Equivalent Characterizations Research Articles

A unified framework of fuzzy implications and coimplications

Fuzzy implications and coimplications play important roles in both theoretic and applied communities of fuzzy set theory. In this paper, we provide a unified framework for fuzzy implications and coimplications. Specifically, firstly, we introduce the concept of uni-implications, which is the unification of fuzzy implications and coimplications, and describe the structure of uni-implications. Secondly, we discuss the relationships among uni-implications, fuzzy boundary weak implications and fuzzy (co)implications. Thirdly, we present two constructions and equivalent characterizations of non-trivial uni-implications, respectively. Finally, we propose two binary operations ♠,♡ on some subset of the set of non-trivial uni-implications, denoted by FSNT, which make (FSNT,♠) a semigroup and (FSNT,♡) a non-commutative and non-idempotent monoid.

Characterization of serrated chip formation based on in-situ imaging analysis in orthogonal cutting

Abstract The in-situ imaging of the cutting process exhibits outstanding advantages in reconstructing the precise and visual thermoplastic deformation fields. The physical and geometric characteristics of deformation fields provide a deeper understanding of the cutting processes. In this paper, a mechanism-image hybrid analysis method is proposed to acquire the characteristics of the serrated chip deformation in the orthogonal cutting of TA15 titanium alloy based on in-situ imaging. The established hybrid analysis method combines the shear-plane theory with the streamline method and image segmentation method, which realizes the identification of pixel coordinates of the main shear plane (MSP) and the primary shear zone (PSZ) and then the extraction of the physical and geometric variables from the digital image correlation (DIC) full-field measurements. Consequently, the variations of equivalent strain rate, strain, temperature, and the geometric characterizations of MSP and PSZ during an individual serration formation of TA15 titanium alloy were quantitatively investigated. It was found that the physical and geometric variables reached stability in the final stage of serration evolution and were averaged as the DIC-based equivalent characterizations to analyze the impact of cutting depth and tool rake angle. Meanwhile, the DIC-based equivalent characterizations were compared with the results obtained by the classical analytical models to illustrate the advantages of the DIC-based analysis. The findings also support that the established hybrid analysis method holds the potential to characterize the serrated chip formation of other materials and improve the models of PSZ.

Front Cover: Equivalent transmission line characterization and multi‐layer material measurement analysis of the signal conversion process in the pulsed electro‐acoustic method

Front Cover: Equivalent transmission line characterization and multi‐layer material measurement analysis of the signal conversion process in the pulsed electro‐acoustic method

Fatigue Reliability Assessment for Orthotropic Steel Decks: Considering Multicrack Coupling Effects

Multiple fatigue cracks are generally present in practical engineering due to the existence of welding; the size and number of cracks of orthotropic steel bridge decks are greatly uncertain. The component failure conditions caused by these cracks may have correlations. Currently, it is still a challenging issue to develop a physical model of multiple fatigue crack propagation in bridge decks and perform a fatigue reliability assessment, which is also the motivation that drives the innovation of this study. A fatigue reliability evaluation method is presented for orthotropic steel bridge decks, considering the coupling effect of multiple cracks and the randomness of vehicle loading. A numerical simulation method for multifatigue crack growth is developed by combining the ABAQUS and FRANC3D programs. The equivalent crack depth under different spacing and depths of collinear cracks is calculated by using numerical simulation and the multicrack equivalent characterization method. The critical damage accumulation function of multiple fatigue cracks is established using linear elastic fracture mechanics. Subsequently, the critical damage accumulation function of multiple fatigue cracks is established based on linear elastic fracture mechanics. In order to solve the time-consuming problem of traditional Monte Carlo method, the iHL-RF method and AK-MCS method are developed for fatigue reliability analysis. The results show that compared with the single-crack model, the fatigue reliability of orthotropic steel deck will be crucially reduced considering the coupling effect of double cracks. The MCS, iHL-RF and AK-MCS methods can effectively solve the fatigue reliability analysis problem. Compared with the MCS method, the reliability calculation time based on AK-MCS method is significantly reduced. The AK-MCS method-based method reduces the time for calculating the reliability of orthotropic steel decks by 50% compared with the iHL-RF method. The reliability analysis of orthotropic steel deck bridge based on AK-MCS method is proved to be efficient and accurate.

Relative injective envelopes and relative projective covers on ring extensions

A ring extension is a ring homomorphism preserving identities. In this paper, we give the definitions of relative injective envelopes and relative projective covers of modules on ring extensions, and study their basic properties. In particular, we give their equivalent characterizations in terms of relative essential monomorphisms and relative superfluous epimorphisms, and prove that relative injective envelopes and relative projective covers on ring extensions are unique up to isomorphism whenever they exist. Moreover, for an extension of Artin algebras, we show that every finitely generated module has both a relative injective envelope and a relative projective cover. In addition, we compare relative injective envelopes and relative projective covers on two ring extensions linked by surjective homomorphisms of rings respectively.

Connectedness degrees in (L, M)-fuzzy convex structures

Connectivity is one of the most essential notions in general topology. Convex structures are topological-like structures. Many properties in topological spaces have been generalized to convex structures, such as separation. However, connectivity has not been studied in convex structures yet. In this paper, firstly, based on the consideration to hull operators, separatedness is defined in classical convex structures, and then we provide the concept of connectivity. Secondly, some equivalent characterizations of connectivity are discussed, and we investigate the related properties of connectivity. In additional, through (L, M)-fuzzy convex hull operators, we propose the separatedness degrees of (L, M)-fuzzy convex structures. Furthermore, the notion of connectedness degrees of (L, M)-fuzzy convex structures is introduced. Finally, many properties of connectivity in general convex structures can be generalized to (L, M)-fuzzy convex structures.

Theoretical analysis and numerical simulation of methane adsorption behavior on rough surfaces featuring fractal property

This work focuses on the control mechanism of adsorption behavior from rough surfaces featuring fractal property numerically. For that, we develop an equivalent characterization method for rough fractal surfaces, reproduce the adsorption process of methane on the surface by combining molecular dynamics and Grand canonical Monte Carlo (GCMC) simulations, analyze the control mechanisms of complex types of surface geometry on the methane adsorption process, and clarity the ratio of vertical roughness to horizontal complexity as key parameter to describe the adsorption capability. Our numerical results indicate that the adsorption density of methane in fractal and non-fractal slit pores varies with the fractal behavior of surface geometry, while the density of gas phase methane remains unaffected (all distributed around 0.06 g/cm3). And, the complexities of surface geometry process various effects on occurrence mode, adsorption potential energy (ɛ), and adsorption amounts. The surface original complexity will influence the force field, and alter the occurrence mode from monolayer adsorption to pore filling. Meanwhile, the width-to-depth ratio of surface original complexity has a negatively effects the ɛ of methane. The behavioral complexity of the surface reflects the number of small pores on it. For fractal slit pores, the maximum adsorption amounts are 2405.77, 2634.90, and 2749.46 mol/m3, respectively. They are smaller than that of the non-fractal slit pore, which is due to the increase of non-adsorption pores for the small diameter of pores. Above results give a clear explanation to the effects of fractal property on methane adsorption, which will provide a reference to study the adsorption process of methane in Coalbed Methane reservoir.

On $\mathbb{Z}^{d}$-odometers associated to integer matrices

We extend the results by Giordano, Putnam, and Skau (2019) on characterization of conjugacy, isomorphism, and continuous orbit equivalence of \mathbb{Z}^{d} -odometers to dimensions d>2 . We then apply these extensions to the case of odometers defined by matrices with integer coefficients.

Unitarily equivalent bilateral weighted shifts with operator weights

The aim of this paper is to study unitarily equivalent bilateral weighted shifts with operator weights. Our purpose is to establish a general characterization of unitary equivalence of such shifts under the assumption that the weights are quasi-invertible. Under further assumptions on weights it was proved that unitary equivalence of bilateral weigthed shifts with operator weights defined on \(\mathbb{C}^{2}\) can always be given by a unitary operator with at most two non-zero diagonals. The paper contains also examples of unitarily equivalent shifts with weights defined on \(\mathbb{C}^{k}\) such that every unitary operator, which intertwines them has at least \(k\) non-zero diagonals.

On Schur Complement in k-Kernel Symmetric Neutrosophic and Intuitionistic Fuzzy Matrices

The present study provides the necessary and sufficient criteria for the k-Kernel symmetry (KS) of a Schur complement (SC) in a k-KS Neutrosophic Fuzzy matrices (NFM) and Intuitionistic Fuzzy Matrices (IFM). Equivalent characterizations of KS and k-KS NFM and IFM are presented in this work. We provide a few fundamental examples about KS NFM and IFM. It is demonstrated that while k-symmetric implies k-KS, but the converse need not be true. A few fundamental characteristics of k-KS IFM and NFM are obtained.

INTELLIGENT EXTRACTION OF COMPLEXITY TYPES IN FRACTAL RESERVOIR AND ITS SIGNIFICANCE TO ESTIMATE TRANSPORT PROPERTY

Fractal pore structure exists widely in natural reservoir and dominates its transport property. For that, more and more effort is devoted to investigate the control mechanism on mass transfer in such a complex and multi-scale system. Apparently, effective characterization of the fractal structure is of fundamental importance. Although the newly emerged concept of complexity assembly clarified the complexity types and their assembly mechanism in a fractal system, equivalent extraction of the complexity types is the key for effective characterization. For these, we proposed a deep learning-based method to extract the original and behavioral complexity assembled in bed-packing fractal porous media for simplification and without loss of generality. In detail, the UNeXt network model was trained to obtain the independent connected regions of scaling objects with different scales, the edge detection and clustering analysis algorithms were employed to extract the number-size relationship between two successive scaling objects, and the unique inversion of fractal behavior was realized by taking the number-size model and fractal topography together. Consequently, an equivalent characterization method for fractal complex pore structure was developed based on the concept of complexity assembly. Our investigation provides a theoretical guidance and method reference for the quantitative characterization of fractal porous media that will guarantee the fundamental requirement for the accurate evaluation of the transport properties of natural reservoir.

Stochastic inversion for equivalent hydraulic fracture characterization using low-frequency distributed acoustic sensing data

Distributed fiber-optic sensing, a game-changing technology, has been successfully applied in monitoring hydraulic fracturing treatments. The cross-well fiber-optic strain/strain-rate responses are directly related to the fracture-propagation process and dynamic fracture geometry. Extracting the insightful information regarding hydraulic fractures requires robust interpretation workflows. In this paper, we aim to develop a stochastic inversion approach to characterize the dynamic equivalent fracture geometry and quantify the associated uncertainties using cross-well low-frequency distributed acoustic sensing (LF-DAS) measurements. A fast analytical forward solver based on the 3D displacement discontinuity method is developed to model the strain. The objective function is the sum-of-squares error between the modeled strain and the measured strain. We focus on an equivalent fracture geometry with a predefined length centered around the monitoring well, which is a reasonable assumption considering the spatial sensitivity of LF-DAS. Therefore, the model parameters reduce to fracture width and height of the equivalent fracture. We adopted the delayed rejection adaptive metropolis (DRAM) algorithm, an efficient Markov-chain Monte Carlo (MCMC)-based method, to perform the optimization. The efficiency and accuracy of the algorithm are tested using a synthetic case that has three monitoring wells at different locations. The mean values of fracture width and height are both close to the true values with negligible standard deviations for all the three monitoring wells. The algorithm performance is not sensitive to the initial guess and the predefined length needs to be large enough. Then, a field case with a single cluster from the HFTS-2 project is presented. The fracture width increases from about 0.5 mm to about 0.9 mm during the pumping stage and gradually decreases during the shut-in period. The fracture height changes during the pumping stage and stabilizes at about 150 m during the shut-in period, the trend of which is consistent with the LF-DAS signals from the offset vertical monitoring well. To the best of our knowledge, this is the first algorithm that can efficiently quantify the fracture width and height simultaneously. The results could provide novel insights on the characteristics of fracture geometry and significantly improve the understanding of complex fracture propagation processes in subsurface reservoirs.

Besov wavefront set

We develop a notion of wavefront set aimed at characterizing in Fourier space the directions along which a distribution behaves or not as an element of a specific Besov space. Subsequently we prove an alternative, albeit equivalent characterization of such wavefront set using the language of pseudodifferential operators. Both formulations are used to prove the main underlying structural properties. Among these we highlight the individuation of a sufficient criterion to multiply distributions with a prescribed Besov wavefront set which encompasses and generalizes the classical Young’s theorem. At last, as an application of this new framework we prove a theorem of propagation of singularities for a large class of hyperbolic operators.

Stability analysis for set-valued inverse mixed variational inequalities in reflexive Banach spaces

This work is devoted to the analysis for a new class of set-valued inverse mixed variational inequalities (SIMVIs) in reflexive Banach spaces, when both the mapping and the constraint set are perturbed simultaneously by two parameters. Several equivalence characterizations are given for SIMVIs to have nonempty and bounded solution sets. Based on the equivalence conditions, under the premise of monotone mappings, the stability result for the SIMVIs is obtained in the reflexive Banach space. Furthermore, to illustrate the results, an example of the traffic network equilibrium control problem is provided at the end of this paper. The results presented in this paper generalize and extend some known results in this area.

Relative regularity conditions and linear regularity properties for split feasibility problems in normed linear spaces

The bounded linear regularity property plays a key role in the study of the strong convergence and/or convergence rate of the CQ algorithm for solving split feasibility problems. To establish some sufficient conditions ensuring the bounded linear regularity property for split feasibility problems in normed linear spaces, we introduce the notion of a relative regularity condition and its associated relative regularity constant in spirit of the regularity condition used in Burke and Ferris (1995) [12]. Based on convex analysis techniques, we explore equivalent characterizations of the relative regularity condition, which in particular extend the classical results in Burke and Ferris (1995) [12] from the Euclidean space to general normed linear spaces, and then establish some important and useful properties in terms of the related relative regularity constant. Consequently, we develop a new technique to establish some sufficient conditions ensuring the bounded linear regularity property for split feasibility problems in normed linear spaces. The sufficient conditions presented in this paper are in terms of the relative regularity constant, which seem completely new. Applied to the case of Hilbert spaces, our results extend and improve the corresponding ones in Wang et al. (2017) [35] by relaxing the relevant assumptions.

Equivalent transmission line characterization and multi‐layer material measurement analysis of the signal conversion process in the pulsed electro‐acoustic method

AbstractThis paper studies the equivalent transmission line model of the pulsed electro‐acoustic (PEA) method with its applications. Based on the consistency of acoustic wave behaviour inside lossy acoustic materials and voltage wave propagation in transmission line, an equivalent simulation model of the PEA system is developed, whose reliability is verified by the output from the transducer and amplifier models and the comparison with measured waveforms. For the problem of acoustic impedance mismatch between different modules, simulation indicates that the unequal impedances of semiconducting electrode and sample can affect the amplitude of the measured signal at the upper electrode side, and the reflected acoustic waves caused by the transducer can affect the charge waveform. Further simulation for multi‐layer materials finds that the reflected acoustic waves of different samples and sound absorbing module can superimpose on the charge signal. Accordingly, a selection criterion is proposed to avoid the effect of the reflected waves at the interface. As for the acoustic reflection caused by internal charge, it needs to be dealt with sequentially in calibration process, starting from the result inside the sample near ground electrode. The research can provide a foundation for analyzing the acoustic properties of the PEA method.

Gradient Ricci solitons on Kropina measure spaces

Let F=α2β be a Kropina metric on a measure space (M,m) with the navigation data (h,W). In this paper, we give an equivalent characterization for (M,F,m) to be a gradient almost Ricci soliton, which implies that every gradient almost Ricci soliton has vanishing SBH-curvature. Based on this, we prove that (M,F,m) is a gradient almost Ricci soliton if and only if (M,h,f) is a Riemannian gradient almost Ricci soliton, W is a unit Killing vector field on M and f satisfies a differential equation, where f is the potential function f of the measure m (see Theorem 1.2). As an application, we construct some new shrinking, steady and expanding gradient Ricci solitons.

An iterative plane stress integrated Transformation Field Analysis for Equivalent Homogeneous Medium characterization and localization — Application to structural holes

Full-scale structure models of high-energy situations exhibited insufficient localization when connector elements were employed to model the assemblies. An alternative approach using a super-element featuring a hole was proposed and successful in mechanical fields localization. However this approach was restrained to linear problems. An extension to materially non-linear problems was thus looked for, and in particular perforated plate materially non-linear fields.An iterative plane stress integrated TFA method is thus developed to relocate the micro-scale elastic–plastic mechanical fields of a plate containing an extremely soft medium/a strong discontinuity: a hole. To this end, a RVE is defined and discretized, the accuracy of the localization relation is assessed, and a radial return algorithm is set-up to integrate the constitutive equation of the micro-scale problem. The results of the proposed TFA approach are compared to an analytical solution and to non-linear FEA. The results show that the localization of elastic–plastic perforated plate mechanical fields is accurate, provided that the method is iterative and that the hole is discretized in the RVE. It is foreseen that both the sequential and integrated TFA approaches will be combined to evaluate criteria in full-scale structure computations.

Wasserstein steepest descent flows of discrepancies with Riesz kernels

The aim of this paper is twofold. Based on the geometric Wasserstein tangent space, we first introduce Wasserstein steepest descent flows. These are locally absolutely continuous curves in the Wasserstein space whose tangent vectors point into a steepest descent direction of a given functional. This allows the use of Euler forward schemes instead of Jordan–Kinderlehrer–Otto schemes. For λ-convex functionals, we show that Wasserstein steepest descent flows are an equivalent characterization of Wasserstein gradient flows. The second aim is to study Wasserstein flows of the maximum mean discrepancy with respect to certain Riesz kernels. The crucial part is hereby the treatment of the interaction energy. Although it is not λ-convex along generalized geodesics, we give analytic expressions for Wasserstein steepest descent flows of the interaction energy starting at Dirac measures. In contrast to smooth kernels, the particle may explode, i.e., a Dirac measure becomes a non-Dirac one. The computation of steepest descent flows amounts to finding equilibrium measures with external fields, which nicely links Wasserstein flows of interaction energies with potential theory. Finally, we provide numerical simulations of Wasserstein steepest descent flows of discrepancies.

Selecting accepted assertions in partially ordered inconsistent DL-Lite knowledge bases

The problem of inconsistency handling in knowledge bases has received considerable research attention in several settings and has met many applications. Inconsistency usually stems from the fact that the information available for reasoning, query answering and decision-making tasks is obtained from different, scattered and potentially unreliable information sources. Performing these tasks is often computationally expensive, especially for knowledge bases in which the data is endowed with preferences and/or uncertainty. In the context of formal ontologies, enriching the assertions (i.e. the data pieces) with conceptual knowledge makes the query answering task harder computationally. Tractable results have been successfully established for the lightweight languages of the DL-Lite family. In this paper, we present two tractable methods for handling inconsistency in partially ordered lightweight ontologies. In essence, both methods are inspired from the well-known Intersection of ABox Repair (IAR) semantics, which proceeds by replacing the initial inconsistent knowledge base with the intersection of all of its maximally consistent sub-bases. The first method assumes a partial preorder over the knowledge base and identifies the accepted assertions, called ‘elected’, in polynomial time in data complexity. The second method captures uncertainty quantitatively in the framework of possibility theory and identifies the so-called ‘π-accepted’ assertions, also in polynomial time in data complexity. However, both characterisations require the conflict set to be readily available. This constitutes a serious limitation in frameworks and applications where the conflict set cannot be exhibited efficiently. In this paper, we propose a new and equivalent characterisation for each method. We show that the elected assertions and also the π-accepted assertions can be identified in polynomial time in the size of the dataset for lightweight ontologies.