Equivalent Relationship Research Articles

Partially-defined equivalence relations: Relationship with orthopartitions and connection to rough sets

We introduce partially-defined equivalence relations as a type of equivalence relation that incorporates uncertainty. In these relations, certain pairs of objects are not definitively determined to be related or unrelated. The relationship with orthopartitions is put forward, providing the conditions under which an orthopartition can be transformed into an equivalent partially-defined equivalence relation and vice versa. Additionally, we explore their connection with reducts in rough set theory, offering insights into the characterization of similarity reducts in terms of orthopartitions.

A conjugated bond-based peridynamic model for laminated composite materials

The bond-based peridynamic (BB-PD) theory is inadequate in describing the four independent engineering material constants of composite lamina, which results in fixed values its Poisson's ratios and shear moduli. This study presents a novel lamina conjugated BB-PD model encompasses not only the fiber bond and matrix bond, but also the transverse bond and conjugated bond pair. By defining these four basic PD bonds, the improved conjugated BB-PD model can overcome the restriction of material properties. The determination of the four basic PD micro-modulus parameters is achieved through the utilization of the equivalent relationship of strain energy density. In addition, the lamina conjugated BB-PD model is extended to deal with composite laminates with different stacking sequences. The present study validates the accuracy and applicability of the conjugated BB-PD model for composite materials by conducting simulations of the elastic deformation and progressive damage behavior of unidirectional laminae and laminates. Moreover, the proposed model provides an elucidation of the damage modes and failure mechanisms of laminated composite materials subjected to uniaxial loading.

Comparative study of damage modeling techniques for beam-like structures and their application in vehicle-bridge-interaction-based structural health monitoring

Damage modeling techniques are essential tools for revealing the impact pattern of damage on structural responses. Currently, different damage level parameters are defined for different damage modeling techniques, but there is no established equivalence among them. This might plague researchers in their selection of damage modeling techniques for theoretical and numerical studies. To address this challenge, comparative studies of different damage modeling techniques for beam-like structures were conducted, and their impact on vehicle-bridge-interaction (VBI)-based structural health monitoring was analyzed. First, the theoretical basis of four damage modeling techniques, that is, element stiffness loss, element mass increase, cracked beam element, and crack spring element, were analyzed, and equivalent damage level relationships were established based on beam frequencies. Then, a finite element simulation of the VBI system consisting of a two-axle vehicle and a beam-like structure with damage was formulated and verified. Finally, the impacts of different damage modeling techniques with unified damage levels on the dynamic responses were studied, and the feasibilities of damage identification using vehicle and bridge responses under different damage modeling techniques were compared. The results indicated that the dynamic responses generated by different damage modeling techniques varied under the same damage level. The damage modeling technique using the crack spring element posed the most significant impact on the VBI responses, the cracked beam element and element stiffness loss techniques had the equivalent impact, but the element mass increase technique showed a negligible impact. Damage location and severity could be well detected by the cracked beam element and element stiffness loss techniques. However, the dynamic responses generated by the element mass increase technique could not be used to identify the damage. Vehicle responses were more useful than bridge responses for damage identification, demonstrating the advancement of indirect monitoring of bridge health conditions using an instrumented passing vehicle.

Equivalent conversion investigation of environmental corrosion of suspenders in long-span suspension bridge

Purpose This paper aims to investigate the equivalent relationship between accelerated corrosion tests and real environmental spectrum of suspenders in long-span suspension bridge considering multiple factors action. Design/methodology/approach Based on Faraday's law, corrosion current was used as a measure of metal corrosion, and the equivalent conversion relationship between laboratory environment and real service environment was established. The equivalent conversion method for bridge structural steel had been determined under different temperature, humidity, pH value and NaCl concentration conditions. The compilation of environmental spectra for large span bridges considering multiple factors and the principle of equivalent conversion have been proposed. Findings Environmental factors, including temperature, humidity, pH value and NaCl concentration, have significant impact on the corrosion degree of suspension steel wires, and only considering these two factors for equivalent conversion cannot accurately reflect the true service environment of the bridge. The 33.8-h salt spray accelerated corrosion test using the standard conditions can be equivalent to one year of suspenders corrosion in a real service environment. Originality/value The equivalent accelerated corrosion method for steel wires proposed in this study can effectively predict the corrosion degree of the suspenders, which has been verified to be correct and can provide theoretical guidance for the development of corrosion test plans for steel wires and engineering technical basis for anti-corrosion control and calendar life research of suspension bridge suspenders.

Study on the Dynamic Mechanical Properties of Ultrahigh-Performance Concrete under Triaxial Constraints.

To confirm the effect of confining pressure on the dynamic mechanical behavior of ultrahigh-performance concrete (UHPC), this study used a true triaxial split Hopkinson pressure bar test system to perform dynamic compression tests on UHPC under triaxial constraints. The confining pressure range considered was 5~10 MPa, the strain rate range was 35~80 s-1, and the steel fiber contents were 0.5%, 1% and 2%. The three-dimensional dynamic engineering stress-strain relationship and equivalent stress-strain relationship of UHPC under different confining pressures and different strain rates were obtained and analyzed in detail. The results show that under the confinement condition, the dynamic peak axial stress-strain and dynamic peak lateral stress-strain of UHPC have strong sensitivity to the strain rate. In addition, the dynamic peak lateral stress-strain is more sensitive to the confining pressure than the dynamic axial stress. An empirical strength enhancement factor (DIFc) that considers the strain rate effect and confining pressure was derived, and the impact of the coupling between the enhancement caused by the confining pressure and the strain rate effect on the dynamic strength of the UHPC under triaxial confinement was discussed. A dynamic strength failure criterion for UHPC under triaxial constraint conditions was established.

Equivalent stress-strain models of components in high-strength concrete-filled circular steel tube columns

Nine circular concrete-filled steel tube (CFST) columns with 109 MPa concrete were tested under eccentric axial loading to derive the equivalent axial stress-strain models of the steel tube and concrete. Based on the measured strain data and the theory of elasticity and plasticity, the progressions of the axial and hoop stresses at different locations of the steel tube section were obtained. For the compression side of the steel tube, the hoop stress was developed at or after yielding; then, the ratio of the axial stress to the effective stress, σsa/fe, gradually decreased to a value of around 0.77. For the tension side of the steel tube, σsa/fe continued to increase after yielding and kept constant when σsa/fe reached a value of approximately 1.15. Using the developed axial stress-strain model of the steel tube, the equivalent axial stress-strain relationship of concrete was determined by matching the axial load-vertical displacement curve obtained from the fiber model analysis to that from the test. The confinement index, ξ, mainly influences the peak compressive stress and strain of concrete, whereas the eccentricity ratio has some influence on the descending branch of the stress-strain curve. The fiber model with the proposed stress-train models of steel and concrete can well simulate the behavior of circular CFST columns with high-strength concrete under compression-flexural loading when 0.35 ≤ ξ ≤ 0.85, 0.14 ≤ e/D ≤ 0.68, and 3.8 ≤ Le/D (Le is the effective length of a column) ≤ 10.6.

Optimal investment problem under behavioral setting: A Lagrange duality perspective

In this paper, we consider the optimal investment problem with both probability distortion/weighting and general non-concave utility functions with possibly finite number of inflection points, and apply a Lagrange duality based relaxation approach for solving this problem. Existing literature has shown the equivalent relationships (strong duality) between the relaxed problem and the original one by either assuming the presence of probability weighting or the non-concavity of utility functions, but not both. In this paper, combining both factors, we prove that the absence of concavity in the utilities may result in strictly positive gaps, thus the strong duality may not hold unconditionally. The necessary and sufficient conditions on eliminating such gaps have been provided under this circumstance. We have applied the solution method to obtain closed-form solutions for the optimal terminal wealth and corresponding investment strategies in a special cumulative prospect theory (CPT) example with an appropriately selected inverse S-shaped probability distortion function. Based on the solutions, the joint effects of non-concave utilities combined with the probability weighting on the trading behaviors can be explicitly characterized. We show that, under this particular example, the co-existence of both factors may water down the loss aversion effect induced by only S-shaped utility or probability distortion when the agents are more cash-strapped in the initial budgets. In addition, we find that the optimal strategies derived from distorted beliefs shall converge to a constant that can be expressed by the standard Merton ratio multiplied by an inflation factor which we name as “distorted” Merton ratio. More importantly, the inflation factor is solely dependent on the probability distortion rather than the features of the utility function.

Anti-Martingale Proximal Policy Optimization.

Since the sample data after one exploration process can only be used to update network parameters once in on-policy deep reinforcement learning (DRL), a high sample efficiency is necessary to accelerate the training process of on-policy DRL. In the proposed method, a submartingale criterion is proposed on the basis of the equivalence relationship between the optimal policy and martingale, and then an advanced value iteration (AVI) method is proposed to conduct value iteration with a high accuracy. Based on this foundation, an anti-martingale (AM) reinforcement learning framework is established to efficiently select the sample data that is conducive to policy optimization. In succession, an AM proximal policy optimization (AMPPO) method, which combines the AM framework with proximal policy optimization (PPO), is proposed to reasonably accelerate the updating process of state value that satisfies the submartingale criterion. Experimental results on the Mujoco platform show that AMPPO can achieve better performance than several state-of-the-art comparative DRL methods.

Effective medium temperature for calculating the deformed Doppler broadening function considering the Tsallis distribution

This paper presents a method for establishing an equivalence relationship between the Doppler Broadening Function based on the Maxwell-Boltzmann Distribution and the Deformed Doppler Broadening Function, according to the generalised Tsallis Distribution, through an effective temperature Teff of the medium. The proposed method allows a precise calculation of the Maxwellian Doppler Broadening Function, which reproduces the value of the Tsallis Doppler Broadening Function (TDBF), where ξ is associated to the temperature of medium T and ξ∼q relates to the effective temperature Teff of the medium. In this paper, we calculate ξ∼q for typical values of the deformation factor q together with a parameterization example for ξ∼q as a result of the ordered pair x,ξ, using a genetic algorithm technique. The results obtained were accurate, with a percentage deviation under 2%.

Two New Matrix Classes Related to the CMP Inverse: CMP and Co-CMP Matrices

This paper focuses on two new matrix classes related to the CMP inverse of a square matrix, called the CMP and co-CMP matrices. Some of their characterizations are identified based on the core-EP decomposition and subspace operations. And, we show an equivalence relationship between the co-CMP matrix set and the intersection of the core matrix set and the co-EP matrix set. The nonsingularity of other matrices closely associated with the co-CMP matrices is considered, and their inverses are presented in a decomposition form.

Study on the compressive residual strength after edge low-velocity impact of T300/69 laminates

PurposeEngineering composite laminates/structures are usually subjected to complex and variable loads, which result in interlayer delamination damage. However, damaged laminate may cause the whole structure to fail before reaching the design level. Therefore, the purpose of this paper is to develop an equivalent model to effectively evaluate compressive residual strength.Design/methodology/approachIn this paper, taking carbon fiber reinforced composite T300/69 specimens as the study object, first, the compressive residual strength under different impact energy is obtained. Then, zero-thickness cohesive elements, Hashin failure criteria and Camanho nonlinear degradation scheme are used to simulate the full-process simulation for compression after edge impact (CAEI). Lastly, based on an improved Whitney–Nuismer criterion, the equation of edge hole stress distribution, characteristic length and compressive residual strength is used to verify the correctness of the equivalent model.FindingsAn equivalent relationship between the compressive residual strength of damaged laminates and laminates with edge hole is established. For T300/69 laminates with a thickness of 2.4 mm, the compressive residual strength after damage under an impact energy of 3 J is equivalent to that when the hole aperture R = 2.25 mm and the hole aperture R = 9.18 mm when impact energy is 6 J. Besides, the relationship under the same size and different thickness is obtained.Originality/valueThe value of this study is to provide a reference for the equivalent behavior of damaged laminates. An equivalent model proposed in this paper will contribute to the research of compressive residual strength and provide a theoretical basis for practical engineering application.

Prestress design and geometric correction method of cable–truss structures based on equivalent equilibrium force model

Cable–truss structure is a typical form of cable–strut tensile structures, which consists of upper cable system, lower cable system and several vertical struts. As with the general cable–strut tensile structure, only when the reasonable geometric shape matches the feasible prestress distribution can the cable–truss structure obtain structural stiffness and bear the external load. Once the geometric shape is unreasonable, the cable–truss structure is just a mechanism without bearing capacity and cannot be stiffened by introducing prestress. Consequently, a reasonable geometry is the premise for cable–truss structure to become an effective load-bearing system. In this paper, an equivalent equilibrium force model, called EEFM, is proposed according to the geometric-mechanical characteristics of cable–truss structures. A cable–truss structure in this model is split into upper and lower cable systems with equivalent nodal forces. The geometric rationality can be easily evaluated from the equivalent nodal force relationship. According to the geometric topology and equilibrium equation of two cable systems, the self–stress mode of the structure with reasonable geometry can be directly obtained. For structures with unreasonable geometry, the node coordinates of one cable system are corrected based on the other cable system. Several cases are presented to verify the accuracy and validity of the proposed method. This method can be used for shape design, geometric correction and force finding, and has greater advantages for cable–truss structures with asymmetric or complex space configuration.

On Existence and Attractivity of Ψ-Hilfer Hybrid Fractional-order Langevin Differential Equations

The work reported in this article studies the equivalence relationship between fractional integral equation and Ψ-Hilfer Hybrid Langevin Differential Equations of fractional order with nonlocal initial conditions, and then we use this relationship to establish the existence of the results by means of Banach algebra and Schauder’s fixed point theorem. We then demonstrate the uniform local attractiveness of all the solutions.

Variation Pattern of the Elastic Modulus of Concrete under Combined Humidity and Heat Conditions.

The coupling effect of moisture content and temperature on the elastic modulus of concrete is experimentally investigated. The elastic modulus of dry concrete exhibits a clear temperature-weakening effect, while the elastic modulus of wet concrete exhibits a water-strengthening effect at room temperature. Under humidity-heat conditions, the elastic modulus of wet concrete declines with the temperature rise. When the temperature is 20 °C, 200 °C, 400 °C, 520 °C, and 620 °C, the humidity-heat coupling factors of the elastic modulus change rate DI˙F with moisture content are 0.08, 0.07, 0.04, 0.01, and -0.03, respectively, and the declining rate increases with the rise of moisture content. The relation between the humidity-heat coupling factor DIF, moisture content, and temperature was established; The equivalent relation between the water-strengthening effect and the temperature-weakening effect of the elastic modulus was obtained. The temperature range of the strengthening effect and "apparent weakening effect" of water stored inside concrete before heating on elastic modulus was determined; The evolutionary mechanism of the competition between the microcrack expansion and healing of concrete under combined humidity and heat conditions was revealed.

Equivalent Relationship between Flood Prevention Storage of Cascade Reservoirs in the Downstream Jinsha River and Three Gorges Reservoir

The equivalent relationships between flood prevention storage of a cascade reservoir system provide useful information for real-time operation. However, those relationships are implicitly hinted at in the optimized operation rules of downstream reservoirs, which may add difficultly in providing feasible operation strategies for engineering practice. In this study, we investigate the equivalent relationship between cascade reservoirs using a flood regional composition-based framework coupled with reservoir inflow and river flow routing techniques. We select the cascade reservoirs in the downstream Jinsha River and Three Gorges Reservoir (TGR) as the case study. Results reveal that (1) the equivalent relationship between flood prevention storage of cascade reservoirs in the downstream Jinsha River and TGR is approximately linear-related; (2) the conversion coefficient of equivalent relationship depends on the flood type, and the intercept term of equivalent relationship is mainly influenced by the design flood frequency; and (3) the TGR flood prevention storage (or water level) can be dynamically adjusted according to the corresponding reserved flood prevention storage of cascade reservoirs in the downstream Jinsha River, which can generate 3.56 billion kW·h (+8.5%) extra hydropower during flood season without increasing flood control risks.

Equivalent uniaxial constitutive relationship for core concrete of cross-shaped RC short columns

Equivalent uniaxial constitutive relationship for core concrete of cross-shaped RC short columns

Experimental and analytical study on the dynamic response of rectangular concrete-filled steel tube under transverse impact loading

Rectangular concrete-filled steel tubes (CFSTs) have been widely employed as prominent structural members in modern constructions. During their life cycles, rectangular CFST members may suffer from impact loads, leading to a need for investigations into their dynamic performance. In this context, 23 rectangular CFSTs subjected to transverse impact loading were experimentally investigated using a drop weight testing system. The instantaneous impact force responses and motion states of the specimens were recorded at high frequencies. The aspect ratio, the steel ratio and the clear span of the specimen, as well as the impact energy conditions, were the key parameters in the test scheme, and their influence on the dynamic response of the rectangular CFST specimens was analyzed. A finite element (FE) model was developed to predict the impact response of rectangular CFSTs, in which the strain rate effects of steel and concrete were well considered, and good accuracy was achieved. Then, an equivalent relationship between rectangular and square CFSTs under transverse impact was proposed and verified, which achieves access for rectangular CFSTs to existing design methods.

УСТОЙЧИВИ СРАВНЕНИЯ С НАЗВАНИЕ НА ЕТНОС В БЪЛГАРСКИЯ И РУСКИЯ ЕЗИК

The subject of the present article are stable comparisons with name of ethnicity. It is part of a linguistic and linguoculturological study on stable comparisonsin Bulgarian and Russian. The material excerpted from dictionaries and texts from the Bulgarian National Corpus and the Russian National Corpusis studied in comparative terms. Equivalent relations are established.

성인교육 분야 국제개발협력에서 임파워먼트 논의의 변화

Purpose: This study aims to explore how the concept of empowerment has been discussed over time by exploring the development process of empowerment discourse, focusing on the field of adult education in international education development cooperation. In addition, it studies the characteristics of change in terms of the content of the discourse and examines the context that influenced the change. Originality: Despite the social movement origin of empowerment, the instrumentalist meaning prevails and the discussions have shifted to emphasizing capacity building of individuals in international development cooperation. It is necessary to explore whether these changes have also occurred in the field of adult education, which has traditionally been interested in the issue of power and the liberation of minorities. This process is important because changes in meaning can affect the participants' lifeworld through policy and project implementation. Methodology: Discourse analysis was applied as a research method, and the conceptual discussions of Laclau and Mouffe's discourse theory were used throughout the research process. Discourse analysis was conducted on UNESCO's official published materials related to empowerment and adult education published from 1984 to 2022. Result: From the late 1980s to the mid-1990s, when the radical meaning of empowerment diffused in the field of international development cooperation, the social transformation meaning of empowerment was also emphasized in UNESCO adult education discourse. From the late 1990s to the early 2010s, when the international community's focus on poverty eradication and human development expanded, discussions on empowerment related to expanding individual capacities, choices, and opportunities increased. After the mid-2010s, the era of sustainable development, the empowerment discourse that ordered learners to be competent in global challenges has spread. Conclusion and Implication: Empowerment has been a floating signifier that flowed without a fixed meaning in UNESCO adult education discourse, and the equivalent relationship of identities constituting the discourse has also changed from time to time. However, since the concept of empowerment with social transformation meaning is still important in the practice of international development cooperation, this study proposed responses in two directions. First, efforts are made to reconstruct the equivalent relationship of identities that creates the discourse of empowerment. Second, the discovery of alternative terms reveals the critical problem consciousness raised by empowerment, which paid attention to the crisis of inequality and the problem of power distribution.

Downpour dynamics: outsized impacts of storm events on unprocessed atmospheric nitrate export in an urban watershed

Abstract. Water quality impacts of stream water nitrate (NO3-) on downstream ecosystems are largely determined by the load of NO3- from the watershed to surface waters. The largest NO3- loads often occur during storm events, but it is unclear how loads of different NO3- sources change during storm events relative to baseflow or how watershed attributes might affect source export. To assess the role of storm flow and baseflow in NO3- source export and how these roles are modulated by hydrologic effects of land-use practices, we measured nitrogen (δ15N) and oxygen (Δ17O) isotopes of NO3- and oxygen isotopes (δ18O) of water in rainfall and stream water samples from before, during, and after eight storm events across 14 months in two Chesapeake Bay watersheds of contrasting land use. Storms had a disproportionately large influence on the export of unprocessed atmospheric NO3- (NO3Atm-) and a disproportionately small influence on the export of terrestrial NO3- (NO3Terr-) relative to baseflow in the developed urban watershed. In contrast, baseflow and storm flow had similar influences on NO3Atm- and NO3Terr- export in the mixed agricultural–forested watershed. An equivalent relationship between NO3Atm- deposition on impervious surfaces and event NO3Atm- stream water export in the urban watershed suggests that impervious surfaces that hydrologically connect runoff to channels likely facilitate the export of NO3Atm- during rainfall events. Additionally, larger rainfall events were more effective at exporting NO3Atm- in the urban watershed, with increased rainfall depth resulting in a greater fraction of event NO3Atm- deposition exported. Considering both projected increases in precipitation amounts and intensity and urban/suburban sprawl in many regions of the world, best management practices that reduce the hydrologic connectivity of impervious surfaces will likely help to mitigate the impact of storm events on NO3Atm- export from developed watersheds.