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The article explores the philosophy and humour in the popular animated science-fiction sitcom Rick and Morty, which premiered in 2013. The series offers productive material through which important philosophical and cultural questions and challenges can be explored. The subject of the study is the explication of the problem of reality and opposition of determinism and freedom in the context of modern society, which is largely characterized by technological advances. The research aims to show how the creators of the series interpret these problems and what place they leave for a human in the world and Universe. The series has already become a target of academic research, and this article shows how researchers use the material of the series to study social theories, ontological and ethical issues, the boundaries of the human, etc. The author attempts to consider the series as an object of complex humanitarian research. The relevance of the study is due to the fact that the growing interaction between humans and technology makes one turn to philosophy and culture in order to preserve the humane and prevent the formation of a non-human-sized world. The author concludes that the main message of Rick and Morty is the rejection of anthropocentrism and human exceptionalism. However, the seemingly pessimistic viewpoint advocated by the creators of the series is justified by the growing complexity of the world. The series motivates productive reflection on the current state of our world and its future.

Abstract Background It is important to determine if a horse is shedding Salmonella spp., but a complete culture series can be cost prohibitive. Objectives Determine the optimal pooling technique to maintain high sensitivity of Salmonella spp. culture using spiked samples, and then demonstrate the efficacy of this protocol on clinical submissions. Hypothesis Pooled fecal samples are as sensitive as 5 individual cultures for the detection of Salmonella shedding. Animals A single Salmonella‐negative horse from the university herd, and 19 hospitalized horses. Methods Salmonella‐free fecal samples were spiked with different amounts of Salmonella spp. (102, 103, 104, and 105 colony forming units [cfu]) and homogenized to evaluate pooled samples. Five individual fecal samples were collected from 19 hospitalized horses. Ten‐gram aliquots of each individual sample were combined to make a pooled sample. Both individual and pooled samples were cultured for Salmonella spp. The identity of bacterial isolates was confirmed by matrix‐assisted laser desorption‐ionization time of flight mass spectrometry. Results A 102 cfu concentration of Salmonella spp. could be recovered from a spiked Salmonella‐free fecal sample. Homogenization protocols indicated that the addition of 20 mL of broth to the pooled sample improved recovery, whereas homogenization time did not. Of the 19 horses tested, 5 were positive for Salmonella. In all instances, Salmonella spp. were recovered from the fecal pool as well as individual samples. Conclusions and Clinical Importance Pooling of 5 fecal samples for Salmonella culture is a sensitive and cost‐effective diagnostic approach to detect horses that are shedding the organism.

This article presents a new beam model that employs a recursive derivation procedure that enables the user to set the order of the governing differential equations as an input parameter, without the need for ad hoc assumptions or methodologies. This article employs a novel system of kinematic variables, section constants, and section functions that facilitate the development of higher-order beam models that retain a clear philosophical link to classical beam models such as Euler–Bernoulli beam theory and Timoshenko beam theory. The present beam model is a type of equivalent single layer beam model, wherein section constants are used to model the global stiffness characteristics of the beam, and section functions are used to recover sectional fields of displacements, strains, and stresses. The present beam model is solved for several example beams, and the results are compared to the results of finite element analyses. It is shown that the present beam model can accurately predict the deformed shapes and stress fields of each of the example beams. This article also reveals an interesting peculiarity of the elastic potential energy that pertains to any unidimensional beam model that is governed by differential equations that are of finite order.

Ficha técnica: Mª José Labrador, Mª José Arrojo, Mª Elena Martín, Carmen Romano, Mª Teresa Nicolás, Carmen Vidal Tirant Humanidades, Valencia, 2023 195 pp. ISBN 978-84-1937-698-5

Objective: This study investigates subjective and objective interaction processes expressed in the series that can foster the construction of representations of girl power today. Methodological design: To do so, I conducted in-depth interviews with individuals who call themselves fans of the series and analyzed journalistic materials published in digital media vehicles that link the concept of girl power to the series' imaginary. Results: The results were interpreted in the light of intersectional feminism and critical marketing. I observed that the act of placing women at the center of narratives represents a shift in contemporary dramaturgy. Research limitations / implications: It is not possible to conclude that this series is feminist, as highlighted by some interviewees. This divergence arises due to conceptual mismatches between female empowerment; post-feminism; neoliberal appeals; the attitude of the characters; and those responsible for the construction of the series observed during the analysis of the study. Originality: The study unites theories from different theoretical heritages, thus stimulating different perspectives and interdisciplinary openings to understand contexts that connect marketing, consumer behavior, and consumption to feminist studies. Furthermore, it stimulates the development of critical thinking capable of impacting societies, organizations, institutions, and consumption focused on the debate. [ABSTRACT FROM AUTHOR]

Copyright of Cuadernos.info is the property of Pontificia Universidad Catolica de Chile, Facultad de Comunicaciones 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.)

Copyright of Sigmae is the property of Universidade Federal de Alfenas (UNIFAL-MG) 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.)

As a company, Netflix is currently demonstrating an unprecedented impact on audiovisual markets around the world. As a part of the global media dynamic, Poland is susceptible to changes resulting from the streaming platforms’ increasing intrusion into local audiovisual markets. While Anglo-American researchers have analyzed in depth the repercussions of Netflix’s involvement in local markets, in Poland the consequences of this media giant’s activities remain neglected in media studies. This article is an attempt to identify areas where Netflix’s impact on the Polish industry is significant and leads to visible changes in the industry’s existing practices and work system. As such, this article contributes to the emerging body of academic work, namely the platformization of the cultural sector, to which we can certainly assign audiovisual production. Based on in-depth interviews with industry practitioners and an analysis of the content produced for Netflix and its institutional positioning in Poland, the article maps the changes in the Polish audiovisual industry that are occurring here and now. [ABSTRACT FROM AUTHOR]

Copyright of Cuadernos del Centro de Estudios de Diseño y Comunicación is the property of Cuadernos del Centro de Estudios de Diseno y Comunicacion 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.)

Copyright of Cuadernos del Centro de Estudios de Diseño y Comunicación is the property of Cuadernos del Centro de Estudios de Diseno y Comunicacion 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.)

The sum range SR x ; X , for a sequence x = (x n) n ∈ N of elements of a topological vector space X, is defined as the set of all elements s ∈ X for which there exists a bijection (=permutation) π : N → N , such that the sequence of partial sums (∑ k = 1 n x π (k)) n ∈ N converges to s. The sum range problem consists of describing the structure of the sum ranges for certain classes of sequences. We present a survey of the results related to the sum range problem in finite- and infinite-dimensional cases. First, we provide the basic terminology. Next, we devote attention to the one-dimensional case, i.e., to the Riemann–Dini theorem. Then, we deal with spaces where the sum ranges are closed affine for all sequences, and we include some counterexamples. Next, we present a complete exposition of all the known results for general spaces, where the sum ranges are closed affine for sequences satisfying some additional conditions. Finally, we formulate two open questions. [ABSTRACT FROM AUTHOR]

The paper proposes a new three-dimensional flexible hinge formed of several serially linked straight- and circular-axis segments that are disposed of in two layers. The novel hinge configuration is capable of large displacements and can be implemented in precision-compliant mechanisms that need to cover large spatial workspaces. Based on simplified geometry, an analytical compliance model is formulated that connects the loads to the displacements at one end of the hinge. Finite element simulation and experimental prototype testing of actual-geometry hinge configurations confirm the analytical model predictions. A related compliance-based analytical model evaluates the maximum loads that can be applied to the hinge and the resulting displacements. The two small-deformation analytical models are subsequently utilized to investigate the relationship between geometric parameters and the hinge performance qualifiers. [ABSTRACT FROM AUTHOR]

In this paper, for a two-dimensional wave equation in a rectangular parallelepiped, the Dirichlet problem. A uniqueness criterion is established. The solution is constructed as the sum of an orthogonal series. When justifying the convergence of a series, the problem of small denominators of two natural arguments arose for the first time. An estimate on separation from zero with the corresponding asymptotics is established, which makes it possible to prove the convergence of the series in the class of regular solutions and the stability of the solution with respect to boundary functions. [ABSTRACT FROM AUTHOR]

The article presents a solution to a boundary value problem for a fourth-order equation with multiple characteristics. The theorems of uniqueness, existence and existence of a regular solution of the problems are proved. [ABSTRACT FROM AUTHOR]

Partindo das fichas de edição de O nosso idioma: curso elementar, que registram, longitudinalmente, os dados editoriais deste livro, tenho por objetivo investigar possibilidades de, teórica e metodologicamente, determinar relações entre livros didáticos e suas condições sócio-históricas de emergência e permanência nos seus espaços sociais de circulação. Para tanto, assumo uma abordagem aplicada de base discursiva, que, por meio da noção de acontecimento discursivo, aproxima-se de procedimentos da História, especialmente, do método serial. Proponho que as relações entre as instâncias de produção, circulação e recepção de livros didáticos sejam concebidas como acontecimentos discursivos, e os dados em série das fichas como enunciados informados pelas condições sócio-históricas de existência dessas instâncias. Os resultados mostram que, ao abordar, nesses termos, um produto editorial como o livro didático, pode-se abrir caminho para capturar suas relações contraditórias com fatos sociopolíticos, como reformas educacionais, afastando, assim, leituras mecanicistas sobre sua emergência e permanência.

É com satisfação que anunciamos o mais novo número da Revista GEMInIS (v. 14, n. 2), uma edição especial por ser a primeira do periódico vinculada ao Mestrado Profissional em Produção de Conteúdo Multiplataforma – PPGCOM/UFSCar, recém aprovado pela CAPES, na área de Comunicação e Informação. Neste número são apresentados trabalhos sobre diferentes temas do campo da comunicação e audiovisual, abrangendo pesquisas sobre televisão, filmes, narrativas seriadas, práticas de fãs nas redes sociais, videogames, e-sport e ensino de roteiro. São estudos que, em seu conjunto, trazem abordagens exploratórias a respeito de fenômenos comunicativos contemporâneos.

The 5G communication system requires an antenna as a receiving device that has high performance including wide bandwidth and high gain. Microstrip antennas have advantages such as low cost, suitable for high frequencies and easy to integrate with other devices. One of the disadvantages of microstrip antennas is their narrow bandwidth and low gain. Therefore, microstrip antennas with wide bandwidth and high gain are especially needed to support 5G communication systems. This paper provides a solution by proposed a wide bandwidth and high gain microstrip antenna operating at a resonant frequency of 3.5 GHz for a 5G communication system. The proposed antenna was developed in four stages starting from a single element, a two-element series array, a 4-element series array and a 4×2-element planar series array. A series planar array technique is proposed to increase the gain and bandwidth of the microstrip antenna simultaneously. In this paper, simulations and measurements from the proposed antenna are displayed and compared comprehensively to show the performance improvement from each stage of the development of the proposed model. Based on the measurement results, the designed antenna has an impedance bandwidth (IBW) of 0.6 GHz and fractional bandwidth (FBW) of 17.14 % with a frequency range of 3.11–3.71 GHz and maximum gain of 12.2 dB at a resonant frequency of 3.5 GHz. The bandwidth and gain of the antennas increased by 205 % and 99.03 % compared to single element antennas, respectively. Therefore, the proposed antenna can be recommended to be used as a receiving antenna for 5G communication systems. [ABSTRACT FROM AUTHOR]

The paper presents formulations of inverse problems for the Helmholtz equation on finding its right-hand side with a Samarskii–Ionkin-type additional integral condition and the justification of their well-posedness in the Hadamard sense in the class of regular solutions. The uniqueness of solutions of the formulated problems is proved on the basis of integral identities. Solutions of the problem are found in explicit form by the methods of separation of variables and integral equations. [ABSTRACT FROM AUTHOR]

Copyright of Prolegomena: Journal of Philosophy is the property of Society for the Advancement of Philosophy 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.)

Copyright of Fórum Lingüístico is the property of Forum Linguistico 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.)

In this article, we obtain an integral representation for a remainder sum of the Dirichlet Eta function. We then obtain numerous generating functions and series concerning the usage of the obtained integral representation. Alternating Fibonacci sum of the remainder sum of the Dirichlet Eta function has been obtained, as well as the squared version of the Fibonacci series concerning the sum. A generalized representation of the product of polynomials concerning the remainder sum of the Dirichlet Eta function has been obtained. Numerous examples have been provided to showcase the derived results. [ABSTRACT FROM AUTHOR]

Copyright of Revista Fotocinema is the property of Revista Fotocinema 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.)

Copyright of International Journal on Criminology is the property of Policy Studies Organization 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.)

Background: The rapid and ongoing phenomenon of global warming has negatively impacted both the Earth’s environment and its inhabitants. Time series and regression analysis techniques play a significant role in weather forecasting and the interpretation of climate data. One of the key characteristics of time series analysis is stationarity. Methods: In this article, we explore how detrending and differencing techniques can be used to transform the time series of global temperature and carbon dioxide into stationary series. Regression models and goodness of fit tests were used to examine the relationship between carbon dioxide and data on global temperature. A cross-correlation time series model is also used to assess those time series’ lagging and leading characteristics. Results: The study of data on global temperature anomalies indicates that detrending and differencing are helpful in transforming temperature time series into stationary time series. However, the first differencing and detrending methods do not make the carbon dioxide time series stationary; instead, an alternate transformation is needed. Neither the carbon dioxide time series nor the global temperature time series lag or lead with regard to the cross-correlation function. Conclusions: In this article, we looked into stationarity and some other topics associated with correlation in terms of data on CO2 and global temperature. Stationarity is one of the important properties to check before conducting a more thorough investigation of the time series. To transform a non-stationary time series into a stationary one, there are numerous techniques available. However, in this article, we just pay attention to detrending and differencing and how those methods perform with respect to time series data for global temperature and carbon dioxide.

Este estudio analiza las principales características de los personajes de las series españolas que se emiten en las plataformas de streaming desde la óptica de la diversidad, poniendo el foco en cuestiones de género, edad, nacionalidad, etnia, orientación sexual y diversidad funcional. En los últimos años, la expansión de este tipo de plataformas ha transformado los niveles de representación e inclusión en sus contenidos audiovisuales que, incluso, son publicitados como diversos. En este artículo se busca comprobar si la representación que ofrecen estos productos es similar a la real o, por el contrario, la diversidad es solo una estrategia de marketing para atraer a los servicios de suscripción o para realizar lo que se denomina diversity washing, esto es, utilizar la diversidad para cubrir cuotas, pero sin considerarla verdaderamente. Para poder determinar los principales rasgos de representación de los personajes, se ha realizado un análisis de contenido de 38 series emitidas en plataformas españolas en 2021, con un total de 749 personajes. Los resultados indican que aún no puede hablarse de una representación diversa en las plataformas de streaming; sigue existiendo un predominio masculino en los papeles protagónicos en un contexto de heteronormatividad, y hay franjas de edad infrarrepresentadas, como la vejez. Asimismo, aunque se haya aumentado la presencia de personajes de diferentes orígenes geográficos y etnias, la gran mayoría de los personajes son caucásicos. Cabe destacar que apenas hay personajes con diversidad funcional en este tipo de ficción seriada.

Some problems of the olympiad are considered. One of them is solved.

Marie Curie es una de las figuras más relevantes no solo en el ámbito científico, sino también históricamente por múltiples motivos diferentes. Esto ha propiciado que el cine y la televisión durante décadas hayan retratado su vida centrándose en uno u otros aspectos. Esta investigación analiza doce producciones audiovisuales en las que se emplea en mayor o menor medida la ficción para recrear la trayectoria de esta científica, dividida en cuatro temas: infancia, trabajo científico, matrimonio y vida personal (Langevin, enfermera e hijas). El estudio de estos campos dentro de cada una de las películas, series y documentales que conforman la muestra revelan interesantes divergencias entre la persona y el personaje de Marie Curie. A su vez, se observan diferentes enfoques según el público al que se han dirigido y el contexto en el que se han realizado estas producciones. Se concluye que la figura de Curie y sus heterogéneas aristas han sido bien aprovechadas por la mayor parte de la filmografía analizada para ir más allá de la divulgación de su trabajo científico y retratarla, en muchos casos, como alguien adelantada a su época e, incluso, avanzada para la actualidad.

Introducción: El auge y apogeo de las plataformas de vídeo bajo demanda han contribuido, en gran medida, a modificar la realidad audiovisual tal y como se conocía hasta la fecha. Dentro de este contexto audiovisual, las series de televisión son un género televisivo que goza de gran popularidad entre la audiencia, donde destacan aquellas dirigidas al público adolescente y juvenil. Metodología: El presente estudio de investigación se ha basado en una metodología cualitativa basada en el análisis de contenido de una serie de televisión, así como de los personajes, analizando para ello los aspectos educomunicativos en materia de educación sexual en la serie Sex Education. Resultados: Cabe destacar que las principales temáticas de la serie giran en torno a las relaciones sexuales entre adolescentes, a enfermedades de transmisión sexual y embarazos adolescentes, entre otros; mientras que, entre los personajes, el grupo más numeroso es el de los familiares, siendo el de los adolescentes el que tiene un mayor peso interpretativo. Discusión: Se observa como la serie Sex Education presenta un patrón similar a otras series de televisión dirigidas al público adolescente, mostrando temáticas basadas en la amistad o las relaciones sexuales, entre otras. Conclusiones: Sex Education presenta la educación sexual a los adolescentes desde un punto de vista educomunicativo, ofreciendo enseñanzas adecuadas y fácilmente comprensibles.

In the present work, two new recurrences of the Jacobsthal sequence are defined. Some identities of these sequences which we call the Jacobsthal array is examined. Also, the generating and series functions of the Jacobsthal array are obtained. [ABSTRACT FROM AUTHOR]

Copyright of Index.Comunicación is the property of Index.comunicacion 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.)

Some new relations for the confluent Horn functions H 3 (c) (a , b , c ; d ; w , z) , H 4 (c) (a , c ; d ; w , z) and H 9 (c) (a , b ; c ; w , z) are obtained including differentiation and integration formulas, series and reduction formulas. Some generating functions for various special functions are given in terms of these Horn functions. [ABSTRACT FROM AUTHOR]

Thermal model is developed to predict the outlet water temperature with respect to time for water-in-tube type evacuated solar collector connected in series. Developed mathematical expression is validated for the single collector and two collectors connected in series. In each collector, there are 20 evacuated tubes connected to the storage tank. Coefficient of determination (R2), reduced chi-square (χ²), and root mean squared error (RMSE) have been calculated to show the prediction accuracy of the developed model. For single and two collectors connected in series, R2 is 99.73% and 99.90%, χ² is 0.46 °C and 0.39 °C, and RMSE is 0.70 °C and 0.65 °C, respectively. Predicted value shows good agreement with the experimental value. At a constant mass flowrate, the maximum outlet temperature reaches 53.10 °C and 71.50 °C for single and two collectors in series, respectively. The maximum energy for the single collector is 4.12 kW and 4 kW, while for two collectors connected in series, the maximum energy is 7.08 kW and 6.69 kW. Average thermal efficiency is 4.45% and 4.51% and average exergy efficiency is 9.66% and 15.17% for single and series-connected collectors, respectively. Developed model can design energy-efficient "water-in-tube type evacuated tube collector" for domestic and industrial applications. [ABSTRACT FROM AUTHOR]

For the equation of vibrations of a rectangular plate, the initial-boundary value and inverse problems of finding the right-hand side (the source of vibrations) are studied. Solutions of the problems are constructed explicitly as sums of series, and the corresponding uniqueness and existence theorems are proved. When substantiating the existence of a solution to the inverse problem of determining the factor on the right-hand side, which depends on spatial coordinates, the problem of small denominators of two natural variables arises, for which estimates of the separation from zero with the corresponding asymptotics are established. These estimates made it possible to prove the existence theorem for this problem in the class of regular solutions by imposing certain smoothness conditions on the given boundary functions. [ABSTRACT FROM AUTHOR]

Binge-watching refers to the consecutive viewing of episodes of a fictional series, usually of the drama genre, in a single session. The approaches to its background, practice, and effects are diverse and controversial. Using a qualitativeexploratory approach analysed with Grounded Theory, this paper studies the experience of binge-watching users from data collected from a sample of 20 individuals combined with techniques such as group meetings, in-depth interviews and projective techniques. Results lead to the identification of two underlying patterns of behaviour associated with the consumption of dramatic content: planned binge-watching and unplanned binge-watching. Planned binge-watching is the intentional consumption of more than two consecutive episodes of a fictional series whose psychological effects are mainly gratification based on evasion. Planned series consumption has a socializing effect, especially among young people. Unplanned binge-watching is the unintentional and spontaneous chained viewing of more than two episodes of a fiction series. The viewing unit is each individual episode, linked to the next by the curiosity aroused by the plot. The psychological effects are gratification derived from evasion, followed by a feeling of guilt derived from the loss of control. The study concludes with the formulation of seven hypotheses for empirical verification, academic and professional implications, and future lines of research. [ABSTRACT FROM AUTHOR]

Insects are often depicted in mainstream movies as antagonists. And no wonder – they seem utterly alien to humans. Flies especially were always pariahs on the silver screen, ever since Frank Langelaan first wrote a short story in 1957 about an unfortunate experiment. Hollywood adapted this horror story to the movie screen twice, once in 1958 and then in 1986. This article is about body-horror, science gone awry, insect politics in (the original and the remade) The Fly movies. [ABSTRACT FROM AUTHOR]

Copyright of Polizei & Wissenschaft is the property of Verlag fur Polizeiwissenschaft 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.)

An initial-boundary value problem is studied for a nonhomogeneous equation of mixed parabolic-hyperbolic type in three variables with a degenerate parabolic part in a rectangular parallelepiped. A uniqueness criterion for its solution is established. The solution is constructed as a sum of an orthogonal series. Justifying the convergence of the series has led to the problem of small denominators of two natural arguments. Estimates on the separation of small denominators from zero with the corresponding asymptotics are established. These estimates have made it possible to substantiate the convergence of the constructed series in the class of regular solutions of this equation. The stability of the solution with respect to the boundary function and the right-hand side of the equation is established. [ABSTRACT FROM AUTHOR]

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Ellipsoidal and plane-elliptical surfaces are widely used as reflective, point-to-point focusing elements in many optical systems, including X-ray optics. Here the classical optical path function approach of Fermat is applied to derive a closed-form expression for these surfaces that are uniquely described by the object and image distances and the angle of incidence at a point on a mirror surface. A compact description facilitates design, modeling, fabrication, and testing to arbitrary accuracy. Congruent surfaces in two useful coordinate systems — a system centered on the ellipsoid's axes of symmetry and a mirror-centered or `vertex' system with the surface tangent to the xy plane at the mirror's center — are presented. Expressions for the local slope and radii of curvature are derived from the result, and the first several terms of the Maclauren series expansion are provided about the mirror center.