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Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 115
Author(s):  
Sakhi Zaman ◽  
Latif Ullah Khan ◽  
Irshad Hussain ◽  
Lucian Mihet-Popa

The paper demonstrates symmetric integral operator and interpolation based numerical approximations for linear and nonlinear ordinary differential equations (ODEs) with oscillatory factor x′=ψ(x)+χω(t), where the function χω(t) is an oscillatory forcing term. These equations appear in a variety of computational problems occurring in Fourier analysis, computational harmonic analysis, fluid dynamics, electromagnetics, and quantum mechanics. Classical methods such as Runge–Kutta methods etc. fail to approximate the oscillatory ODEs due the existence of oscillatory term χω(t). Two types of methods are presented to approximate highly oscillatory ODEs. The first method uses radial basis function interpolation, and then quadrature rules are used to evaluate the integral part of the solution equation. The second approach is more generic and can approximate highly oscillatory and nonoscillatory initial value problems. Accordingly, the first-order initial value problem with oscillatory forcing term is transformed into highly oscillatory integral equation. The transformed symmetric oscillatory integral equation is then evaluated numerically by the Levin collocation method. Finally, the nonlinear form of the initial value problems with an oscillatory forcing term is converted into a linear form using Bernoulli’s transformation. The resulting linear oscillatory problem is then computed by the Levin method. Results of the proposed methods are more reliable and accurate than some state-of-the-art methods such as asymptotic method, etc. The improved results are shown in the numerical section.


Author(s):  
Umesh Kumar Sharma ◽  
Shweta ◽  
Ambuj Kumar Mishra

The presence of exotic matter for the existence of the wormhole geometry has been an unavoidable problem in GR. In recent studies, researchers have tried to deal with this issue using modified gravity theories where the WH geometry is explained by the extra curvature terms and NEC’s are not violated signifying the standard matter in the WH geometry. In this paper, we investigate the solutions of traversable wormholes with normal matter in the throat within the framework of symmetric teleparallel gravity [Formula: see text], where [Formula: see text] is the non-metricity scalar that defines the gravitational interaction. We analyze the wormhole geometries for three forms of function [Formula: see text]. First is the linear form [Formula: see text], second a nonlinear form [Formula: see text] and third one a more general quadratic form [Formula: see text] with [Formula: see text], [Formula: see text] and [Formula: see text] being the constants. For all the three cases, the shape function is taken as [Formula: see text] where [Formula: see text] is the throat radius. A special variable redshift function is considered for the discussion. All the energy conditions are then examined for the existence and stability of the wormhole geometry.


2021 ◽  
Vol 10 (3) ◽  
pp. 303-306
Author(s):  
Elmira Sherifovna Shefieva ◽  
Olga Nikolaevna Bessarabova

The paper considers the features of development and practical use of an electronic foreign language textbook at the technical university. This study is dictated by the need to resolve contradictions between the provisions declared by the higher education standards of the latest generation and the real level of students knowledge of a foreign language. The authors analyze and systematize the requirements for printed and electronic foreign language textbooks. Attention is paid to the advantages of electronic publications over printed ones. The key advantage of the electronic textbook is the presence of hypertext, which makes it possible to implement a nonlinear form of information organization. The paper formulates basic principles of an electronic textbook development, describes its structure and components and highlights the issues of filling the content with language material. The authors proposed the options for tasks aimed at stimulating students communicative and cognitive activity. It is shown that podcasts can be used as multimedia resources to intensify the development of students listening skills. It is emphasized that the availability of special programs for creating electronic textbooks allows the teacher to carry out its development without any special training in the field of programming. As a result of the analysis, the authors come to the conclusion about a high linguodidactic potential of the electronic textbook as a teaching tool.


Fluids ◽  
2021 ◽  
Vol 6 (9) ◽  
pp. 311
Author(s):  
Marcello Lappa ◽  
Alessio Boaro

The present study aims to probe the role of an influential factor heretofore scarcely considered in earlier studies in the field of thermovibrational convection, that is, the specific time-varying shape of the forcing used to produce fluid motion under the effect of an imposed temperature gradient. Towards this end, two different temporal profiles of acceleration are considered: a classical (sinusoidal) and a pulse (square) wave. Their effects are analyzed in conjunction with the ability of a specific category of fluids to accumulate and release elastic energy, i.e., that of Chilcott–Rallison finitely extensible nonlinear elastic (FENE-CR) liquids. Through solution of the related governing equations in time-dependent, three-dimensional, and nonlinear form for a representative set of parameters (generalized Prandtl number Prg=8, normalized frequency Ω=25, solvent-to-total viscosity ratio ξ=0.5, elasticity number ϑ=0.1, and vibrational Rayleigh number Raω=4000), it is shown that while the system responds to a sinusoidal acceleration in a way that is reminiscent of modulated Rayleigh–Bénard (RB) convection in a Newtonian fluid (i.e., producing a superlattice), with a pulse wave acceleration, the flow displays a peculiar breaking-roll mode of convection that is in between classical (un-modulated) RB in viscoelastic fluids and purely thermovibrational flows. Besides these differences, these cases share important properties, namely, a temporal subharmonic response and the tendency to produce spatially standing waves.


Author(s):  
Sergey V. Lesnikov ◽  

This article discusses the construction of the terminological code of the Russian language in the form of information-search hypertext thesaurus. The code is developed in the form of a hypertext system in a nonlinear form, taking into account the relational, hierarchical and network paradigmatic relations through the implementation of syntagmatic relations in an interactive mode on a personal computer digitized lexicographic materials of the Russian language, which will allow on the basis of digital technologies through appropriate classification and systematization, digitalization and retrodigitization of dictionaries, reference books and encyclopedias and other lexicographic materials of the Russian language to structure, to systematize and unify the lexicographical material in a single body, thus providing operational input in a scientific turn with the purpose of optimization of scientific research in modern lexicography.


2021 ◽  
Author(s):  
Shivani Mulekar

Sanctuary is a documentary film in virtual reality (VR). The film uses 360-camera technology to offer a sensory immersive viewing experience. The film attempts to transcend the borders of filmmaking by merging new 360-camera technology and a nonlinear form of storytelling. The film is an observational piece. 360-degree videos are an emerging technology, which offers the viewer a sensory, immersive experience in virtual reality. Influenced by the 360-panoramic mural paintings created in 1860s, the use of the 360-camera breaks away from the syntax of documentary filmmaking and gives the audience an active role in the film-viewing experience. It breaks the traditional semantics of filmmaking and sets new rules of viewing which are personal and unique to each viewer. Sanctuary documents the Juhasz family, which has been living in a church since November 2014. The film is an eight-minute experience that gives the audience a 360- degree glimpse into the Juhasz family’s life and their living conditions. The film is presented as an installation, using Samsung’s Gear VR as the exhibition technology.


2021 ◽  
Author(s):  
Shivani Mulekar

Sanctuary is a documentary film in virtual reality (VR). The film uses 360-camera technology to offer a sensory immersive viewing experience. The film attempts to transcend the borders of filmmaking by merging new 360-camera technology and a nonlinear form of storytelling. The film is an observational piece. 360-degree videos are an emerging technology, which offers the viewer a sensory, immersive experience in virtual reality. Influenced by the 360-panoramic mural paintings created in 1860s, the use of the 360-camera breaks away from the syntax of documentary filmmaking and gives the audience an active role in the film-viewing experience. It breaks the traditional semantics of filmmaking and sets new rules of viewing which are personal and unique to each viewer. Sanctuary documents the Juhasz family, which has been living in a church since November 2014. The film is an eight-minute experience that gives the audience a 360- degree glimpse into the Juhasz family’s life and their living conditions. The film is presented as an installation, using Samsung’s Gear VR as the exhibition technology.


2021 ◽  
Vol 71 (1) ◽  
pp. 161-180
Author(s):  
Mile Bošnjak

AbstractThe research examines the sustainability of trade flows for two European post-communist economies: Serbia and Romania. We analysed two nonlinear forms of the relationship between exports and imports that cannot be explained by frequently applied linear model specifications. Newly developed nonlinear autoregressive distributed lag approach revealed the asymmetric and nonlinear long-run equilibrium between Serbian exports and imports. Nonlinearity tests indicated and the SETAR model specification confirmed threshold nonlinearity form in the Serbian trade flows pattern. Serbian trade flows still approach its sustainable equilibrium but the development pattern is promising. The results for Romania revealed another nonlinear form of the relationship between exports and imports, indicating a dependent cointegration. The paper provides robust results and supports the hypothesis that the relationship between exports and imports can be nonlinear and symmetric.


2021 ◽  
Vol 22 (1) ◽  
pp. 201-262
Author(s):  
Mark Spottswood

Abstract This Article explores settlement incentives under three different burden of proof rules. The conventional burden of proof is a discontinuous step-function, jumping from no damages to full damages at the 0.5 jury confidence level. Continuous burdens of proof, by contrast, would permit sanctions to steadily increase as juror confidence rises from 0 to 1, with no discontinuity. Linear burdens, which have received extensive attention in prior literature, escalate sanctions steadily across the whole range of confidence levels, while the logistic burden takes a nonlinear form. Using a data simulation approach guided by the empirical realities of American civil litigation, I consider the incentives that each of these rules creates for parties contemplating settlement, using a model in which parties make divergent forecasts of their expected outcomes at trial due to optimism bias. Based on this analysis, I conclude that a linear burden would likely raise our settlement rate by a modest amount, except in very large cases and in “easy” cases, in which an unbiased person would predict that a trial factfinder would have a level of confidence in liability quite close to either zero or one. I also compare the expected error rate of the settlements that each rule produces, and find that the linear rule modestly lowers the expected error rate of settlement overall, although this benefit does not hold for easy cases or those with very high damages. Lastly, I conduct a similar analysis for the logistic burden, finding that it induces a similar quality and quantity of settlements as we currently achieve using conventional burdens.


2021 ◽  
Vol 264 ◽  
pp. 04089
Author(s):  
Shavkat Muzafarov ◽  
Abdusaid Isakov ◽  
Ruzimurat Choriev ◽  
Zukhra Ismailova ◽  
Durdona Mustafoyeva

The optimal modes of the existing compensating devices under operating conditions were determined. Minimum power and energy losses were taken as optimality criteria. The unconstrained optimization problem was considered, i.e., finding the absolute minimum. When solving the problem to find the optimal mode of operation of the “SUV OKOVA” network, a relative minimum was found since the system of constraints has a nonlinear form. The problem of conditional optimization in terms of reactive power is solved, for which the gradient method of quadratic programming is used.


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