Equivalent Theory Research Articles

A Complete Finite Axiomatisation of the Equational Theory of Common Meadows

We analyse abstract data types that model numerical structures with a concept of error. Specifically, we focus on arithmetic data types that contain an error value \(\bot\) whose main purpose is to always return a value for division. To rings and fields, we add a division operator \(x/y\) and study a class of algebras called common meadows wherein \(x/0=\bot\) . The set of equations true in all common meadows is named the equational theory of common meadows . We give a finite equational axiomatisation of the equational theory of common meadows and prove that it is complete and that the equational theory is decidable.

Research on the Criteria for Determining the Starting Performance of an Inward-Turning Inlet by Integrating the Concept of the Equivalent Contraction Ratio

The prediction of hypersonic inlet starting performance is crucial for the successful ignition of the combustion chamber, directly impacting the overall performance of the propulsion system. This challenge arises especially when freestream conditions vary. Therefore, this paper proposes the concept of the equivalent contraction ratio, and establishes and analyzes the intrinsic correlation between the geometric contraction ratio and angle of attack on the starting performance of three-dimensional inward-turning inlet. The results indicate the following: (1) The startability index can be applied to determine the start boundary of the three-dimensional inward-turning inlet under conditions of the freestream Mach number of 6.0 and an altitude of 27 km, with a deviation of no more than 6.6% from the optimal SI = 0.087 criterion; (2) The start boundary after applying the equivalent contraction ratio shows deviations not exceeding 4.0% under positive angle-of-attack conditions compared to the startability index, while the deviation is larger under negative angle-of-attack conditions, reaching a maximum of 13.3%. After applying a correction formula, the deviations can be reduced to within 2.0%; (3) For the same equivalent contraction ratio, the differences in starting performance between different positive and negative angle-of-attack conditions may fundamentally arise from the degree of compression of the inlet. Finally, the equivalent contraction ratio theory is proven to be able to quickly and easily predict the accurate starting performance of the inward-turning inlet at different angles of attack, improving the breadth and efficiency of engineering predictions.

Experimental Study on Mechanical Properties of Artificial Cores Saturated With Ice: An Analogical Simulation to Natural Gas Hydrate Bearing Sediments

ABSTRACTThis work takes the natural gas hydrate (NGH) reservoir in the Shenhu area at the South China Sea as the target. Using the quartz sand, calcite grains, and illite powder as the main mineral composites, and Portland cement as the bonding material, the host skeleton with similar porosity and mechanical properties to the target reservoir were prepared. Ice was used to simulate natural gas hydrates for their high similarity in mechanical properties and distributions within porous host. The ice saturation in the host skeleton is quantitatively controlled by the quality method. As an analogical simulation, artificial samples with different ice saturations were tested by uniaxial compression measurements and the Brazilian tensile tests, aiming to reveal the mechanical behavior of NGH sediments. The results indicated that the plasticity of the artificial sample increases and its damage form transitions from brittleness to ductility as the ice saturation increases. The effects of free water and ice on the strength of saturated samples are quite different. The free water tends to reduce the strength of the sample due to illite hydration and change of internal friction. The bonding effect of ice tends to increase the strength of the sample, while the ice could also reduce the internal friction. When the ice saturation is larger than 30%, the compressive and tensile strengths of the sample increase with ice saturation, which could be regressed as yc = 2.2628S + 0.8322, and yt = 0.411S + 0.0273, respectively. The constitutive model was developed based on the equivalent medium theory and the D‐P criterion, which could describe the experiment data well with deviations less than 10%.

Research on ultrasonic testing method for tangential contact stress based on equivalent medium theory

As a weak link, the joint surface of machine tools directly affects the stiffness and machining accuracy of the entire machine tool. However, obtaining the distribution of contact stress is a key problem that urgently needs to be solved in exploring the mechanical properties of joint surface connections. In this paper, a tangential contact stress ultrasonic testing method based on the equivalent medium theory is proposed, providing data support for accurately characterizing the contact state of the joint surface. A virtual material model of rough contact interface based on fractal theory is established to explore the coupling relationship between the propagation speed of ultrasonic critical refracted longitudinal waves, the tested object’s material parameters, and stress. Moreover, the expression of the equivalent material parameters of the ultrasonic critical refracted longitudinal wave propagation layer with stress variation is derived. An ultrasonic acoustic time difference model considering changes in contact surface material parameters is constructed based on the principle of acoustic elasticity of ultrasound. Furthermore, a critical refractive detection model for longitudinal wave’s tangential contact stress is established based on equivalent medium theory. Experimental specimens and stress detection plans are designed, and the tangential contact stress of the specimens is measured based on the division of surface grids. The equivalent stress value of each node is calculated based on the von Mises stress by measuring the stress in the X/Y direction. In addition, a shear stress distribution cloud map of the contact surface is drawn. Finally, the accuracy of the detection results is confirmed by combining theory, simulation, and experimental methods. The proposed tangential contact stress detection method based on critical refractive longitudinal waves is significant for low-stress assemblies.

Optimization Method Incorporating Equivalent Circuit Theory and Space Mapping for Metamaterial Absorbers

Optimization Method Incorporating Equivalent Circuit Theory and Space Mapping for Metamaterial Absorbers

Sum and Tensor of Quantitative Effects

Inspired by the seminal work of Hyland, Plotkin, and Power on the combination of algebraic computational effects via sum and tensor, we develop an analogous theory for the combination of quantitative algebraic effects. Quantitative algebraic effects are monadic computational effects on categories of metric spaces, which, moreover, have an algebraic presentation in the form of quantitative equational theories, a logical framework introduced by Mardare, Panangaden, and Plotkin that generalises equational logic to account for a concept of approximate equality. As our main result, we show that the sum and tensor of two quantitative equational theories correspond to the categorical sum (i.e., coproduct) and tensor, respectively, of their effects qua monads. We further give a theory of quantitative effect transformers based on these two operations, essentially providing quantitative analogues to the following monad transformers due to Moggi: exception, resumption, reader, and writer transformers. Finally, as an application, we provide the first quantitative algebraic axiomatizations to the following coalgebraic structures: Markov processes, labelled Markov processes, Mealy machines, and Markov decision processes, each endowed with their respective bisimilarity metrics. Apart from the intrinsic interest in these axiomatizations, it is pleasing they have been obtained as the composition, via sum and tensor, of simpler quantitative equational theories.

A Study on the Translation of Instructions for Heat-Clearing and Detoxifying Traditional Chinese Medicines under the Functional Equivalence Theory

Heat-clearing and detoxifying traditional Chinese medicines are an important part and distinctive advantage of China’s medical and health undertakings. Traditional Chinese medicine is an outstanding traditional culture of the Chinese nation and a unique and significant health resource in our country. The rapidly growing international market has created excellent opportunities for the export of heat-clearing and detoxifying traditional Chinese medicines. Currently, the English translation of instructions for proprietary Chinese medicines lacks unified translation standards and the guidance of translation theories. The existing English translations of instructions for proprietary Chinese medicines in our country have problems such as confusion and non-standardization. Therefore, the research on the instructions of heat-clearing and detoxifying medicines under the functional equivalence theory is highly significant. This paper takes several common heat-clearing and detoxifying medicines available on the market as examples, analyzes the problems and their causes in the translation of the instructions from the perspective of the functional equivalence theory, and finds more reasonable and standardized translation methods. It helps foreign consumers understand the characteristics and functions of traditional Chinese medicine, thereby stimulating their consumption desires. This paper studies the translation process using the functional equivalence theory, investigates the structure and language features of the instructions for traditional Chinese medicine, and discusses the corresponding translation strategies for the instructions of heat-clearing and detoxifying traditional Chinese medicines at the lexical and syntactic levels respectively to achieve functional equivalence.

TRANSLATION OF THE MYSTERY PLAY NOAH, FROM THE PERSPECTIVE OF DYNAMIC EQUIVALENCE THEORY

The general aim of this work was to translate the mystery play Noah, from medieval English literature. To this end, this article presents the theory behind the translation proposal: Dynamic Equivalence Theory (Nida, 2001). In addition to Nida (idem), our research was based on Orlin (2006), Herenkov (2011), Palmer (2008), Bell (1991), Venuti (1995) and Pym (2010). Since the methodological proposal is a Middle English work, we consulted online dictionaries of Middle English terms, online libraries specializing in medieval literature, and online translation tools. The result of this work (translation of the play Noah into Portuguese) can be found at the end of this article. In this way, we hope to have contributed to the democratization of reading, the dissemination of knowledge, and the perpetuation of knowledge.

Advancements to generalized equivalence theory for preserving cross-sections of whole core simulations

The conventional two-step approach, without the use of an equivalence method, can introduce significant error for the simulation of non-LWRs (Light Water Reactors), especially fast reactors, due to the large leakage and high anisotropic neutron distribution. To improve upon the accuracy of the two-step approach, a 3D whole core model is simulated with a transport method to generate region-wise homogenized cross-sections (XS). These XS can then be used in a diffusion whole core solver during the second step to extend the application to cycle and transient analysis. Discontinuity factors (DFs) are then introduced to improve the accuracy during the simulation of the second step. With properly generated DFs from Generalized Equivalence Theory (GET), the region-averaged solutions from the first transport step can then be reproduced by the second step diffusion solver. The Monte Carlo method was selected to perform the whole core transport simulation to generate region-wise XS. However, simulating whole core problems with Monte Carlo may result in poor statistics near the peripheral region especially for partial current tallies. This paper introduces an advancement to GET to reproduce region-wise solutions for select regions when the reaction rates and surface currents have good statistics in these regions but poor statistics in other regions. A reference high-fidelity model was constructed using the Serpent 2 Monte Carlo code based on the EBR-II benchmark evaluation and verification was carried out using the TriPEN-4 method in PARCS. The results show that it is possible to reproduce the exact eigenvalue and power distributions of whole core problems in a feasible manner.

Analysis and Experimental Study for Fatigue Performance of Wing-Fuselage Connection Structure for Unmanned Aerial Vehicle

(1) Background: As the principal structural element of an unmanned aerial vehicle (UAV), a lightweight, high-performance wing-fuselage connection structure plays an important role in UAV structural integrity. Previous studies focused on the static strength characteristics of aluminum and high-strength steel wing-fuselage connection structures. With the widespread usage of titanium material in aviation, research should address the fatigue performance of titanium wing-fuselage connection structures. This paper aims to investigate the fatigue performance of the titanium wing-fuselage connection structure by using analysis and experimental methods, and to develop a reliable fatigue assessment method based on the experimental results. (2) Methods: General and detail finite element models were established, and the stress distribution at the detail fatigue design point was obtained via finite element analysis. Based on the equivalent life curve theory, a dimensionless value, detail fatigue value (DF), was proposed to characterize the fatigue performance for structure. By using detail fatigue value (DF) method, the theoretical fatigue performance value was calculated. The fatigue test of the wing-fuselage connection structure was conducted, and the fatigue life was determined according to the test results. (3) Results: For the wing joint with fatigue failure in the test, the test fatigue performance was close to the theoretical value. It can be concluded from the DF value that the analysis and test results are consistent, and the values obtained from the analysis are more conservative than test results. (4) Conclusions: The error between the test DF value and the theoretical analysis DF value is small, and the theoretical analysis of fatigue performance can represent the fatigue characteristics of the wing-fuselage connection structure. The detail fatigue value (DF) method can predict the fatigue performance of the structure quite well.

Logics for contact and measure

Abstract We enrich contact algebras with a new binary relation that compares the size of regions, and provide axiom systems for various logics of contact and measure. Our contribution is three-fold: (1) we characterize the relations on a Boolean algebra that derive from a measure, thereby improving an old result of Kraft, Pratt and Seidenberg; (2) for all $n \geq 1$, we axiomatize the logic of regular closed sets of ${\mathbb{R}}^{n}$ with null boundary; (3) considering a broad class of equational theories that contains all logics of contact, we prove that they all have unitary or finitary unification, and that unification and admissibility are decidable.

On the Complications of Nepali-English Legal Translation

This article explores the complications of Nepali-English legal translation by examining linguistic and extra linguistic complications between Nepali and English languages and proposes a solution. Law offers rights and binds people with duties within a jurisdiction, and translating law from one language to another language brings complications for equal communication. The knowledge of comparative law and the incompetence of the source and the target language culture interfere with natural communication. Even a minor mistake in translation brings major disputes and conflicts. As the theoretical framework, this research uses equivalence and cultural theories of legal translation. It collects primary and secondary data from freelance and institutional translations applying juritraductological methods used in legal translation. The significance of the study is to professionals, novice translators, and university student’s curious about Nepali-English legal translation. This research finds that translating law or legal documents from one language to another language brings linguistic and extra linguistic complications, but a translator can resolve the musing the proposed solutions. It concludes that exploring the complications of Nepali-English legal translation with solutions enhances the quality of Nepali legal translation.

Strength degradation characteristics and damage constitutive model of sandstone under freeze-thaw cycles.

Thorough investigation into the laws governing frozen rock damage in high-altitude and cold regions can offer valuable insights for advancing infrastructure construction, ecological environment protection, and sustainable development on the Qinghai-Xizang Plateau. This study combined with the seasonal variation patterns of frozen rocks in the Qinghai-Xizang Plateau, and processed the rock samples using a freeze-thaw interval of -20 °C~20 °C. Uniaxial compression test was conducted based on the MTS816 rock mechanics testing system. The porosity changes of rock samples with different freeze-thaw cycles were analyzed using the MesoMR12-060H-I nuclear magnetic response analysis system. A rock freeze-thaw load coupled damage constitutive model was derived using the Lemaitre equivalent strain theory. Research has shown that during the freezing process, the pore water inside the rock sample is affected by the phase change of water-ice, resulting in frost heave force, which further promotes the expansion of the pore walls and the initiation of new cracks. When melted, pore water migrates towards newly formed micropores, thereby affecting the changes in the pores of rock samples. The increase in porosity at the micro level weakens the mechanical parameters of rocks at the macro level. The segmented freeze-thaw damage constitutive model based on Lemaitre equivalent strain theory can well fit the experimental results involved in this study, as well as the experimental results obtained by other researchers. The compaction stage can partially reflect the changes in sandstone pore structure under freeze-thaw cycles.

Completeness Theorems for Kleene algebra with tests and top

We prove two completeness results for Kleene algebra with tests and a top element, with respect to guarded string languages and binary relations. While the equational theories of those two classes of models coincide over the signature of Kleene algebra, this is no longer the case when we consider an additional constant ``top'' for the full element. Indeed, the full relation satisfies more laws than the full language, and we show that those additional laws can all be derived from a single additional axiom. We recover that the two equational theories coincide if we slightly generalise the notion of relational model, allowing sub-algebras of relations where top is a greatest element but not necessarily the full relation. We use models of closed languages and reductions in order to prove our completeness results, which are relative to any axiomatisation of the algebra of regular events. For one of our constructions, we extend the concept of finite monoid recognisability to guarded-string languages; this device makes it possible to obtain a PSpace algorithm for the equational theory of binary relations.

Subsidence Prediction Method Based on Elastic Foundation Beam and Equivalent Mining Height Theory and Its Application

Grouting technology in overburden separation is recognized as an effective method to prevent surface subsidence and reuse solid waste. This study used mechanical analysis to explore deflection characteristics of key strata and accurately predict and control surface subsidence. Conceptualizing the coal–rock mass beneath the key strata as an elastic foundation, we developed a method to calculate the elastic foundation coefficients for various regions and established an equation for key strata deflection, validated through discrete element numerical simulations. This simulation also examined subsidence behavior under different grout injection–extraction ratios. Additionally, combining the equivalent mining height theory with the probability integral method, we formulated a predictive model for surface subsidence during grouting. Applied to the 8006 working face of the Wuyang Coal Mine, this model was supported by numerical simulations and field data, which showed a maximum surface subsidence of 546 mm at a 33% injection–extraction ratio, closely matching the theoretical value of 557 mm and demonstrating a nominal error of 2%. Post-grouting, the surface tilt was reduced to below 3 mm/m, meeting regulatory standards and eliminating the need for ongoing surface structure maintenance. These results confirm the model’s effectiveness in forecasting and controlling surface subsidence with grouting. The study can provide a basis for determining the grouting injection–extraction ratios and evaluating the effectiveness of surface subsidence control in grouting into overburden separation projects.

A Study on Chinese Translation of English-Japanese Movie Titles from the Perspective of Linguistic Conformity Theory

Movie translation plays an important role in the dissemination of a movie, just like the trademark and promotion card of a movie. It not only needs to match the style of the original movie, but also needs to have commercial value. The quality of title translation directly affects the box office and audience attendance. This paper takes the 250 movies with the highest Douban ratings as the research object, and collects relevant data by constructing a database. Through the literature survey, it is found that the current Chinese translation of movie title translation is mostly studied from the perspective of Purpose Theory and Dynamic Equivalence Theory, but a systematic framework has not yet been formed, so it is difficult to solve the problem of actual title translation. The purpose of this paper is to analyze the current problems in movie translation from the perspective of linguistic conformity theory, including copying and reproducing, formatting translation, unclear meaning, and words deviating from the theme. This paper argues that the proposed title translation should truly and accurately reflect the core of the original title and more deeply combine with the local culture, with the intention of providing new perspectives for movie translation to improve the translation quality of Chinese titles.

Linear equivalence for motion amplification devices in earthquake engineering

AbstractMotion amplification devices utilized to amplify the motion of dampers can effectively improve the energy dissipation performance of dampers to reduce seismic responses of engineering structures. This study systematically develops a linear equivalence theory for motion amplification devices based on the proposed equivalent Maxwell model. This equivalent model accurately predicts the supplemental damping effect provided by motion amplification devices without approximation. Also, the equivalent model is capable of quantifying the amplification effect of motion amplification devices by means of deriving the analytical expressions of the equivalent damping and stiffness coefficients, which reveal that motion amplification devices simultaneously enhance the original damping and stiffness coefficients by , where is the proposed rigidity motion amplification factor. The representative value of member stiffness is developed to comprehensively evaluate the supporting stiffness of motion amplification devices. All the achieved results strongly support that the proposed linear equivalence theory provides a generic paradigm to explain, measure and compare different types of motion amplification devices in terms of their supplemental damping effects, and hence helps researchers and engineers gain valuable insight into the dynamic properties of motion amplification devices.

Sharing proofs with predicative theories through universe-polymorphic elaboration

As the development of formal proofs is a time-consuming task, it is important to devise ways of sharing the already written proofs to prevent wasting time redoing them. One of the challenges in this domain is to translate proofs written in proof assistants based on impredicative logics to proof assistants based on predicative logics, whenever impredicativity is not used in an essential way. In this paper we present a transformation for sharing proofs with a core predicative system supporting prenex universe polymorphism. It consists in trying to elaborate each term into a predicative universe-polymorphic term as general as possible. The use of universe polymorphism is justified by the fact that mapping each universe to a fixed one in the target theory is not sufficient in most cases. During the elaboration, we need to solve unification problems in the equational theory of universe levels. In order to do this, we give a complete characterization of when a single equation admits a most general unifier. This characterization is then employed in a partial algorithm which uses a constraint-postponement strategy for trying to solve unification problems. The proposed translation is of course partial, but in practice allows one to translate many proofs that do not use impredicativity in an essential way. Indeed, it was implemented in the tool Predicativize and then used to translate semi-automatically many non-trivial developments from Matita's library to Agda, including proofs of Bertrand's Postulate and Fermat's Little Theorem, which (as far as we know) were not available in Agda yet.

Nonequivalence of Carroll limits in relativistic string theory

We construct new Carroll strings in flat space by considering the Carroll limit of equivalent relativistic string theories at the classical level. In the limit these Carroll strings are no longer equivalent and have different degrees of freedom. This fact is due to a general phenomenon that the configuration space and canonical Lagrangians are no longer equivalent after a singular redefinition of the variables and of the parameters of the starting Lagrangians. Published by the American Physical Society 2024

An Efficient Hybrid Method for Calculating the Focal Field of a Cassegrain Antenna

The evaluation of the focal field of Cassegrain antennas is crucial for the design and optimization of the complex feeds in quasi-optical systems. However, employing traditional physical optics methods generates high computational complexity and is inefficient. An accurate and efficient calculation method of Cassegrain antennas’ focal fields that involves a range of incidence angles is proposed, which integrates ray tracing and vector diffraction integration (RT-VDI) theories. It can calculate the focal field in any given or predefined incident direction, not limited to the case of axial incidence. In addition, the use of the equivalent parabolic theory greatly simplifies the process of integral calculation. Moreover, ray tracing and integration operations are executed upon the calculation of the reflector to further improve efficiency. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method.