Equivalent Theory Research Articles

With a Few Square Roots, Quantum Computing Is as Easy as Pi

Rig groupoids provide a semantic model of Π, a universal classical reversible programming language over finite types. We prove that extending rig groupoids with just two maps and three equations about them results in a model of quantum computing that is computationally universal and equationally sound and complete for a variety of gate sets. The first map corresponds to an 8th root of the identity morphism on the unit 1. The second map corresponds to a square root of the symmetry on 1+1. As square roots are generally not unique and can sometimes even be trivial, the maps are constrained to satisfy a nondegeneracy axiom, which we relate to the Euler decomposition of the Hadamard gate. The semantic construction is turned into an extension of Π, called √Π, that is a computationally universal quantum programming language equipped with an equational theory that is sound and complete with respect to the Clifford gate set, the standard gate set of Clifford+T restricted to ≤2 qubits, and the computationally universal Gaussian Clifford+T gate set.

Parikh’s Theorem Made Symbolic

Parikh’s Theorem is a fundamental result in automata theory with numerous applications in computer science. These include software verification (e.g. infinite-state verification, string constraints, and theory of arrays), verification of cryptographic protocols (e.g. using Horn clauses modulo equational theories) and database querying (e.g. evaluating path-queries in graph databases), among others. Parikh’s Theorem states that the letter-counting abstraction of a language recognized by finite automata or context-free grammars is definable in Linear Integer Arithmetic (a.k.a. Presburger Arithmetic). In fact, there is a linear-time algorithm computing existential Presburger formulas capturing such abstractions, which enables an efficient analysis via SMT-solvers. Unfortunately, real-world applications typically require large alphabets (e.g. Unicode, containing a ‍million of characters) — which are well-known to be not amenable to explicit treatment of the alphabets — or even worse infinite alphabets. Symbolic automata have proven in the last decade to be an effective algorithmic framework for handling large finite or even infinite alphabets. A symbolic automaton employs an effective boolean algebra, which offers a symbolic representation of character sets (i.e. in terms of predicates) and often lends itself to an exponentially more succinct representation of a language. Instead of letter-counting, Parikh’s Theorem for symbolic automata amounts to counting the number of times different predicates are satisfied by an input sequence. Unfortunately, naively applying Parikh’s Theorem from classical automata theory to symbolic automata yields existential Presburger formulas of exponential size. In this paper, we provide a new construction for Parikh’s Theorem for symbolic automata and grammars, which avoids this exponential blowup: our algorithm computes an existential formula in polynomial-time over (quantifier-free) Presburger and the base theory. In fact, our algorithm extends to the model of parametric symbolic grammars, which are one of the most expressive models of languages over infinite alphabets. We have implemented our algorithm and show it can be used to solve string constraints that are difficult to solve by existing solvers.

Decision and Complexity of Dolev-Yao Hyperproperties

The formal analysis of cryptographic protocols traditionally focuses on trace and equivalence properties, for which decision procedures in the symbolic (or Dolev-Yao, or DY) model are known. However, many relevant security properties are expressed as DY hyperproperties that involve quantifications over both execution paths and attacker computations (which are constrained by the attacker's knowledge in the underlying model of computation). DY hyperproperties generalise hyperproperties, for which many decision procedures exist, to the setting of DY models. Unfortunately, the subtle interactions between both forms of quantifications have been an obstacle to lifting decision procedures from hyperproperties to DY hyperproperties. The central contribution of the paper is the first procedure for deciding DY hyperproperties, in the usual setting where the number of protocol sessions is bounded and where the equational theory modelling cryptography is subterm-convergent. We prove that our decision procedure can decide the validity of any hyperproperty in which quantifications over messages are guarded and quantifications over attacker computations are limited to expressing the attacker's knowledge. We also establish the complexity of the decision problem for several important fragments of the hyperlogic. Further, we illustrate the techniques and scope of our contributions through examples of related hyperproperties.

Wideband close perfect meta surface absorber for solar photovoltaic and optical spectrum applications

The leading research challenge is to develop a meta-surface absorber design for optimal performance across ultraviolet, visible, and near-infrared wavelengths. In ongoing research, a meta-surface absorber is being introduced, designed to achieve near-perfect absorption of 99% across the 250–2500 nm UV–Vis-NIR spectrum for both Transverse electric (TE) and Transverse magnetic (TM) polarized waves. The aimed design features a symmetrical resonator pattern, resulting in a polarization-insensitive absorption response. Additionally, the absorption response demonstrates robustness when altering the geometric parameters of the meta-surface unit cell. Precise simulation and modelling of the proposed meta-surface absorber are achieved by Employing a Finite Difference Frequency Domain (FDFD) solver, coupled with the Finite Integration Technique (FIT) and a tetrahedral mesh component. Verification of absorption characteristics is conducted through three frameworks: impedance matching, interference, and an equivalent circuit model. The suggested meta-structure design exhibits a uniform absorption response, as determined through considerations of impedance matching, interference theory, and the equivalent circuit theory. The PCR value is significantly lower than recent studies, reinforcing that the proposed meta-surface primarily serves as an absorber, not a polarization converter. The absorption response of the suggested meta-structure design remains consistent across the range of electromagnetic wave polarization angles from 0 to 90 for both TE and TM waves. Furthermore, the absorption response of the proposed design demonstrates stability up to an incident angle of 70 for electromagnetic waves. The distribution of electric and magnetic fields, along with surface current density on the proposed design, validates the existence of localized, propagating, and cavity surface plasmon resonance. These collectively create anti-parallel current flow, leading to the absorption of incident EM waves. Furthermore, the suggested design achieves a solar energy thermal conversion efficiency of 99% across the operational spectrum at a working temperature of 573 K, substantiating its potential for use as a solar absorber. Thus, this study presents a meta-structure unit cell that addresses the challenge with near-perfect absorption, polarization independence, and angle robustness. Applications include photodetection, thermal mapping, solar harvesting, and photo-trapping.

A novel evaluation method of natural gas hydrate saturation in reservoirs based on the equivalent medium theory

Natural gas hydrate saturation (NGHS) in reservoirs is one of the critical parameters for evaluating natural gas hydrate resource reserves. Current widely-accepted evaluation methods developed for evaluating conventional natural gas saturation in reservoirs, to some extents, are not sufficient enough to obtain accurate predicted results. In light of the equivalent medium theory, the natural gas hydrate is regarded as the fluid (Mode A) when NGHS is relatively low, while it is regarded as the rock matrix (Mode B) when NGHS is high. Two mathematical model are then developed for evaluating NGHS at Mode A and B. Experimental verification shows that R2 of the predicted results based upon the proposed model is 0.968, and the average absolute relative error percentage is 8.90%. The error of the predicted results gradually decreases with increasing NGHS, whereas increases with increasing confining pressure. In addition, the proposed model has been applied to the 142.9–147.7 m well section of Well DK-1 in the permafrost region, Qilian Mountains. The results show that the error of the predicted results is less than 13.92%, with its average error being 10.51%. The predicted value gradually increases with its error decreasing as the depth continues to increase, which is consistent with the change behavior of measured data. NGHS evaluation method proposed in this paper fully considers the occurrence form of natural gas hydrate in reservoirs. The model parameters are easy to determine and the predicted results are reliable.

Enhancing Angular Stability in Magnitude and Phase of Frequency Selective Slabs Using Partial Derivatives Expansion Based on Equivalent Medium Theory

Enhancing Angular Stability in Magnitude and Phase of Frequency Selective Slabs Using Partial Derivatives Expansion Based on Equivalent Medium Theory

Analysis and simulation of X-band high-power microwave generation based on T-shaped four-period slow-wave structure

In this study, a T-shaped, four-period resonant slow-wave structure is optimally designed, and its high-frequency performance is comprehensively analyzed in theory. By using the image theory, the T-shaped waveguide unit is transformed into an equivalent ridge waveguide configuration. The high-frequency characteristics of the equivalent ridge waveguide, such as resonant frequency and structure of the T-shaped waveguide are analyzed by using equivalent circuit theory. The analysis has confirmed that in the ridge waveguide, starting from the second-highest order mode, the frequency points of the even-order modes are very consistent with those of the T-shaped waveguide; however, the odd-order modes have no such corresponding mode in the T-shaped waveguide, for they do not fulfill the electric boundary conditions required by the image method. On this basis, a T-shaped four-period resonant slow-wave structure is constructed, and its dispersion characteristics are analyzed to determine the resonant modes and frequencies, as well as the range of mode synchronization voltages. Simulations are subsequently performed to validate the effectiveness of the relativistic extended interaction radiation source, which includes the novel T-shaped periodic resonant slow-wave structure. Advanced three-dimensional particle simulations, in conjunction with optimization techniques show that a high-power microwave output at a frequency of 9.8 GHz, is achieved, which can delivers an average power of 71.4 MW. This output is attained under the conditions of a 448 kV beam voltage, 400 A beam current, and a 0.4 T uniform axial magnetic field, with an electron efficiency reaching 39.8%. This structure, characterized by the T-shaped waveguide, is demonstrated to be capable of producing high-efficiency, high-power microwaves with fewer periods, presenting a compact and efficient solution for generating high-power microwaves in advanced scientific applications.

Translating advertisements from Chinese to English: Strategies and methods

This study explores the strategies and methods of translating advertisements from Chinese to English. It adopts a functional approach to translation studies, encompassing the Skopos theory and equivalent translation theory. The translation strategies are divided into semantic, structural, language, and rhetorical levels. At the semantic level, the use of literal translation, liberal translation, and semantic conversion is employed to convey both the literal meaning and intended meaning of the advertisements. At the structural level, supplementary translation, condensed translation, and the division and merging of sentences are utilized to adjust the structure to meet the translation requirements. At the language level, extensive use of adjectives, frequent use of imperative verbs, and personal pronouns are employed to highlight features, prompt actions, and establish connections. At the rhetorical level, the use of puns, simulation, personification and exaggeration is employed to enhance interest, convey messages, and imbue products with human-like qualities. By employing a functional approach and various translation strategies, advertisements can be effectively translated, capturing the interest and resonance of the target audience. However, this study has certain limitations in terms of sample selection and research scope. Future research can further explore additional translation strategies and methods to improve the effectiveness and quality of advertisement translation.

Modeling and admittance recursive simulation of anti-reflective coatings for photothermal conversion: synergy between subwavelength structures and gradient refractive index layers.

In the field of photothermal conversion, light-absorbing layers show limitations such as low solar energy utilization and excessive surface reflection. This paper proposes a new anti-reflective coating consisting of a gradient-doped fluorescent glass film covering a subwavelength structural layer for photothermal conversion. Its transmittance was simulated using equivalent medium theory and the admittance recursion method. The subwavelength structure provides a refractive index gradient, and its shape solves the problem of the sharp decrease in transmittance at high angles of incidence. Subsequently, we adjust the material parameters of the gradient refractive layers and control the thickness of each layer to minimize interlayer Fresnel reflections. Finally, the efficient light-trapping ability of the model was verified by calculating and comparing the transmittances of the optimized model and bare glass. Notably, within the visible spectrum, our model achieves an average transmittance of over 95% across wavelength and angle ranges, effectively suppressing surface reflections. At a larger light incident angle, the transmittance increases by 29.7%, and the minimum angle transmittance reaches 92.7%. This study proposes an innovative method to enhance the performance of transmission layers in photothermal conversion devices.

The Utilization of Functional Equivalence Theory and Context Hierarchy Theory in the Translation of Excellent Traditional Chinese Culture

The Utilization of Functional Equivalence Theory and Context Hierarchy Theory in the Translation of Excellent Traditional Chinese Culture

Translation Strategies for Long Sentences in International Maritime Treaties into Chinese from the Perspective of Functional Equivalence Theory

Translation Strategies for Long Sentences in International Maritime Treaties into Chinese from the Perspective of Functional Equivalence Theory

An Analysis of the Use of Functional Equivalence Theory in Novel Translation—Taking Everything I Never Told You as an Example

An Analysis of the Use of Functional Equivalence Theory in Novel Translation—Taking Everything I Never Told You as an Example

A Study of the English Translation of Chinese Buzzwords from the Perspective of Functional Equivalence Theory

As the internet and social media develop further, there are numerous buzzwords used by the citizens, which are the fashion phenomena in China. As inter-cultural communication between China and other countries becomes deeper and frequent, an increasing number of foreigners have good command of Chinese culture. As a result, as the cultural bridge between the source and the target receptors, Chinese-English (CE) words translation become increasingly important, playing an obvious role in facilitating our communications. This study aims to apply the functional equivalence theory to the English translation in translating Chinese buzzwords so as to translate the original texts accurately. Four main methods including lexical equivalence, syntactic equivalence, discourse equivalence and stylistic equivalence are applied to have the C-E translation. The result is that lexical and syntactic equivalence are widely applied in the translation practice, which conveys the implicated cultural meanings correctly and feasibly. Furthermore, the methods of discourse equivalence and the stylistic equivalence can also be used to elaborate the implicit meaning as close as the target language. This study examines the translation practice under the guidance of Nida’s theory, providing the proper strategies for interpreters.

Budget Deficit Financing and Economic Well-Being in Benin: Testing the Ricardian Equivalence Theory

This article examines the validity of Ricardian equivalence theory in Benin over the period 1980 to 2020. The study uses a time series with the Autoregressive Long-Lived Regressions (ARDL) model. The results show that budget deficit financing has a positive effect on household consumption in the short term, and a negative effect in the long term. On the other hand, budget deficit financing has a positive effect on gross domestic product in the short term and no significant effect in the long term. These results suggest that budget deficit financing has different short- and long-term effects on economic well-being in Benin. Consequently, policymakers should consider complementary strategies to support long-term economic growth and ensure the sustainability of fiscal policies.

Examining the English Publicity Materials of the Cultural Heritage in Xi’an from the Perspective of Functional Equivalence Theory

Xi’an, one of the political, economic and cultural centers of ancient China and the starting point of the New Silk Road, has increasingly become an important window through which Chinese culture is introduced to the outside world. The publicity materials of Xi’an cultural attractions contain rich Chinese cultural elements. At present, the study of their English translation in the academic circle is still fragmented, relatively macro and insufficient in the cases, which seriously affects the communication and exchange between Shaanxi and foreign cultures. In this essay, a series of important cultural terms were selected from the publicity materials of Xi’an cultural attractions issued by Shaanxi Tourism Bureau. Then the literal and cultural meanings of these terms in Chinese and English were compared so that the problems in their translation were studied. It is found that there were three kinds of translation problems: disparity in both the literal and cultural meaning; disparity in acquired meaning; disparity in associated cultural meaning. The results of this study have some theoretical value in the translation of important cultural terms, and have certain practical value in introducing the Chinese culture to the rest of the world and improve the image of Xi’an.

Analysis of Subtitle Translation Based on Functional Equivalence Theory—Taking <i>Dead Poets Society</i> as an Example

Analysis of Subtitle Translation Based on Functional Equivalence Theory—Taking <i>Dead Poets Society</i> as an Example

Study on the English Translation of Chinese Cuisine from the Perspective of Functional Equivalence Theory: Taking Yue Cuisine for Example

Study on the English Translation of Chinese Cuisine from the Perspective of Functional Equivalence Theory: Taking Yue Cuisine for Example

Research of Translation Strategies of Culture-Loaded Terms in Three Kingdoms from the Perspective of Functional Equivalence Theory

Research of Translation Strategies of Culture-Loaded Terms in Three Kingdoms from the Perspective of Functional Equivalence Theory

A breakdown-free block conjugate gradient method for large-scale discriminant analysis

<abstract><p>Rayleigh-Ritz discriminant analysis (RRDA) is an effective algorithm for linear discriminant analysis (LDA), but there are some drawbacks in its implementation. In this paper, we first improved Rayleigh-Ritz discriminant analysis (IRRDA) to make its framework more concise, and established the equivalence theory of the solution space between our discriminant analysis and RRDA. Second, we proposed a new model based on positive definite systems of linear equations for linear discriminant analysis, and certificated the rationality of the new model. Compared with the traditional linear regression model for linear discriminant analysis, the coefficient matrix of our model avoided forming a centralized matrix or appending the original data matrix, but the original matrix itself, which greatly reduced the computational complexity. According to the size of data matrix, we designed two solution schemes for the new model based on the block conjugate gradient method. Experiments in real-world datasets demonstrated the effectiveness and efficiency of our algorithm and it showed that our method was more efficient and faster than RRDA.</p></abstract>

The Application of Functional Equivalence Theory in the Translation of Children’s Literature - Using “Red Rose and Tiger Lily or in A Wider World” as an Example

The Application of Functional Equivalence Theory in the Translation of Children’s Literature - Using “Red Rose and Tiger Lily or in A Wider World” as an Example