecy outage probability are deduced, and the influence of system parameters on the secrecy outage probability becomes more intuitive through a strict mathematical asymptotic behavior analysis. In addition, considering the energy limitation of Internet of Things devices, we propose a power allocation algorithm to minimize the total transmission power given the security requirements. The numerical results show the effectiveness of our schemes and are consistent with the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this work, we study the stability of the expanding configurations of radiation gaseous stars. Such expanding configurations exist for a thermodynamic model, given as a class of self-similar solutions to the associated dynamic system with viscosity coefficients satisfying 2 μ + 3 λ = 0 for the monatomic gas; that is, the bulk viscosity is vanishing. With respect to small perturbations, this work shows that the linearly expanding homogeneous solutions are stable for a large expanding rate. This is an extensive study of the result in [14] by Hadžić and Jang. [ABSTRACT FROM AUTHOR]

In this paper, we give a generalization of the well-known Minkowski distance family in the n-dimensional Cartesian coordinate space. Then we consider three special cases of this family, which are also generalizations of the taxicab, Euclidean, and maximum metrics, respectively, and we determine some circle properties of them in the real plane. While we determine some properties of circles of these generalized distances, we discover a new definition of ellipses, and then we also determine a similar definition of hyperbolas, which will be new members among different metrical definitions of central conics in the Euclidean plane. [ABSTRACT FROM AUTHOR]

Topology analysis and geometric feature determination for curves and surfaces are basic problems in geometric modeling and computer aided design. When the curves and surfaces are given in implicit expressions, the problems become more difficult. This paper presents a complete algorithm framework for the problem of certified G 1 approximation of a planar algebraic curve under global error control. Compared to other work on topology and geometric analysis of algebraic curves, this method presents a new topology analysis as well as a geometric information computation. Moreover, this method uses generalized asymptotes as the approximation of the unbounded part, which makes it achieve global approximation with given precision. [ABSTRACT FROM AUTHOR]

Various numerical methods have been being extensively used to estimate the diffusion parameters of pertechnetate (99TcO4−) in compacted MX80 bentonite clay using through-diffusion (TD) techniques. In this study, an improved TD column test was applied, and the diffusion fluxes of tritium (HTO) as a non-reactive radionuclide, and 99TcO4− with various dry densities, were compared under the same experimental conditions. Similar results were obtained for the apparent diffusion coefficients of HTO and 99TcO4− using three estimation methods: a graphical method applying the asymptote calculation, an analytical solution using Lsqcurvefit installed in MATLAB, and the Marquardt–Levenberg optimization algorithm in the HYDRUS-1D inverse method. The statistical analysis showed that the densities using a one-way analysis of variance (ANOVA) for the three estimation methods ranged from 1200 to 2000 kg/m3, which indicated that there were no obvious differences between HTO and 99TcO4−. In general, the diffusion parameters of 99TcO4− were lower than those for HTO due to anion exclusion effects and lower accessible porosity.

High school students often ask questions about the nature of infinity. When contemplating what the "largest number" is, or discussing the speed of light, students bring their own ideas about infinity and asymptotes into the conversation. These are popular ideas, but formal ideas about the nature of mathematical sets, or "set theory," are generally unknown to high school students. The authors propose a method for introducing basic ideas in set theory to high school trigonometry students by connecting prior knowledge of the tangent function and the unit circle to Georg Cantor's ideas about infinity. By doing so, high school teachers have an opportunity to inspire their students with rich mathematics. [ABSTRACT FROM AUTHOR]

In this paper the invariants of the second order curves under unsymmetrical and non-orthogonal linear transformation in Euclidian space is studied. [ABSTRACT FROM AUTHOR]

Given a real rational parametrization P (t) of a plane curve C , we present an algorithm to compute polynomial curves to approximate C for the whole parameter domain. In this case, the denominators often have real roots in the whole interval. We decompose the interval as the union of finitely many intervals according to the real roots of the denominators. The key technique of the paper is to approximate the given curve by their asymptotes and error analysis at each interval is also presented. The asymptotes are associated with the infinity points corresponding to the real roots of the denominators. Numeric algorithms and examples are proposed to illustrate our results. [ABSTRACT FROM AUTHOR]

The paper analyses a problem of great theoretical importance in practice of perspective: the nature of the perspective of a circle from the horizontal plane according to the relative position between the spectator plane (parallel to the picture plane) and the given circle. Depending on the position of the neutral line to the circle, the nature of the perspective of a point describing the circle can be determined, because the corresponding visual radius generates a conical surface, and the perspective of the mobile point becomes the conical section made in the conical surface by the picture plane. The paper intends to highlight the validity of Dandelin's theorem when putting a circle into perspective. A discussion of examples characteristic for this problem is offered. Several conclusions distinguish the main points and results of the paper.

The study investigated learners’ mathematical discourse on the hyperbola from a commognitive perspective, and focused on algebraic, graphic, and numeric representations of the hyperbola. Task-based interviews were conducted with five Grade 10 learners from a township school. Learners’ mathematical discourse was analysed by means of the Discourse Profile of the Hyperbola, which was adapted from the Arithmetic Discourse Profile of Ben-Yahuda et al. We found that, while learners’ graphs were mainly mathematically correct, their word use was colloquial and their interpretation of the mediators and their narratives were generally visual. Taken together, this suggests that their routines were ritualised. Learners’ tables of values did not show asymptotic behaviour yet they drew graphs showing two asymptotes. However, four learners tended to talk as if there were only one asymptote and they had difficulty in seeing the axes as asymptotes. [ABSTRACT FROM AUTHOR]

The goal of improving reading rate and fluency is to positively impact reading comprehension; however, it is unclear how fast students with learning disabilities (LD) need to read to reap this benefit. The purpose of this research was to identify the point of diminishing return for students who were dysfluent readers. Participants included 337 students with reading difficulties in second and fourth grade (61% eligible for special education; 80% with a diagnosis of LD in the area of reading) and 150 typical readers from the same general education classes. LOESS (LOcal regrESSion) plots (logistic regression) were used to determine where linear relations between reading rate and comprehension broke down for these students: the rate at which getting faster no longer contributed clearly to reading comprehension improvement. Although typical readers in this sample showed patterns of oral reading rate and comprehension similar to students in other studies, patterns for students with reading difficulties differed. For dysfluent readers, improving reading rate improved comprehension only in the bands between 35 and 75 words correct per minute in second grade and between 40 and 90 words correct in fourth grade. Reading at faster rates revealed no clear advantage for reading comprehension. [ABSTRACT FROM AUTHOR]

The paper analyses a problem of great theoretical importance in practice of perspective: the nature of the perspective of a circle from the horizontal plane according to the relative position between the spectator plane (parallel to the picture plane) and the given circle. Depending on the position of the neutral line to the circle, the nature of the perspective of a point describing the circle can be determined, because the corresponding visual radius generates a conical surface, and the perspective of the mobile point becomes the conical section made in the conical surface by the picture plane. The paper intends to highlight the validity of Dandelin's theorem when putting a circle into perspective. A discussion of examples characteristic for this problem is offered. Several conclusions distinguish the main points and results of the paper. [ABSTRACT FROM AUTHOR]