Rational Equivalence Research Articles

A rational function quantum equivalence relation on the set of all prime numbers

In this paper, we prove new results which make it possible to vastly simplify solution of the problem of Nathanson concerning the enlargement of support bases and thus of the corresponding semigroup supports of rational function solutions to the quantum functional equations arising from multiplication of quantum integers. In particular, we establish a certain quantum equivalence relation on the set of all prime numbers which encodes the symmetry of these solutions and thus solve a problem which simplify in crucial ways the criteria for the problem posed by Nathanson concerning extensions of the support bases of these solutions.

Framing effects from misleading implicatures: an empirically based case against some purported nudges

Some bioethicists argue that a doctor may frame treatment options in terms of effects on survival rather than on mortality in order to influence patients to choose the better option....

Study of the Accuracy of the Ronen Method at Material Interfaces

The Ronen Method (RM) is a nonlinear iterative scheme that demands successive resolutions of the diffusion equation, where local diffusion constants are modified to reproduce more accurate estimates of the neutron currents by a transport operator. The methodology is currently formulated using the formalism of the collision probability method for evaluation of the current. The RM was recently tested on a complete suite of one-dimensional (1-D) multigroup benchmark problems. Small differences in the flux (less than 2%) were reported at material interfaces and close to the vacuum boundary with respect to the reference solution from transport. This work investigates first a possible numerical equivalence between transport and diffusion in some representative 1-D problems from the same benchmark test suite. The equivalence is sought with optimal diffusion coefficients computed using reference transport solutions that allow for adjusting the diffusion model. The RM, which attempts to obtain such equivalent diffusion coefficients without knowing the reference solution, is then compared to the optimal coefficients. The accuracy of the flux distribution at material interfaces is investigated for different approximations of the vacuum boundary and by decreasing progressively the RM convergence tolerance set in the iterative scheme. Using tighter convergence criteria, the RM calculates more accurate flux distributions at all material interfaces, regardless of the value of the diffusion coefficient and the extrapolated distance set at the beginning of the iterative scheme. Maximum flux deviations are remarkably reduced when the RM convergence tolerance is set to eight or more significant digits, leading to improvements in the flux deviation of two orders in magnitude and providing numerical proof for equivalence with transport in the tested configurations.

Isotropic and numerical equivalence for Chow groups and Morava K-theories

In this paper we prove the conjecture claiming that, over a flexible field, isotropic Chow groups coincide with numerical Chow groups (with Fp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}${\\Bbb {F}}_{p}$\\end{document}-coefficients). This shows that Isotropic Chow motives coincide with Numerical Chow motives. In particular, homs between such objects are finite groups and ⊗ has no zero-divisors. It provides a large supply of new points for the Balmer spectrum of the Voevodsky motivic category. We also prove the Morava K-theory version of the above result, which permits to construct plenty of new points for the Balmer spectrum of the Morel-Voevodsky A1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}${\\mathbb{A}}^{1}$\\end{document}-stable homotopy category. This substantially improves our understanding of the mentioned spectra whose description is a major open problem.

P3LS: Partial Least Squares under privacy preservation

Modern manufacturing value chains require intelligent orchestration of processes across company borders in order to maximize profits while fostering social and environmental sustainability. However, the implementation of integrated, systems-level approaches for data-informed decision-making along value chains is currently hampered by privacy concerns associated with cross-organizational data exchange and integration. We here propose Privacy-Preserving Partial Least Squares (P3LS) regression, a novel federated learning technique that enables cross-organizational data integration and process modeling with privacy guarantees. P3LS involves a singular value decomposition (SVD) based PLS algorithm and employs removable, random masks generated by a trusted authority in order to protect the privacy of the data contributed by each data holder. We demonstrate the capability of P3LS to vertically integrate process data along a hypothetical value chain consisting of three parties and to improve the prediction performance on several process-related key performance indicators. Furthermore, we show the numerical equivalence of P3LS and PLS model components on both a synthetic and a real-world dataset and provide a thorough privacy analysis of the former. Moreover, we propose privacy-preserving explained X- and Y-block variance computations for determining the contribution of each data holder to the federated process model as a basis to incentivize data federation and fair profit-sharing.

Chow–Lefschetz motives

We develop Milne’s theory of Lefschetz motives for general adequate equivalence relations and over a not necessarily algebraically closed base field. The corresponding categories turn out to enjoy all properties predicted by standard and less standard conjectures, in a stronger way: algebraic and numerical equivalences agree in this context. We also compute the Tannakian group associated to a Weil cohomology in a different and more conceptual way than Milne’s case-by-case approach.

Deterministic observability calculations for zero-dimensional models of lithium–sulfur batteries

Among the various energy storage technologies under development, the lithium‑sulfur (Li–S) battery has considerable promise due to its higher theoretical energy density, small environmental footprint, and low projected costs. One of the main challenges posed by Li–S is the need for a battery management system (BMS) that can accommodate the system's complex multi-step redox behaviours; conventional approaches for lithium-ion batteries do not transfer. Most existing approaches rely on equivalent circuit network models, but there is growing interest in ‘zero-dimensional’ electrochemical models which can potentially give insights into the relative polysulfide species concentrations present at any given time. To be useful for state estimation, a model must be ‘observable’: it must be possible to uniquely determine the internal state through observation of the system's behaviour over time. Previous studies have assessed observability using numerical methods, which is an approximation. This study derives an analytic expression for the observability criterion, which allows greater confidence in the results. The analytic observability criterion is then validated against a numerical comparator. A zero-dimensional model from the literature is translated into an ordinary differential equation (ODE) form to define the state variables matrix A, the output matrix C, and subsequently the observability matrix O. These are compared to simulated numerical equivalents. In addition, the sensitivity of the numerical process has been demonstrated. The results have the potential to offer greater confidence in conclusions around observability, which in turn gives greater confidence in the effects of any algorithms based on them.

Numerical Equivalence of Diabatic and Adiabatic Representations in Diatomic Molecules.

The (time-independent) Schrödinger equation for atomistic systems is solved by using the adiabatic potential energy curves (PECs) and the associated adiabatic approximation. In cases where interactions between electronic states become important, the associated nonadiabatic effects are taken into account via derivative couplings (DDRs), also known as nonadiabatic couplings (NACs). For diatomic molecules, the corresponding PECs in the adiabatic representation are characterized by avoided crossings. The alternative to the adiabatic approach is the diabatic representation obtained via a unitary transformation of the adiabatic states by minimizing the DDRs. For diatomics, the diabatic representation has zero DDR and nondiagonal diabatic couplings ensue. The two representations are fully equivalent and so should be the rovibronic energies and wave functions, which result from the solution of the corresponding Schrödinger equations. We demonstrate (for the first time) the numerical equivalence between the adiabatic and diabatic rovibronic calculations of diatomic molecules using the ab initio curves of yttrium oxide (YO) and carbon monohydride (CH) as examples of two-state systems, where YO is characterized by a strong NAC, while CH has a strong diabatic coupling. Rovibronic energies and wave functions are computed using a new diabatic module implemented in the variational rovibronic code Duo. We show that it is important to include both the diagonal Born-Oppenheimer correction and nondiagonal DDRs. We also show that the convergence of the vibronic energy calculations can strongly depend on the representation of nuclear motion used and that no one representation is best in all cases.

Developing a realistic numerical equivalent of a GPR antenna transducer using global optimizers

AbstractNumerical modelling of a ground‐penetrating radar (GPR) has been widely used for predicting and assessing its performance. As the transmitter and the receiver are the most essential components of a GPR system, an accurate representation of them should be included in a model. Simulating a real system is particularly challenging, especially when it comes to commercial GPR systems. A three‐dimensional model based on a 2000 MHz ‘palm’ antenna from Geophysical Survey Systems, Inc. (GSSI) is presented in this paper. The geometric features of the transducers were modelled via visual inspection, whereas their unknown dielectric properties were estimated using global optimizers in order to minimize the differences between real and synthetic measurements. In particular, the antenna was calibrated in free space and on top of a metal plate. Subsequently, the resulting model was successfully tested in various case studies to assess its performance. Models of two units of the same transducer were developed, showing that units of the same system in general are not identical. The results support the premise that global optimizers can be used to provide information on key aspects of the dielectric structure of the transducer and allow us to accurately model its behaviour in various environments.

A coupling algorithm of ordinary and non-ordinary state-based peridynamic models for fracture analysis in brittle and ductile materials

In this work, a novel coupling algorithm of the ordinary state-based peridynamic (OSB-PD) model and non-ordinary state-based peridynamic (NOSB-PD) model is provided under the peridynamic framework. The salient advantages of both OSB-PD and NOSB-PD models can be simultaneously inherited in this coupling model and approach. The feasibility of coupling these two models is first analyzed by demonstrating the numerical equivalence of their constitutive formulations in isotropic elastic and elastoplastic problems, and the detailed numerical implementation strategy of coupling formulation is given as well. With the coupling model in this study, the main calculation procedure of numerical simulations is accomplished in OSB-PD, while the damage and failure analysis is conducted in NOSB-PD. Moreover, different failure criteria are introduced in this coupling model to describe the damage and failure of brittle and metallic materials. Several typical examples, including the mode I and mixed mode I/II fracture of brittle materials, and the ductile fracture and impact failure of metallic materials, are conducted to demonstrate the robustness and accuracy of the presented coupling model and approach.

Optimized inversion method for thermal parameters of concrete dam under the insulated condition

It is crucial to study how thermal characteristics of concrete dam change over time, especially in cold regions, in order to guarantee long-term safety of the engineering projects. In this manuscript, an inverse analysis method by coupling the numerical simulation model and dam safety monitoring data, is proposed to solve the problem that true thermal parameters of the whole structure cannot be obtained by laboratory experiments or field tests of single points. Moreover, a numerical equivalence method of the dam and its insulation layer is introduced, in order to overcome the problem that the thickness of the insulation layer is much smaller than that of the concrete dam, resulting in low accuracy of the simulation model. Thirdly, the particle swarm optimization is introduced, in order to solve the ill-posed problems occurring during the solution process of multi-parameter inverse analysis. Considering the problem that the original particle swarm algorithm is easy to fall into local optimum and stuck edge, this study improves particles velocity and inertia weights. Benchmark function tests are applied to show the performance compared to several typical optimized algorithms. Numerical simulation and engineering verification are used to demonstrate the rationality and feasibility of the proposed method. The cases show that the residual box diagram of two typical measuring points calculated by inversion value is smaller than the median line and mean point calculated by design value. Moreover, the change law of the temperature field of the finite element calculation using the inversion values is closer to the actual measured value than that of the design value. The results indicate that the multi-parameter inverse method is feasible in insulated dam engineering. In addition, the result of the improved PSO optimization converges faster and has a higher fitness value than that of the original algorithm. It suggests that the improved PSO algorithm for thermal parameters inversion has fitting accuracy and rationality for insulated concrete dams in cold regions.

Rational equivalence for enveloping algebras of three-dimensional Lie algebras

We study from the point of view of rational equivalence the enveloping algebras of Lie algebras of dimension 3 whose derived Lie subalgebra is of dimension 2, over an algebraically closed base field in arbitrary characteristics.

ENGLISH INDEFINITE PRONOUN ANY AND ITS SERBIAN TRANSLATION EQUIVALENTS

This study aims to analyse a contrastive relation between the English indefinite pronoun any and its Serbian equivalents. Beside the simple pronoun any, the study also focuses on how its compounds with other words – nouns (-body, -thing), numerals (-one) and interrogatives (-where) are performed and translated into Serbian. In this sense, the study is result-oriented. In order to reveal the equivalence relevance and equivalence distribution in practice, the analysis was based on a parallel corpus. The source text ʻThe Sense of an Endingʼ by J. Barnes was confronted with the corresponding target text in Serbian ʻOvo liči na krajʼ, to investigate the appropriate forms.
 Although belonging to different language families, English and Serbian have shown a significant degree of similarities and differences among the elements in scope. Indefinite pronouns are a linguistic universal. Thus they occur systematically in both English and Serbian. Nevertheless, the Serbian pronominal equivalents are not categorised only as indefinites, but they also have a negative (niko, ništa, nikakav), free-choice (neko, nešto, neki) and universal functions26 (svako, bilo koji, bilo kakav). There is rarely any reciprocity in a direct Serbian implication for each English pronoun – an English indefinite pronoun usually has numerous Serbian equivalents. The proportion of the pronominal and non-pronominal (adverbs, particles, prepositional phrases, etc) Serbian equivalents is 2:1. Zero equivalence has appeared to be unexpectedly frequent – predominantly in negative and interrogative contexts. But even when the indefinites are not explicitly translated, due to stylistic and pragmatic differences between the two languages, there is equivalence at a syntactic level. The analysis revealed various equivalents, but they can be roughly brought down to the following: any is mostly omitted in Serbian negatives, and interrogatives, and translated as svaki in affirmatives; anything is translated as ništa in negatives, išta in interroatives and nešto in affirmatives; anyone is translated as niko in negatives, and iko in affirmatives; anybody is translated as bilo ko in affirmatives; anyway is translated as bilo kako bilo in affirmatives; anywhere is translated as ikud in negatives. Such an asymmetry of equivalence shows that there is not obvious and apparent compatibility between English and Serbian indefinite pronouns.
 The aim of this paper has therefore been to offer a better understanding of the various forms among the corresponding English and Serbian indefinite pronominals, in terms of their practical relevance.

On application of the regularized lattice Boltzmann method for isothermal flows with non-vanishing Knudsen numbers

Despite the advances in microscale modelling capabilities, physically observed non-zero Knudsen number (Kn) effects still elude the lattice Boltzmann method (LBM). This article details various Regularized LBM (RLBM) strategies used to model microscale flows and presents a thorough analysis on their applicability for the force-driven Poiseuille flow problem. In particular, we compare the formulations of eight schemes: Projected RLBM (P-RLBM), standard and Galilean Invariant Filtered Collision RLBM, Kn-dependant P-RLBM, Recursively Regularized LBM (R-RLBM), Hybrid R-RLBM, Central-Moment RLBM, and Onsager-Regularized LBM. We demonstrate, at different Kn with discrete Maxwell’s diffuse kinetic wall boundary conditions, the numerical equivalence of the considered RLBM schemes for hard sphere molecules on the D2Q9 lattice. Thereafter, we include a Kn-dependant wall-modified mean-free-path and extend the characterization onto higher-order D2Q17, D2Q21 and Q2Q25-Zero-One-Three, Q2Q49-Zero-One-Two-Three lattices. The study indicates that RLBM schemes are Navier-Stokes solvers which fail to entirely capture all the non-equilibrium phenomenon of slip/transition regime flows.

Determining Accuracy of Temperature Limit Change in Power Transformer Core Using Temperature-Time Parameter Method

The efficient transmission of electrical energy depends on amplifying voltage values with power transformers. To obtain higher efficiency from transformers, the core and winding type of transformer, the geometric structure of the core, and the shaping techniques in the windings are changed. This requires modeling transformer windings with equivalent circuits and calculating the inductance and electrical parameters appropriately. In this study, two-dimensional (2D) finite element solutions with energy perturbation and flux-coupling methods are used. The correctness of the inductance values of transformer windings was established, and the design was performed, by considering the inductance and electrical parameter values, which are comparable to the energy perturbation and flux connection. However, when two-dimensional calculated fields are used, the flux coupling method requires less computation and gives numerically more accurate results than the energy perturbation method. So, it is concluded that the flux-coupling approach should be chosen as the preferred method for calculating the inductance and electrical parameters of transformer windings. The numerical properties and equivalence of energy perturbation and flux-connection methods, the “apparent” inductance value of the primary and secondary field windings of power transformer operating under transient conditions, using the temperature-time parameter method, are calculated and its accuracy is demonstrated.

Validation of the current and pressure coupling schemes with nonlinear simulations of TAE and analysis on the linear stability of tearing mode in the presence of energetic particles

Both current and pressure coupling schemes have been adopted in the hybrid kinetic–magnetohydrodynamic code CLT-K recently. Numerical equivalences between these two coupling schemes are strictly verified under different approximations. First, when considering only the perturbed distribution function of energetic particles (EPs), the equivalence can be proved analytically. Second, when both the variations of the magnetic field and the EP distribution function are included, the current and pressure coupling schemes numerically produce the same result in the nonlinear simulations. On this basis, the influences of co-/counter-passing and trapped EPs on the linear stabilities of the m/n = 2/1 tearing mode (TM) have been investigated (where m and n represent the poloidal and toroidal mode numbers, respectively). The results of scanning of EPs show that the co-passing and trapped EPs are found to stabilize the TM, while the counter-passing EPs tend to destabilize the TM. The behind (de)stabilization mechanisms of the TM by EPs are carefully analyzed. Furthermore, after exceeding critical EP betas, the same branch of the high-frequency mode is excited by co-/counter-passing and trapped EPs, which is identified as the m/n = 2/1 energetic particle mode.

Prefigované ekvivalenty francúzskych verb percepcie v slovenčine

The presented article deals with the translation of verbs of perception from French into Slovak in the novel Passing Timeby M. Butor. The focus, in particular, is on the numerous Slovak prefix equivalents of these French non-prefixed verbs. The main goal is the analysis of their meanings. We will observe how the prefix, in addition to changing the imperfect form into the perfect one, modifies the meaning of the basic verb of perception and thus fulfils its lexical-perfective function. We assume that most of the initial non-prefixed verbs in the French source language will be in the compound past tense - passé composé. The partial goal of the research is to find out which prefixes are ​​the most productive in terms of verbal word formation by prefixing. We have found out that in the majority of cases, the prefix not only fulfils a grammatical function, but also has a lexical function that significantly modifies the meaning of the basic non-prefixed verb. For example, it enriches the verb with the meanings of the beginning of the action.

Frequency‐to‐spectrum mapping GAN for semisupervised hyperspectral anomaly detection

AbstractMost unsupervised or semisupervised hyperspectral anomaly detection (HAD) methods train background reconstruction models in the original spectral domain. However, due to the noise and spatial resolution limitations, there may be a lack of discrimination between backgrounds and anomalies. This makes it easy for the autoencoder to capture the low‐level features shared between the two, thereby increasing the difficulty of separating anomalies from the backgrounds, which runs counter to the purpose of HAD. To this end, the authors map the original spectrums to the fractional Fourier domain (FrFD) and reformulate it as a mapping task in which restoration errors are employed to distinguish background and anomaly. This study proposes a novel frequency‐to‐spectrum mapping generative adversarial network for HAD. Specifically, the depth separable features of backgrounds and anomalies are enhanced in the FrFD. Due to the semisupervised approach, FTSGAN needs to learn the embedded features of the backgrounds, thus mapping and restoring them from the FrFD to the original spectral domain. This strategy effectively prevents the model from focussing on the numerical equivalence of input and output, and restricts the ability of FTSGAN to restore anomalies. The comparison and analysis of the experiments verify that the proposed method is competitive.

Basics of computational fluid dynamics: An overview

Computational fluid dynamics (CFD) deals with equations that control fluid motion. CFD has several applications in diverse technical domains. In this review paper, a discussion was made on the basics of CFD and its applications in multiple domains. To tackle the fluid problem, CFD has some said procedure that needs to be followed to arrive at the solution step. The first step is to write down a mathematical equation for fluid flow. These mathematical equations are a set of partial derivatives. Discretizing is the next step to deriving this equation concerning numerical equivalent. After that, the domain is divided into tiny grids, popularly known as meshing. The final step involves deciding whether boundary conditions align with the fluid problem. In all CFD standards, these three aspects play an essential role, i.e. (1) A pre-processor is responsible for creating geometry, mesh generation, and providing flow characteristics and boundary conditions to the standard code. (2) A flow solver is utilized to solve equations related to the fluid issue. Researchers commonly use flow solvers, including the finite element method, finite difference method, and finite volume method. (3) A post-processor gives the final display output graphically and understandably. According to most researchers, recent improvements in computational fluid dynamics have created low-cost opportunities. This paper helps to comprehend the CFD standards procedure to solve the fluid problem.

Stellahedral geometry of matroids

Abstract We use the geometry of the stellahedral toric variety to study matroids. We identify the valuative group of matroids with the cohomology ring of the stellahedral toric variety and show that valuative, homological and numerical equivalence relations for matroids coincide. We establish a new log-concavity result for the Tutte polynomial of a matroid, answering a question of Wagner and Shapiro–Smirnov–Vaintrob on Postnikov–Shapiro algebras, and calculate the Chern–Schwartz–MacPherson classes of matroid Schubert cells. The central construction is the ‘augmented tautological classes of matroids’, modeled after certain toric vector bundles on the stellahedral toric variety.