Equivalent Theory Research Articles

Equivalent Circuit Models of a Bifunctional Optical Metasurface for Beam Splitting and Refractive Index Sensing

Metasurfaces have attracted extensive attention in the micro/nano-optics field depending on their significant ability to modulate optical parameters. However, the current numerical simulation technology cannot meet the demand of the design and analysis of metasurfaces efficiently due to consuming substantial calculating time and memory. Besides, they cannot illustrate the physical mechanism straightforwardly behind the optical responses. Herein, we propose and demonstrate two equivalent circuit models systematically for a bifunctional metasurface with metal–dielectric–metal structural meta-atoms based on polarization multiplexing in the visible band. In the y-polarization state, the equivalent circuit model is established to interpret the phase shift exactly with a high goodness of fit of 0.931, resulting in the beam splitting function from the anomalous reflection phenomenon. The polychromatic light splits from 34 to 69° to produce the grating-type high-saturation structural colors with a large gamut of about 170.07% of the DCI-P3 standard. In the x-polarization state, the metasurface produces the surface lattice resonance that is suitable for the refractive index sensing function due to the high sensitivity to environmental changes. The second equivalent circuit model simulates the linewidth narrowing and red-shift phenomenon with a sensitivity relative error of 7.00%. We introduce a branch with a narrow-band-pass filter and a capacitor in series into the model to mimic the characteristic of Rayleigh anomalies. Both models extend the application of equivalent circuit theory in optics further and provide a crucial approach to enhance the insights into the mechanism of metasurfaces.

Damage analysis of hybrid carbon/Glass-Epoxy pipe elbows under bending and pressure loading

Given their many advantages, composite materials have always proven their effectiveness. As in aeronautical structures where reinforcement techniques are used, their application is widened in various fields. Analyzing these composite structures or proposing new concepts for reinforcements remains an interest of several researchers. This work opts for the use of a hybrid composite of a tubular structure of an elbow attached by straight parts. The structural composite is twill. The aim of the elbow damage study is to evaluate the proposed reinforcement concept. The stiffness and damage parameters of the plies are introduced at the size of the fiber and according to the thickness per row of finite elements, hence the use of an adequate meshing technique. The linear behavior follows the equivalent stress flow theory of Von Mises. The results presented as moment-rotation curves were evaluated under design effect and bending moment mode. Depending on the loading conditions, the proposed concept of the hybrid composite showed an overcapacity of resistance where the location of the fiber qualities played the optimization of this capacity. The structure has shown even more resistance for certain locations of the folds which are reinforced in thickness. Depending on the bending moment mode applied, the results show that the damage is caused at very low deformations by ovalization of the elbow and in fiber tension.

A Study of the Aesthetics of Translation Using Functional Equivalence Theory

A Study of the Aesthetics of Translation Using Functional Equivalence Theory

A micromechanical model of multi-scale nano-reinforced composites

Nano-reinforced composites have a wide range of useful applications thanks to their exceptional all-encompassing characteristics. Understanding the micromechanical model and the reinforcing process in nano-composites is crucial for a quantitative assessment of the reinforcement impact of nano-fillers and performance optimization. The original micromechanical model for common composite materials is no longer applicable since mechanical modeling of composite materials takes into consideration variables like multi-scale, multi-phase, and multi-morphology. The multi-scale parameter equivalent modeling theory of nano-reinforced composites is examined in this work. It is suggested to use a generalized modified Halpin-Tsai micromechanical model, which may accommodate any reinforcement form, size, or orientation, after theoretical and experimental comparison and verification. A tiny sample of the nano-reinforced composite material's mechanical tensile characteristics was examined, and its microscopic.

Design and Preparation of Anti-Reflection Nanoarray Structure on the Surface of Space Solar Cell Glass Cover

Space solar cell glass covers require high radiation resistance and wide-spectrum high light transmittance. The existing research on the preparation of thin films or special optical structures on the surface of solar cells rarely involves systematic research and the precise control of the high transmittance structural parameters of specific spectral bands by glass covers. Nanoarray structures were designed and constructed on high-purity quartz glass covers, achieving high anti-reflection within the 350–1100 nm range, the high energy part of the solar spectrum on Mars, regardless of the preparation of antireflective film and its radiation resistance. First, G-Solver software package was used to establish a nanoarray structure model according to the equivalent medium theory, and the effects of structural parameters such as the grating period, grating depth, and duty cycle on the glass cover transmittance were investigated. The results show that when the grating period is 50–200 nm, the transmittance ranges from 97.8% to 99.9%. When the grating period further increases from 300 nm, the lowest point of the transmittance spectrum moves to the longwave direction, and the transmittance from 350 nm to the lowest transmittance point significantly reduces. The optimal grating depth is 500 nm for a 300 nm grating period, the transmittance at 350 nm reaches 88.91%, and the average transmittance is 98.23%. When the period is 300 nm and the depth is 500 nm, the optimal duty cycle is 0.67, the transmittance at 350 nm reaches 96.52%, and the average transmittance is 99.23%. Nanoarray structures were constructed on the glass covers with nanoimprint and plasma etching, then modified with atomic layer deposition (ALD) to adjust their depth and duty cycle. The influence rules of the grating period, depth, and duty cycle on the cover transmittance from the experimental results are basically consistent with those from the simulation calculation. The nanoarray structure increases the average transmittance within 350–1100 nm of the glass cover by an average of 2.02% and the peak transmittance by 2.66%. The research results and experimental methods of this study have application value and promotion prospects for improving the photoelectric conversion efficiency of space solar cells and ground solar cells.

Nonreciprocal absorption properties of a magneto-optical microstructure with suppressed photothermal effects

In this work, a magneto-optical microstructure of titanium (Ti)-doped ellipsoidal particles is designed, and an improved equivalent medium theory (EMT) combined with thin-film optics theory are proposed. The doped magneto-optical microstructures obtain strong broadband nonreciprocal absorption spectra in the near-infrared band, and the nonreciprocal absorption spectra remain above 0.9 at 4.5 to 5μm with nonreciprocity up to 0.53. In addition, the effects of dopant layer thickness, filling ratio and incident angle on the nonreciprocal absorption are also discussed in detail. It worth nothing that the photothermal effect of the magneto-optical microstructures are numerically studied. The optical power of the incident light affects the overall temperature rise, which results in nonreciprocal effect due to the unequal forward and reverse incident absorption spectra. It is found that the photothermal effect for our magneto-optical model caused by the plasmon effect does not produce a normal high temperature rise. The highest temperature rise is only 5.45 K for a single cycle irradiated by 50 mW of optical power, which effectively suppresses the photothermal effect, this is important for maintaining optical devices such as solar cells, optical isolators, and infrared camouflagers at optimal operating temperatures. This property provides new ideas for the design of solar cells, infrared camouflage, optical isolators, radiation-cooled films, and other applications.

Vibration behaviours of foam-filled grille composite sandwich cylindrical shells

In this study, a novel lightweight composite sandwich cylindrical shell, namely an all-composite sandwich cylindrical shell (ACSCS) with a hollow grille core (HGC) filled with polyurethane foam (PF), is designed and prepared, and its free and forced vibration behaviours are investigated for the first time. First, an analytical model of the PFHGC-ACSCSs subjected to both base excitation and single-point pulse excitation loads is developed by employing the shear deformation theory enriched by the layerwise method, virtual artificial spring technique, Rayleigh-Ritz approach, modal superposition principle, Newmark-Beta approach, and improved cross-fill equivalent theory. Furthermore, the solution procedures for the natural frequencies, mode shapes, and vibration responses in the time and frequency domains of the PFHGC-ACSCSs are defined. Convergence investigations are performed to determine the appropriate truncation numbers and stiffness values for the virtual artificial springs used in the prediction model. Both literature and experimental validations are conducted on the current model, the results of which indicate that it is reliable for predicting the concerned dynamic parameters. Finally, the effects of the critical parameters on the free and forced vibrations of the PFHGC-ACSCSs are studied. The results suggest that the vibration suppression capability could be significantly strengthened by adopting a large core-to-skin thickness ratio, high ratio of the circumferential length of the hollow grille ribs to the whole thickness, large axial and circumferential number of the hollow grille ribs, high ratio of the wall thickness to the circumferential length of the hollow grille ribs, and type of foam with a high elastic modulus. The modelling and solving techniques, preparation processes, testing methods, and conclusions of this study pave the way for the application of such shell structures.

EQUIVALENCE IN THE TRANSLATION OF METAPHORS AND IDIOMS IN KING ABDULLAH II'S POLITICAL SPEECHES

Translation is a process of converting the meaning of a certain message from one language to another language.one of the major problems encountered by translators of political speeches is translating figures of speech like metaphors and idioms and finding equivalent meaning for them. This research aims at finding the equivalent translation provided by the Royal Court translators when translating metaphors and idioms from English into Arabic in the political speeches of king Abdullah II of Jordan. In the current study, Nida (1969) theory of equivalence in translation is adapted in order to achieve the objectives of the study. Nida (1969) proposes two types of equivalence in translation, namely formal and functional/dynamic translation. This study deploys descriptive and comparative methods in dealing with the selected examples of the political speeches and discussions papers of king Abdullah II of Jordan which are published in his official website: (http://www.kingabdullah.jo) . The findings of the study revealed that translators of the royal court apply Nida (1969) theory of equivalence in translating both metaphors and idioms in the political speeches of king Abdullah II. namely, Formal and functional equivalence.

CONCEPTS OF CAUSATION IN CRIMINAL LAW: PROBLEMS, ANALYSIS AND SOLUTIONS

The article widely uses logical, inductive, deductive, systematic, logical-legal, comparative-legal research methods. In particular, it was noted that the issue of causation in the institutions of general and special parts of criminal law is very complicated and there are many problems with it. In the theory of criminal law, scientists put forward eleven theories of causation in their scientific works, and the content of the most important of them is analyzed in this article, as well as specific shortcomings of theories of causation are recognized. The scientific views and researches of scientists regarding the theories of causation in criminal law, the similarities and differences between them are described in detail. At the same time, two of the theories of causation in foreign criminal law are widely used: the theory of equivalence and adequacy, and among them: the first contains the necessary conditions ("conditio sine qua non" - "there is no condition without a necessary condition..."), and the second is adequate( exactly the same, equal, suitable) are stated to represent conditions. Also, the legal nature of eleven theories of causation in the theory of criminal law, their specific rules are comparatively analyzed, their problematic aspects are identified and sequentially described. This article focuses on eleven theories of causation in criminal law theory and provides an instrumental and comparative analysis of their intertwined provisions. Also, out of the eleven theories of causation, the theory of direct causation was found to be the most widely used. At the same time, the doctrine of criminal law and existing scientific research were analyzed, and reasonable theoretical recommendations were developed in this regard.

Flattened Gaussian focal spot with uniform phase produced by photon sieve

The equivalent pupil and the point spread function constitute the Fourier–Bessel transform relation. Based on this, we established the equivalent pupil function theory of rotating symmetric photon sieve and derived the Fourier transform of the flattened Gaussian function. The focal spot produced by this type of photon sieve exhibits a uniform intensity and phase distribution. According to the numerical results, the flattened Gaussian field distribution is consistent with the designed function. In addition, the nonuniformity in intensity and phase is approximately 1% and less than 1/170 wavelength, respectively.

Equivalent Transformation Between Axial- and Radial-Flux Permanent-Magnet Machines

In this paper, an equivalent transformation approach for permanent-magnet (PM) electrical machines using coordinate transformation theory is presented. With the proposed method, an axial-flux PM (AFPM) machine can be transformed to an equivalent radial-flux PM (RFPM) machine or vice versa. The main purpose of proposing such a transformation method is to simplify the design of AFPM for specific applications. Besides, according to the working space requirement, the shape of PM machines can be changed while maintaining magnetic performances. The proposed transformation theory is based on the basic magnetic theory and the theoretical derivation is presented in detail. The resulted transformation equations for RFPM and AFPM machines with surface-mounted PMs are friendly to engineers. Moreover, an AFPM machine is used to validate the proposed theory, both FEM and experimental results have good agreement with the results of the proposed method. With the equivalent transformation theory, engineers could design, simulate and evaluate the AFPM machines with an exist well-developed machines.

A discretization of Holst’s action for general relativity

We present a simplicial model for gravity written in terms of a discretized Lorentz connection and a discretized tetrad field. The continuum limit of its action is Holst’s action for general relativity. With the intention of using it to construct spin foam modes for quantum gravity, we write two other equivalent models written in terms of a discretized and constrained B field. The differences between our model and existing models are most likely inessential in the sense that a quantization would lead to equivalent quantum theories in the Wilsonian continuum limit. Nevertheless, we mention two features leading to possible advantages: Curvature degrees of freedom are described at the level of each 4-simplex. Our model offers a picture of bulk geometry leading to actions for matter couplings that split as a sum over 4-simplices.

Design and Analysis of a Broadband Microwave Metamaterial Absorber

In this article, a broadband metamaterial absorber suitable for the S, C, and X bands is designed and manufactured. The absorber is made of FR-4 substrate, resonant metal structure, lumped resistance, and metal backplate, has a unit size of 0.11λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</sub> , and a total thickness of 0.084λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</sub> . The absorption principle of the absorber is analyzed using equivalent medium theory and parametric research. The calculation results show that the absorber achieves more than 90% broadband absorption (relative bandwidth of 130%) between 2.7 GHz and 12.7 GHz, has a good polarization angle and incidence angle insensitivity, uses electromagnetic resonance to explain its absorption characteristics, and experiments confirm that the absorber has good broadband absorption. The proposed absorber has higher absorption and simpler construction than the previously described broadband absorber, and it has the potential for practical applications in EMC, radar, and electromagnetic protection.

Design and Analysis of a Miniaturized Broadband Resistive Film Absorber to Reduce Chip System Radiation

This study designed a resistive film absorber (RFA) with > 90% absorptivity in the 16–27 GHz broadband to reduce electromagnetic radiation in on-board chip architectures. The size of the RFA unit is miniature, which is only 0.1λ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">_L</i> × 0.1λ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">_L</i> × 0.06λ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">_L</i> (where λ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">_L</i> is the lowest operating frequency cutoff wavelength). First, the impedance matching and loss principle of the RFA are analyzed based on the intrinsic parametric method and equivalent circuit theory. This explains the influences of each parameter on absorption performance and verifies that the designed RFA has good polarization insensitivity and angle stability. In addition, the measurements of a prototype RFA were obtained and found to be consistent with simulation results, which proves the feasibility of the RFA. Finally, the RFA was added to a chip architecture to verify its electromagnetic suppression effect with consideration of the influence of temperature on absorption performance. The combined simulation results indicate a significant reduction in the far-field radiation values of the chip architecture, with the maximum electromagnetic radiation suppression effect being 12 dB. These results demonstrate the reliability of the proposed electromagnetic suppression scheme and indicate that the RFA has wide application prospects for radiation suppression in chip systems and electronic packaging.

Variants and satisfiability in the infinitary unification wonderland

So far, results about variants, the finite variant property (FVP), variant unification, and variant satisfiability have been developed for equational theories E∪B where B is a set of axioms having a finitary unification algorithm, and the equations E, oriented as rewrite rules E→, are convergent modulo B. The extension to the case when B has an infinitary unification algorithm, for example because of non-commutative symbols having associative axioms, was not developed. This paper develops such an extension. In particular, the relationships between the FVP and the boundedness (BP) properties, the identification of conditions on E∪B ensuring FVP, the effective computation of variants and variant unifiers, and criteria making possible the existence of variant satisfiability procedures for the initial algebras of theories E∪B that are either FVP or BP are all explored in detail. The extension from the finitary to the infinitary B-unification case includes some surprises. Furthermore, since all the results are extended beyond FVP theories to the wider class of BP theories, new opportunities are opened up to use these symbolic techniques in wider classes of theories and applications.

Transition to hybrid teaching of mathematics: challenges and coping strategies of Swedish teachers

Sweden was one of the few countries that did not close down their schools during the Covid-19 pandemic. Different hybrid teaching methods were adopted, some of which are here to stay. This qualitative study explores the challenges that Swedish mathematics teachers had transitioning from face-to-face to hybrid teaching and the coping strategies that they adopted to reduce the effect of these challenges on their practices, well-being and students’ learning experiences. The results from the study were gathered from some 51 primary and secondary mathematics teachers in Stockholm using a semi-structured questionnaire. The data were analysed with cognisance of Lazarus and Folkman’s coping theory and Simonson’s equivalence theory. The results revealed that hybrid teaching had some negative impact on teaching quality, student achievement, student health, teacher workload, and teacher-student dialogue, which underpins the Swedish school curriculum. This lack of dialogue and high-quality interaction undermines the equivalency theory principle, which suggests that the format of instruction should not influence the quality of students’ learning experiences. Also, the results revealed that majority of the teachers ascribed positively to problem-based coping strategies as compared to the emotion-based coping strategy as they worked hard to provide students with good learning opportunities.

The Aging Behavior and Life Prediction of CFRP Rods under a Hygrothermal Environment.

Carbon fiber-reinforced polymer (CFRP) composites have been widely used in civil engineering structures due to their excellent mechanical and durability properties. The harsh service environment of civil engineering leads to significant degradation of the thermal and mechanical performances of CFRP, which then reduces its service reliability, service safety, and life. Research on the durability of CFRP is urgently needed to understand the long-term performance degradation mechanism. In the present study, the hygrothermal aging behavior of CFRP rods was investigated experimentally through immersion in distilled water for 360 days. The water absorption and diffusion behavior, the evolution rules of short beam shear strength (SBSS), and dynamic thermal mechanical properties were obtained to investigate the hygrothermal resistance of CFRP rods. The research results show that the water absorption behavior conforms to Fick's model. The ingression of water molecules leads to a significant decrease in SBSS and glass transition temperature (Tg). This is attributed to the plasticization effect of the resin matrix and interfacial debonding. Furthermore, the Arrhenius equation was used to predict the long-term life of SBSS in the actual service environment based on the time-temperature equivalence theory, obtaining a stable strength retention of SBSS of 72.78%, which was meaningful to provide a design guideline for the long-term durability of CFRP rods.

Types of Interlingual Equivalents of Phraseological Units and Metaphors in Literary Translation

In the following research, the types of interlingual phraseological equivalents, similes, and some metaphors in the novels of Turgenev Rudin and A Nest of the Gentry are studied from the perspective of their structure, semantics, and origin; attention is paid to differences related to the specifics of realia and lacunae translation (when reproduced in Slovak and English). We focus on biblical and ancient phraseology, aphorisms, catchphrases, allusions, reminiscences, and similes, which are translated in different ways. Based on the theory of equivalence in general and the translation of idioms in the fiction text, and the principle of structural-semantic modeling and variability of phraseological units, analogs and partial equivalents are analyzed from the point of existing lexical-grammatical and stylistic differences and formal-semantic transformations. The latter is a sign of the specific idiostyle and individual writer’s manner of Turgenev. When the original phraseological unit is translated without noticeable emotional and expressive connotations with the help of metaphors or a free word combination, or when, on the contrary, a free word combination or metaphor is replaced by a phraseological equivalent, various cases of transfer, reproduction of figurative and expressive means, and literary and lexical tropes are distinguished. In the meantime, the original phraseological unit may correspond to a comparative phrase during translation.

Method based on the membrane theory for equivalence between arbitrarily shaped pressure pulse applied on circular plate and rectangular pressure pulse

Obtaining a theoretical solution for the response of plate structures to arbitrarily shaped pressure pulses is often difficult. For engineering purposes, arbitrarily shaped pressure pulses are often simplified to equivalent rectangular pressure pulses to calculate the theoretical responses of the plate structures. Therefore, the semi-empirical method proposed by Youngdahl is often used. Although the effectiveness of Youngdahl's method has been verified in small deformation cases, the method lacks a theoretical explanation of the equivalence basis for cases of large deformation. In this paper, a method based on the membrane theory (MEM) is established for equivalence between arbitrarily shaped pressure pulse applied on circular plate and rectangular pressure pulse, and the differences and similarities between the MEM and the Youngdahl's equivalent method (YEM) are analyzed. Using the membrane theory, the responses of five different pressure pulses are compared, revealing that the pulse shape has a significant influence on the theoretical deformation obtained by the membrane theory. Then, a load equivalent method based on the membrane theory is proposed. In particular, for a linearly decaying pressure pulse, an analytical solution of the equivalent load is provided, and the equivalent pressure and pulse duration of the MEM and YEM are calculated. Notably, the pressure and pulse duration obtained by the MEM under the large deformation theory significantly differ from those obtained by the YEM. A numerical simulation indicates that the response errors of the equivalent load relative to the original linearly decaying pressure pulse of the two methods are close, both within the acceptable range of engineering. The theoretical analysis shows that the product of the characteristic frequency of the membrane response and pulse duration — a dimensionless number — affects the relative magnitude of the equivalent pressure of the YEM and MEM. When the final deformation time occurs after the duration of the linearly decaying pressure pulse, the deformation of the circular plate under the equivalent load obtained by the YEM is greater than that obtained by the MEM.

Fibered universal algebra for first-order logics

We extend Lawvere-Pitts prop-categories (aka. hyperdoctrines) to develop a general framework for providing fibered algebraic semantics for general first-order logics. This framework includes a natural notion of substitution, which allows first-order logics to be considered as structural closure operators just as propositional logics are in abstract algebraic logic. We then establish an extension of the homomorphism theorem from universal algebra for generalized prop-categories and characterize two natural closure operators on the prop-categorical semantics. The first closes a class of structures (which are interpreted as morphisms of prop-categories) under the satisfaction of their common first-order theory and the second closes a class of prop-categories under their associated first-order consequence. It turns out that these closure operators have characterizations that closely mirror Birkhoff's characterization of the closure of a class of algebras under the satisfaction of their common equational theory and Blok and Jónsson's characterization of closure under equational consequence, respectively. These algebraic characterizations of the first-order closure operators are unique to the prop-categorical semantics. They do not have analogues, for example, in the Tarskian semantics for classical first-order logic. The prop-categories we consider are much more general than traditional intuitionistic prop-categories or triposes (i.e., topos representing indexed partially ordered sets). Nonetheless, to the best of our knowledge, our results are new, even when restricted to these special classes of prop-categories.