Equivalent Conditions Research Articles

Investigation of microstructure evolution and its effect mechanism on high temperature tensile properties of 304L stainless steel processed by laser powder bed fusion

Laser Powder Bed Fusion (LPBF) 304L stainless steel has garnered significant attention due to its unique blend of strength and ductility at room temperature. However, there is limited understanding of its high-temperature tensile properties. In this study, we conducted tensile testing on LPBF 304L at temperatures ranging from 623K to 1023K in its as-built state. Additionally, we performed a comparative tensile test on traditionally hot-rolled (at 1433K) 304L stainless steel under equivalent test conditions. The results revealed that LPBF 304L steel exhibited high ductility at 973K (ultimate tensile stress (UTS) is 257.3 ± 3.6 MPa)-1023K (UTS is 218.7 ± 3.8 MPa), but its strength (yield strength (YS) decreased from 346.0 ± 4.5 MPa to 182.7 ± 3.8 MPa) and plasticity (UTS decreased from 405.7 ± 5.3 MPa to 218.7 ± 6.4 MPa) decreased slowly as the testing temperature increases. We also delved into the microstructure and its impact on high-temperature tensile deformation. The fine grains and ensuing dynamic recovery were found to be responsible for the reduced strength and ductility of LPBFed 304L samples at elevated temperatures. Furthermore, a sawtooth fluctuation emerged in the stress-strain curve at 873K, which could be attributed to dynamic strain aging (DSA) and the interaction between solute elements and dislocations.

N-prime elements and the primality of x − α in D⟦x⟧

Let D be an integral domain and D [ ​ [ x ] ​ ] be the power series ring over D. In this paper, we study the primality of x − α in D [ ​ [ x ] ​ ] , where α ∈ D . For this purpose, we generalize the definition of a prime element as follows. For a positive integer N, a nonzero nonunit α ∈ D is called an N-prime element if for any a , b ∈ D , α N | ab implies α | a or α | b . We prove that if α is an N-prime element for some N, then x − α is a prime element in D [ ​ [ x ] ​ ] . Surprisingly, it is shown that the converse also holds when D is a PID, a valuation domain, or a Dedekind domain. In other words, when D is a PID, a valuation domain, or a Dedekind domain, a necessary and sufficient condition for x − α to be a prime element in D [ ​ [ x ] ​ ] is α is an N-prime element in D for some N. This however does not hold for other types of integral domains such as UFDs or Krull domains. We also investigate the N-prime property in an arbitrary integral domain and give other (equivalent) conditions for an element α in the aforementioned types of integral domains to be an N-prime element.

An improvement and a generalization of Rotfel'd type inequalities for sectorial matrices

By using equivalence conditions for sectorial matrices obtained by Alakhrass and Sababheh in Linear Algebra Appl. (2020;586), we improve a Rotfel'd type inequality for sectorial matrices derived by Zhang in Linear Multilinear Algebra (2015;63) and generalize a recent result of Mao and Ji in Linear Algebra Appl. (2024;691).

On dense, locally finite subgroups of the automorphism group of certain homogeneous structures

AbstractLet be a countable structure such that each finite partial isomorphism of it can be extended to an automorphism. Evans asked if the age (set of finite substructures) of satisfies Hrushovski's extension property, then is it true that the automorphism group of contains a dense, locally finite subgroup? In order to investigate this question, in the previous decades a coherent variant of Hrushovski's extension property has been introduced and studied. Among other results, we provide equivalent conditions for the existence of a dense, locally finite subgroup of in terms of a (new) variant of the coherent extension property. We also compare our notion with other coherent extension properties.

Necessary and Sufficient Conditions for State Feedback Equivalence to Negative Imaginary Systems

Necessary and Sufficient Conditions for State Feedback Equivalence to Negative Imaginary Systems

The Intrinsic Characterization of a Fuzzy Consistently Connected Domain

The concepts of a fuzzy connected set (fc set) and a fuzzy consistently connected set (fcc set) are introduced on fuzzy posets, along with a discussion of their basic properties. Inspired by some equivalent conditions of crisp connected sets, the characterizations of the fc sets are given, and we also explore fuzzy completeness and fuzzy compactness in addition to defining a new fuzzy way-below relation based on fcc complete sets. Using this relationship as a basis, the fcc domain is also provided and studied, and its equivalent characterizations are obtained. In summary, we develop a method to establish fcc completeness from a continuous poset.

A Novel Construction of the g-Riesz Decomposition in Hilbert Spaces

The concept of the g-frame, a generalized frame in Hilbert spaces, has garnered attention in recent research. While numerous properties of g-frames have been explored, certain aspects remain unexamined, including a novel construction approach for the g-Riesz decomposition in Hilbert spaces. While prior works such as [12] presented the equivalence conditions for g-Riesz decomposition and Khosravi [10] proposed a new construction method for g-frames, neither addressed a new construction method for g-Riesz decomposition. This paper aims to fill this gap by investigating a novel construction method for the specialized g-frame-g-Riesz decomposition. Leveraging operator theory from generalized functional analysis and function space techniques in complex Hilbert spaces, we establish necessary and sufficient conditions for constructing g-Riesz decompositions, an area insufficiently explored by Khosravi and [12]. Furthermore, we introduce two annotations and provide proofs demonstrating that g-Riesz bases are equivalent to Riesz bases, aligning with the findings of W.C. Sun in [6]. This underscores the significance of our research. The newly proposed g-Riesz decomposition not only contributes to mathematical inquiry but also holds promise for various applications, particularly in signal and image processing.

Quantitative Single‐Cell Comparison of Sensitization to Radiation and a Radiomimetic Drug for Diverse Gold Nanoparticle Coatings

Metal‐based nanoparticles (NPs) have entered clinical use for enhancing radiotherapy, but the underlying mechanisms remain ambiguous. Herein, single‐cell analysis of two cell lines in response to megavolt irradiation and a radiomimetic drug, neocarzinostatin (NCS) after coculture with gold NPs with different surface coatings, polyethylene glycol (AuPEG), PEG, and transferrin (AuT) or silica (AuSiO2), is reported. Different surface chemistry presents a major challenge for objective comparison between the biological impacts where major differences in cell‐uptake exist. AuSiO2 NPs are the most efficient for promoting radiosensitization despite being associated with cells 10 times less than the actively targeted AuT NPs. Conversely, for cells exposed to NCS, AuSiO2 NPs impede the radiomimetic action and promote cell survival. AuT NPs enhance death of cells in combination with NCS showing that NPs can sensitize against cytotoxic agents in addition to radiation. While NPs contribute to radiosensitization (or enhancing/impeding chemotherapeutic drug activity), due to cell and cell line heterogeneity, the ultimate radiosensitivity of a cell appears to be dominated by its inherent radiosensitivity and how this cell‐regulated response is manipulated by NPs. This is evidenced through comparison of radiobiological response of cells with equivalent NP association rather than equivalent coculture conditions.

A randomised controlled trial of the Learning Skills Together (LST) intervention to improve dementia family caregivers’ self-efficacy with complex care

BackgroundNearly two-thirds of family caregivers of persons living with Alzheimer’s disease or related dementias (AD/ADRD) provide complex care, including medical care. Family caregivers typically receive little to no training on how to provide this care. Furthermore, family caregivers simultaneously grapple with the presence of behavioral and psychological symptoms of dementia (BPSD), diminished communication abilities, and comorbidities such as diabetes. We developed Learning Skills Together (LST), a 6-week digitally delivered psychoeducational program, to facilitate family caregiver abilities to administer complex care tasks. The goal of the present study is to test the efficacy of LST and to reduce adverse outcomes associated with caregiving, such as depressive symptomology and negative appraisal of BPSD.MethodsTo test the efficacy of LST, we will conduct a two-arm single-site randomized controlled trial (RCT) with N = 200 family caregivers of persons living with AD/ADRD. Eligible family caregivers will be randomly assigned to participate in either the LST intervention or a structurally equivalent control condition focused on healthy living. All family caregivers will complete four surveys, including a baseline survey administered prior to randomization, a post-intervention survey, and a 3- and 6-month follow-up survey to assess change in study outcomes. Between-group comparisons of each outcome will be evaluated using generalized estimating equation models. Mediation analyses will assess family caregiver self-efficacy as the intervention’s mechanism of change in depressive symptomology and BPSD. We will also examine caregiver race, ethnicity, and gender as effect modifiers of the intervention.DiscussionLST findings will inform the field of AD/ADRD and caregiving regarding optimally supporting family caregivers in managing complex care tasks. If efficacious, the LST intervention will support family caregivers in preserving their own mental health while providing complex care.Trial registrationClinical Trials.gov NCT05846984. This study was registered on May 6, 2023.

Fourier coefficients of Jacobi forms of real weights

Let [Formula: see text] and [Formula: see text] be positive integers and [Formula: see text] be a negative real number. Let [Formula: see text] be a multiplier system of weight [Formula: see text] on [Formula: see text]. In this paper, we give an exact formula for the Fourier coefficients of the holomorphic part of a harmonic Maass–Jacobi form of weight [Formula: see text], index [Formula: see text], and multiplier system [Formula: see text] on [Formula: see text]. As an application, we investigate the number of ratios of the Fourier coefficients of the holomorphic parts of two harmonic Maass–Jacobi forms. Moreover, we obtain the equivalent conditions for the principal part of a harmonic Maass–Jacobi form to be the principal part of a weak Jacobi form with poles only at infinity.

Optimal fuzzy event-triggered fault-tolerant control of fractional-order nonlinear stochastic systems

This paper considers the optimal fuzzy fault-tolerant control issue for fractional-order nonlinear stochastic systems (FONSS) using event-triggered mechanisms with fractional-order derivative α∈(0,1). First, in order to weaken the impacts of actuator and sensor faults, a fuzzy observer and augmented system are developed. Since stochastic disturbance can adversely affect stability, based on fractional Barbalat lemmas and Lyapunov theory, an adaptive fault-tolerant controller and the corresponding adaptive update law are designed to ensure the stability of FONSS. Then, the architecture of identifier-critic-actor NN, which is more concise than the traditional one, is described. This NN architecture recognizes unknown dynamics and completes control actions after evaluating the control performance, driving control toward optimization. Furthermore, the event-triggered mechanism is devised to save control resources and avoid Zeno behavior. Finally, simulation results demonstrate that under equivalent conditions, the proposed optimal event-triggered control reduces the number of information transmissions compared to traditional time-triggered control, saving communication resources and enhancing the overall control performance.

Full time-dependent SOLPS-ITER simulation of the SPARC tokamak: actuator design for particle and divertor condition control *

This paper presents the application of full time-dependent SOLPS-ITER simulations for actuator design in the SPARC tokamak. This study employs both the EIRENE module, a neutral solver, and the B2.5 plasma module in a time-dependent mode. This is in contrast to most SOLPS simulations, which focus on steady-state solutions, where the neutral distribution is evolved without any time limit or for a time step of 1 ⋅10−3 second, which is several orders of magnitude larger than the fluid plasma time step. The time-dependent EIRENE was tested with a fixed B2.5 background and compared with a simple conductance based model in a simplified pump chamber geometry. This comparison aimed to verify the reliability of the neutral relaxation timescale derived from the time-dependent EIRENE. Subsequently, a full time-dependent simulation was performed in a realistic geometry, with the Monte-Carlo neutral time step synchronized with the plasma fluid time step. The numerical setup of the code, including relative time steps and the size of the census data used to store Monte-Carlo particle information is considered. The full-time dependent simulations are then applied to inform the design of the SPARC louver structure, which affects divertor plasma parameters by regulating the neutral conductance from the divertor to the pump. The response of the plasma and neutral parameters was captured on a timescale that enables the design of the actuator to consider time-dependent control capability. It was found that changing the louver opacity has an equivalent effect as varying the gas throughput via puff actuation. Therefore, equivalent divertor plasma conditions can be obtained from both actuators, while the neutral pressure distribution in the pump and divertor differs for each actuator.

A strong subadditivity‐like inequality for quantum entropy in semifinite von Neumann algebras

AbstractLet be a semifinite von Neumann algebra with a normal faithful semifinite trace , and let , , be its subalgebras such that and that restricted to any of these subalgebras is semifinite. Denote by , , and the normal conditional expectations from onto , and , respectively, such that is invariant with respect to any of them. The quadruple , , , is said to be a commuting square if In this note, we show that the property of being a commuting square is characterized by a sort of the SSA‐like (strong subadditivity of entropy) inequality for an arbitrary normal state on , where denotes the Segal entropy of the state . The situation when we have equality in the inequality above is also investigated, and various equivalent conditions are obtained, in an especially appealing form for finite von Neumann algebras. For such algebras, one more condition is obtained under the assumption of independence of the algebras and .

Numerical investigation of the influence of different barrel lengths on the interior ballistic process within an underwater submerged launch

Although underwater submerged launching has been rigorously investigated for decades, there remains a dearth of comprehensive understanding regarding the underwater interior ballistic characteristics for varying barrel lengths. To address this knowledge gap, the present study aims to explore, via numerical simulations, the initial velocity of interior ballistics, projectile drag, and the mechanism of initial flow field formation at the muzzle under various barrel lengths, thereby considering the influence of differing barrel lengths. The five distinct lengths of barrels are expressed as dimensionless ratios of the weight of water column in front of the projectile to the weight of the projectile in order to be more general. Five different ratios of water-to-projectile weight are investigated: 1.0, 1.2, 1.5, 1.8, and 2.0, all possessing identical diameters and evaluated under equivalent launch conditions. Different ratios significantly impact muzzle velocity, with shorter barrels yielding higher muzzle velocities, while ensuring complete propellant combustion. Further investigations indicate that variations in drag constitute the fundamental cause of initial velocity changes. Furthermore, it is observed that barrels of different lengths exhibit identical characteristics at the point of maximum drag. The initial flow field at the muzzle exhibits considerable variations in terms of length, profile dimensions, and intensity. The findings of this study offer valuable insights into exploring the mechanism of submerged launching and will be utilized to investigate the optimal barrel length.

Mechanism study on the control of cloud cavitation by leading-edge tubercles on NACA0015

Abstract In order to control cloud cavitation, the bio-inspired leading-edge tubercles are implemented on a NACA0015 hydrofoil. The cavitation experiments in a water tunnel are conducted to elaborate on the dynamic behaviors and control mechanisms. As observed, the cavitation with a mean length of 0.38 times chord length on baseline hydrofoil performs three-dimensional features and multiple shedding by the re-entrant jet impingements. Under the equivalent cavitation condition on LET hydrofoil, the cavities with a frothy appearance are produced and confined within the troughs, and the large-scale shedding and re-entrant jet are not identified. The proper orthogonal decomposition (POD) based on cavitation images is carried out to extract the dominant shedding structures. The leading modes of POD on baseline hydrofoil dictate the main shedding of cloud cavitation. The lateral cavities on the LET hydrofoil are well separated by the spanwise periodic tubercles and then the dominant POD modes appear as small-scale vortex pairs. The leading-edge tubercles could depress the three-dimensional cloud cavitation and the re-entrant jets, which is a promising method to control cavitation unsteadiness in hydraulic machinery.

Utilizing phased array ultrasound technique to examine seal surface contact status in premium connections

Premium connections are commonly employed in wells subjected to high temperature and high pressure (HTHP) conditions. The key parameter in evaluating the sealing capability of premium connections is the contact condition between the sealing surface. This paper presents a method based on phased array ultrasound testing (PAUT) technique to examine the metal-to-metal contact states of the seal surface in premium conditions, and presents experimental work on contact status of the seal surface in premium tubing connections using PAUT, testing impacts of torque, seal surface defects and thread compounds dosage. The experimental findings demonstrate an inverse relationship between the observed ultrasonic reflection amplitude and the applied torque on the premium. Additionally, there is a robust exponential correlation manifested between the ultrasonic reflection amplitude and the torque exerted on the premium. The ultrasonic reflection amplitude at the defect of the seal surface increases. Under equivalent make-up torque conditions, the ultrasonic reflection amplitude on the sealing surface of premium connections escalates as the dosage of thread compounds diminishes, and the importance of precise control of the amount of thread compound used was confirmed. These data demonstrate that PAUT provides a reliable detection technique for performance assessment on premium connections, both in quality control and field inspection.

Legal fuzzy incidence blocks and legal flow reduction sets with application to water distribution networks

Directed fuzzy incidence graphs (DFIGs) are fuzzy incidence structures where each edge and incidence pair has a specific direction. In these graphs, the relationships are not symmetric, making it easier to identify the extent of interaction between nodes and arcs. The comprehensive investigation of connectivity in directed fuzzy incidence graphs holds the potential to provide solutions for a wide range of real-world problems including traffic flow optimization in one-way traffic networks and migration analysis of refugees across various countries. The main objective of this paper is to extend the connectivity concepts of directed fuzzy incidence graphs, which help to analyze various stochastic networks influenced by external factors. The major concepts discussed in this article are legal fuzzy incidence blocks, legal flow reduction sets, and the DFIG-version of Menger's theorem. Directed fuzzy incidence graphs having no legal flow reduction nodes are defined as legal fuzzy incidence blocks (LFI-blocks). Legal flow reduction nodes (LFR-nodes) are distinct elements, the elimination of which results in a reduction of the directed incidence connectivity between some other pair of nodes. Since LFI-blocks lack these elements, the removal of none of the nodes reduce the legal flow between other pair of nodes. Consequently, for each node under consideration, any other pair of nodes connected by at least one di-path must possess a widest legal di-path which avoids that specific node. LFI-blocks exhibit differing attributes in contrast to their counterparts in fuzzy graphs and fuzzy incidence graphs. This viewpoint motivated the authors to investigate these distinctions and assess the possibility of defining equivalent conditions for LFI-blocks, similar to the equivalent conditions established for fuzzy blocks and fuzzy incidence blocks. A key characteristic of legal fuzzy incidence blocks is their capacity to incorporate legal flow reduction links, even allowing for the presence of shared nodes among two legal flow reduction links. This contrasts with fuzzy graphs and fuzzy incidence graphs, where if two fuzzy bridges happen to share a common node, it results in that node being a fuzzy cutnode. Two equivalent conditions are proposed for a directed fuzzy incidence graph to become a legal fuzzy incidence block. It is shown that any two nodes in a legal fuzzy incidence block which are connected by at least one di-path, but not by a legal flow reduction link will have at least two internally disjoint widest legal di-paths joining them. To identify the maximum number of such internally disjoint widest legal di-paths, the notion of legal flow reduction set of nodes and arcs is introduced. These sets are characterized using widest legal di-paths. Moreover, the DFIG-version of Menger's theorem for nodes is established, which explains the relation between number of internally disjoint widest legal di-paths and cardinality of legal flow reduction sets in a directed fuzzy incidence graph. Also, an illustration of Menger's theorem is proposed for water distribution networks.

Quantum barriers engineering toward radiative and stable perovskite photovoltaic devices

Efficient photovoltaic devices must be efficient light emitters to reach the thermodynamic efficiency limit. Here, we present a promising prospect of perovskite photovoltaics as bright emitters by harnessing the significant benefits of photon recycling, which can be practically achieved by suppressing interfacial quenching. We have achieved radiative and stable perovskite photovoltaic devices by the design of a multiple quantum well structure with long (∼3 nm) organic spacers with oleylammonium molecules at perovskite top interfaces. Our L-site exchange process (L: barrier molecule cation) enables the formation of stable interfacial structures with moderate conductivity despite the thick barriers. Compared to popular short (∼1 nm) Ls, our approach results in enhanced radiation efficiency through the recursive process of photon recycling. This leads to the realization of radiative perovskite photovoltaics with both high photovoltaic efficiency (in-lab 26.0%, certified to 25.2%) and electroluminescence quantum efficiency (19.7 % at peak, 17.8% at 1-sun equivalent condition). Furthermore, the stable crystallinity of oleylammonium-based quantum wells enables our devices to maintain high efficiencies for over 1000 h of operation and >2 years of storage.

A randomised controlled trial of the Learning Skills Together (LST) intervention to improve dementia family caregivers' self-efficacy with complex care.

Background Nearly two-thirds of family caregivers of persons living with Alzheimer's disease or related dementias (AD/ADRD) provide complex care, including medical care. Family caregivers typically receive little to no training on how to provide this care. Furthermore, family caregivers simultaneously grapple with the presence of behavioral and psychological symptoms of dementia (BPSD), diminished communication abilities, and comorbidities such as diabetes. We developed Learning Skills Together ( LST ), a six-week digitally delivered psychoeducational program, to facilitate family caregiver abilities to administer complex care tasks. The goal of the present study is to test the efficacy of LST and to reduce adverse outcomes associated with caregiving, such as depressive symptomology and negative appraisal of BPSD. Methods To test the efficacy of LST , we will conduct a two-arm single-site randomised controlled trial (RCT) with N = 200 family caregivers of persons living with AD/ADRD. Eligible family caregivers will be randomly assigned to participate in either the LST intervention or a structurally equivalent control condition focused on healthy living. All family caregivers will complete four surveys, including a baseline survey administered prior to randomisation, a post-intervention survey, and a three- and six-month follow-up survey to assess change in study outcomes. Between-group comparisons of each outcome will be evaluated using generalized estimating equation models. Mediation analyses will assess family caregiver self-efficacy as the intervention's mechanism of change in depressive symptomology and BPSD. We will also examine caregiver race, ethnicity, and gender as effect modifiers of the intervention. Discussion LST findings will inform the field of AD/ADRD and caregiving regarding optimally supporting family caregivers in managing complex care tasks. If efficacious, the LST intervention will support family caregivers in preserving their own mental health while providing complex care. Trial registration This study was registered on Clinical Trials.gov on May 6, 2023 (NCT05846984). https://clinicaltrials.gov/study/NCT05846984?cond=learning%20skills%20together&rank=2.

On $G$-$(n,d)$-rings and $n$-coherent rings

Let $n$ and $d$ be non-negative integers. We introduce the concept of $strongly$ $(n,d)$-$injective$ modules to characterize $n$-coherent rings. For a right perfect ring $R$, it is shown that $R$ is right $n$-coherent if and only if every right $R$-module has a strongly $(n,d)$-injective (pre)cover for some non-negative integer $d \leq n$. We also provide equivalent conditions for an $(n,d)$-ring being $n$-coherent. Then we investigate the so-called $right$ $G$-$(n,d)$-$rings$, over which every $n$-presented right module has Gorenstein projective dimension at most $d$. Finally, we prove a Gorenstein analogue of Costa's first conjecture.