Cohen Model Research Articles

Borel conjecture for the Marczewski ideal

We show in ZFC that there is no set of reals of size continuum which can be translated away from every set in the Marczewski ideal. We also show that in the Cohen model, every set with this property is countable.

Quantitative analysis of the micromechanical behavior and work hardening in Fe-0.1C–10Mn steel via in-situ high-energy X-ray diffraction

In the current work, the micromechanical behavior and work hardening behavior of Fe-0.1C–10Mn (in wt.%) steel deformed at 100, 63, 25 and −50 °C were investigated via in-situ high-energy X-ray diffraction (HE-XRD) technique. As the deformation temperature decreased, the yield strength (YS) and ultimate tensile strength (UTS) increased, while the total elongation (TE) reached a maximum value at 25 °C. The transformation kinetics of retained austenite (RA) was fitted by the Olson and Cohen (OC) model. The phase stress and flow stress contributed by the constituent phases were obtained based on the lattice strain and the volume fraction of the corresponding phase. The work hardening rate was decomposed into four contributors related to the TRIP effect and load partitioning, ie., the austenite phase stress, load partitioning between austenite and martensite, martensitic formation rate and load partitioning between ferrite and austenite. The influence of each contributor on the work hardening behavior was quantitatively evaluated and stacked, the stacked results agreed reasonably well with the experimental work hardening rate obtained from the true stress-strain curve. Finally, the volume fraction of austenite to martensite transformation promoted by the Lüders band (LB) and the stacking fault energy (SFE) of RA were found to be highly temperature-dependent. A linear relationship was revealed between the volume fraction of austenite to martensite transformation during the LB propagation and the SFE of RA. These findings offer insights into the TRIP effect and the LB propagation in medium-Mn steels.

The modified Swift constitutive model of 304L stainless steel at the cryogenic temperature based on the Olson–Cohen model

The nonlinear behavior of austenitic stainless steel (ASS) is significantly affected by the temperature and strain during plastic deformation. However, the conventional constitutive model is often inadequate to accurately describe its mechanical properties, particularly at cryogenic temperatures. Therefore, the development of a constitutive model for ASS at cryogenic temperatures is of paramount importance in order to fully understanding the performance of liquefied natural gas (LNG) membrane tank structures under such conditions. In this study, we have derived a modified constitutive model using 304L stainless steel that incorporates a phase transition model through theoretical derivations. First, the stress and strain data for 304L stainless steel within the range of 108–293 K have obtained from quasi-static tensile experiments. Subsequently, the XRD test results are utilized to calculate the volume fraction of martensite across various temperatures and strains. Next, a modified constitutive model is proposed by combining the Olson–Cohen phase transition model and the Swift constitutive model. Finally, the accuracy of the modified Swift constitutive model is verified through experimental data. The results demonstrate that the modified Swift constitutive model is precise for characterizing the properties of 304L stainless steel across a wide range of temperatures. Furthermore, multiple case studies have proven the feasibility of using the modified Swift constitutive model to predict the properties of various austenitic materials. By incorporating the Olson-Cohen phase transition model, the modified Swift constitutive model showcases its wide applicability and potential in designing and assessing the safety of ASS structures.

Filter‐Menger set of reals in Cohen extensions

AbstractWe prove that for every ultrafilter on there exists a filter on which is ‐Menger and . We show that in the Cohen model there exists such which are tall by using a construction of Nyikos's [10]. These answer a question of Das [2, Problem 7]. We prove that there is a Menger filter of character that is not Hurewicz in the ‐Cohen model where is uncountable regular. This shows that the positive answer to a question of Hernández‐Gutiérrez and Szeptycki [3, Question 2.8] is consistent with . We also study the filter generated by the set of mutually Cohen reals in the ‐Cohen model. We prove that and and every ‐dominating family in the ground model is ‐unbounded in extension. Two questions are posed.

Developing a fall prevention program in an inpatient spinal cord injury rehabilitation unit: A participatory action research study.

Spinal cord injury is a lifelong disability necessitating early management of falls during inpatient admissions. However, there is a paucity of research on fall prevention and management in Spinal cord injury rehabilitation. This study aimed at developing a fall prevention program in an inpatient rehabilitation Spinal cord injury unit. A participatory action research approach utilizing a before-and-after, mixed-method design was employed for this study. The study was performed at Rofaydeh Rehabilitation Hospital in Tehran, Iran, from 2021 to 2022. the study implemented Cohen's four-stage model, encompassing the design of a change program, action, observation and evaluation, and feedback stages. A purposeful sampling method was utilized to select 19 nurses and members of the rehabilitation team from the hospital, ensuring maximum diversity. Data collection involved semi-structured interviews, focus groups, and a checklist for fall prevention measures. Qualitative content analysis, alongside descriptive (frequency, mean, and standard deviation) and inferential statistics (paired t-tests and Chi-square tests), were employed for data analysis. The study adhered to COREQ guidelines. Falls were most common among patients aged fifty years or older (P = 0.026). Throughout the study period, men were more likely to experience falls than women (P = 0.01). Preventive interventions have led to significant improvements in indicators of patient monitoring and care, patient education, and environmental safety, as demonstrated by a paired-sample t-test (P<0.001). Moreover, factors contributing to patients' falls included "shortcomings in fall prevention policies" and "lack of knowledge and participation among patients and caregivers." Changes implemented in the Spinal Cord Injury unit involved enhancing interprofessional interactions, conducting educational workshops for patients and their companions, and identifying high-risk patients. These findings indicate a significant decrease in the incidence of falls following the intervention (P = 0.02). The study found that a multifaceted intervention can increase knowledge about fall risks and substantially reduce both falls and associated minor injuries.

A property of forcing notions and preservation of cardinal invariants

AbstractWe define a property of forcing notions and show that there exists a model of its forcing axiom and the negation of the continuum hypothesis in which the Cichoń‐Blass diagram of cardinal invariants is the same as in the Cohen model. As a corollary, its forcing axiom and the forcing axiom for σ‐centered forcing notions are independent of each other.

Can you take Akemann–Weaver's [formula omitted] away?

By Glimm's dichotomy, a separable, simple C⁎-algebra has continuum many unitarily inequivalent irreducible representations if, and only if, it is non-type I while all of its irreducible representations are unitarily equivalent if, and only if, it is type I. Naimark asked whether the latter equivalence holds for all C⁎-algebras.In 2004, Akemann and Weaver gave a negative answer to Naimark's problem using Jensen's Diamond Principle ⋄ℵ1, a powerful diagonalization principle that implies the Continuum Hypothesis (CH). By a result of Rosenberg, a separably represented, simple C⁎-algebra with a unique irreducible representation is necessarily of type I. We show that this result is sharp by constructing an example of a separably represented, simple C⁎-algebra that has exactly two inequivalent irreducible representations, and therefore does not satisfy the conclusion of Glimm's dichotomy. Our construction uses a weakening of Jensen's ⋄ℵ1, denoted ⋄Cohen, that holds in the original Cohen's model for the negation of CH. We also prove that ⋄Cohen suffices to give a negative answer to Naimark's problem. Our main technical tool is a forcing notion that generically adds an automorphism of a given C⁎-algebra with a prescribed action on its space of pure states.

Pengaruh Environmental Policy, Environmental Pollution, Environmental Energy, Dan Environmental Financial Terhadap Kualitas Laba

This research is a quantitative research and the aim of this research is to empirically examine the influence of environmental policy, environmental pollution, environmental energy, and environmental finance on earnings quality and profitability, leverage, and company size as control variables. Earnings quality is measured using real earnings management as a measurement.This study uses secondary data, namely non-financial companies listed on the Indonesia Stock Exchange for the period during 2019-2021 . The total sample in this study was 198 samples using the panel data regression analysis method and using data analysis with STATA. The research results show that environmental policy, environmental pollution, environmental energy, and environmental financial no significant effect on earnings quality. But there is a significant and positive effect on the control variables including: profitability, company size and debt ratio on earnings quality. The limitation of this study is that the population is non-financial companies and only measures the disclosure of sustainability reports only from pollution, energy, finance and policy. The practical implication of this research is that the more sustainability report disclosures made by companies, including: policies, pollution, energy and finance, no significant effect on the quality of earnings in companies listed on the IDX, and the increasing profitability, debt ratios and company size, the higher earnings quality, so that investors can consider profitability, company size and debt ratio in investment decisions because one of the considerations of investors is profit. The original value of this research is that this research measures more specific environmental reporting disclosures including: environmental policy, environmental pollution, environmental energy, and environmental financial and earnings quality measurement in this study uses real earnings management with the Cohen and Zarowin (2010) model which is still rarely used.

Base matrices of various heights

AbstractA classical theorem of Balcar, Pelant, and Simon says that there is a base matrix of height ${\mathfrak h}$ , where ${\mathfrak h}$ is the distributivity number of ${\cal P} (\omega ) / {\mathrm {fin}}$ . We show that if the continuum ${\mathfrak c}$ is regular, then there is a base matrix of height ${\mathfrak c}$ , and that there are base matrices of any regular uncountable height $\leq {\mathfrak c}$ in the Cohen and random models. This answers questions of Fischer, Koelbing, and Wohofsky.

Anti-classification results for groups acting freely on the line

We explore countable ordered Archimedean groups from the point of view of descriptive set theory. We introduce the space of Archimedean left-orderings Ar(G) for a given countable group G, and prove that the equivalence relation induced by the natural action of GL2(Q) on Ar(Q2) is not concretely classifiable. Then we analyze the isomorphism relation for countable ordered Archimedean groups, and pin its complexity in terms of the hierarchy of Hjorth, Kechris and Louveau [29]. In particular, we show that its potential class is not Π30. This topological constraint prevents classifying Archimedean groups using countable subsets of reals. We obtain analogous results for the bi-embeddability relation, and we consider similar problems for circularly ordered groups, and o-minimal structures such as ordered divisible Abelian groups, and real closed fields. Our proofs combine classical results on Archimedean groups, the theory of Borel equivalence relations, and analyzing definable sets in the basic Cohen model and other models of Zermelo-Fraenkel set theory without choice.

Identifying high-risk hospitalised chronic kidney disease patient using electronic health records for serious illness conversation

This study aimed to identify risk factors that are associated with increased mortality that could prompt a serious illness conversation (SIC) among patients with chronic kidney disease (CKD). The electronic health records of adult CKD patients admitted between August 2018 and February 2020 were retrospectively reviewed to identify CKD patients with >1 hospitalisation and length of hospital stay ≥4 days. Outcome measures were mortality and the duration of hospitalisation. We also assessed the utility of the Cohen's model to predict 6-month mortality among CKD patients. A total of 442 patients (mean age 68.6 years) with median follow-up of 15.3 months were identified. The mean (standard deviation) Charlson Comorbidity Index [CCI] was 6.8±2.0 with 48.4% on chronic dialysis. The overall mortality rate until August 2020 was 36.7%. Mortality was associated with age (hazard ratio [HR] 1.51, 95% confidence interval [CI] 1.29-1.77), CCI≥7 (1.58, 1.08-2.30), lower serum albumin (1.09, 1.06-1.11), readmission within 30-day (1.96, 1.43-2.68) and CKD non-dialysis (1.52, 1.04-2.17). Subgroup analysis of the patients within first 6-month from index admission revealed longer hospitalisation stay for those who died (CKD-non dialysis: 5.5; CKD-dialysis: 8.0 versus 4 days for those survived, P<0.001). The Cohen's model demonstrated reasonable predictive ability to discriminate 6-month mortality (area under the curve 0.81, 95% CI 0.75-0.87). Only 24 (5.4%) CKD patients completed advanced care planning. CCI, serum albumin and recent hospital readmission could identify CKD patients at higher risk of mortality who could benefit from a serious illness conversation.

SET THEORY AND A MODEL OF THE MIND IN PSYCHOLOGY

AbstractWe investigate the mathematics of a model of the human mind which has been proposed by the psychologist Jens Mammen. Mathematical realizations of this model consists of what the first author (A.T.) has called Mammen spaces, where a Mammen space is a triple $(U,\mathcal S,\mathcal C)$ , where U is a non-empty set (“the universe”), $\mathcal S$ is a perfect Hausdorff topology on U, and $\mathcal C\subseteq \mathcal P(U)$ together with $\mathcal S$ satisfy certain axioms.We refute a conjecture put forward by Hoffmann-Jørgensen, who conjectured that the existence of a “complete” Mammen space implies the Axiom of Choice, by showing that in the first Cohen model, in which ZF holds but AC fails, there is a complete Mammen space. We obtain this by proving that in the first Cohen model, every perfect topology can be extended to a maximal perfect topology.On the other hand, we also show that if all sets are Lebesgue measurable, or all sets are Baire measurable, then there are no complete Mammen spaces with a countable universe.Further, we investigate two new cardinal invariants $\mathfrak u_{M}$ and $\mathfrak u_{T}$ associated with complete Mammen spaces and maximal perfect topologies, and establish some basic inequalities that are provable in ZFC. Then we show $\mathfrak u_{M}=\mathfrak u_{T}=2^{\aleph _{0}}$ follows from Martin’s Axiom, and, contrastingly, we show that $\aleph _{1}=\mathfrak u_{M}=\mathfrak u_{T}&lt;2^{\aleph _{0}}=\aleph _{2}$ in the Baumgartner–Laver model.Finally, consequences for psychology are discussed.

HIGHER DIMENSIONAL CARDINAL CHARACTERISTICS FOR SETS OF FUNCTIONS II

AbstractWe study the values of the higher dimensional cardinal characteristics for sets of functions $f:\omega ^\omega \to \omega ^\omega $ introduced by the second author in [8]. We prove that while the bounding numbers for these cardinals can be strictly less than the continuum, the dominating numbers cannot. We compute the bounding numbers for the higher dimensional relations in many well known models of $\neg \mathsf {CH}$ such as the Cohen, random and Sacks models and, as a byproduct show that, with one exception, for the bounding numbers there are no $\mathsf {ZFC}$ relations between them beyond those in the higher dimensional Cichoń diagram. In the case of the dominating numbers we show that in fact they collapse in the sense that modding out by the ideal does not change their values. Moreover, they are closely related to the dominating numbers $\mathfrak {d}^\lambda _\kappa $ .

Gully erosion and climate induced chemical weathering for vulnerability assessment in sub-tropical environment

Land degradation significantly impacts habitats, agriculture and economy, particularly in regions with high population density. Gully erosion poses one of the major challenges for land degradation despite several conservation measures. Here we present a novel technique of gully erosion susceptibility mapping by employing EBO (Eco-geography based optimization) with its ensembles: Bagging, Dagging, and Decorate. The EBO and its ensembles model were evaluated by various statistical approaches such as SST (sensitivity), PPV (positive predictive values), NPV (negative predictive values), SPF (specificity), ACC (accuracy), RMSE (root mean square error) and Cohen's Kappa model. We measured the morphological characteristics and chemical weathering in addition to gully head cut that is responsible for surface soil erosion where chemical weathering indirectly increases gullying process. The AUC values of EBO (Eco-biogeography-based optimization), EBO-Bagging, EBO-Dagging and EBO-Decorate for training datasets are 0.969, 0.915, 0.954 and 0.920 respectively. The AUC values of EBO, EBO-Bagging, EBO-Dagging and EBO-Decorate for validation datasets are 0.934, 0.901, 0.912 and 0.842 respectively. We apply this technique in the Kangsabati catchment area where we found that the upper part is more vulnerable to gullying leading to land degradation. Truer novel technique would aid in identifying land degradation-prone areas, and in formulating better strategies for better land use.

Deformation mechanism and microstructure evolution of medium-Mn AHSS under various loading conditions

Third-generation advanced high-strength steels possess an exceptional combination of high strength and ductility owing to their high work-hardening rate during deformation. In this study, the mechanical properties and microstructure/texture evolution of medium-Mn steel under various loading conditions (uniaxial tension, in-plane torsion, and equibiaxial tension) were investigated. Interrupted electron back-scattered diffraction and X-ray diffraction characterizations were carried out to track the microstructure and texture evolution of individual phases. Digital image correlation was employed for the in-situ measurement of formation and expansion of deformation bands, i.e., the Lüders and the Portevin-Le Châtelier (PLC) bands. The dynamic strain aging effect in terms of the formation of PLC bands and stress serrations was significantly affected by the loading conditions and stress level. Multiple types of stress serrations were observed in all tested specimens at different deformation stages. The texture evolution of the steel under various deformation modes was further tracked. Ferrite and fresh martensite exhibited the plain texture evolution like most body-centered cubic metals, whereas austenite showed a more complex texture evolution. The martensitic transformation notably decreased the RD||<001> intensity of the austenite; austenite debris was rotated with ferrite grains, while some intact austenite grains self-rotated to a stable orientation, which is unfavorable for martensitic transformation. The obvious intragranular orientation gradient observed in the austenite intact grains implies that considerable deformation occurred in the austenite. Finally, the experimental results indicate that equibiaxial tension primarily promoted the martensitic transformation, and the classical Olson–Cohen model was calibrated to capture the volume fraction evolution of austenite under various stress states.

On the relationship between mutual and tight stationarity

We construct a model where every increasing ω-sequence of regular cardinals carries a mutually stationary sequence which is not tightly stationary, and show that this property is preserved under a class of Prikry-type forcings. Along the way, we give examples in the Cohen and Prikry models of ω-sequences of regular cardinals for which there is a non-tightly stationary sequence of stationary subsets consisting of cofinality ω1 ordinals, and show that such stationary sequences are mutually stationary in the presence of interleaved supercompact cardinals.

Temperature Effects on Tensile Deformation Behavior of a Medium Manganese TRIP Steel and a Quenched and Partitioned Steel

Third-generation advanced high-strength steels (AHSS) containing metastable retained austenite are being developed for the structural components of vehicles to reduce vehicle weight and improve crash performance. The goal of this work was to compare the effect of temperature on austenite stability and tensile mechanical properties of two steels, a quenched and partitioned (Q&amp;P) steel with a martensite and retained austenite microstructure, and a medium manganese transformation-induced plasticity (TRIP) steel with a ferrite and retained austenite microstructure. Quasi-static tensile tests were performed at temperatures between −10 and 85 °C for the Q&amp;P steel (0.28C-2.56Mn-1.56Si in wt.%), and between −10 and 115 °C for the medium manganese TRIP steel (0.14C-7.14Mn-0.23Si in wt.%). X-ray diffraction measurements as a function of strain were performed from interrupted tensile tests at all test temperatures. For the medium manganese TRIP steel, austenite stability increased significantly, serrated flow behavior changed, and tensile strength and elongation changed significantly with increasing temperature. For the Q&amp;P steel, flow stress was mostly insensitive to temperature, uniform elongation decreased with increasing temperature, and austenite stability increased with increasing temperature. The Olson–Cohen model for the austenite-to-martensite transformation as a function of strain showed good agreement for the medium manganese TRIP steel data and fit most of the Q&amp;P steel data above 1% strain.

Strain‐Induced Martensite Formation and Mechanical Properties of Fe–19Cr–4Ni–3Mn–0.15N–0.15C Austenitic Stainless Steel at Cryogenic Temperature

Herein, considerable insight is provided into the evolution of strain‐induced martensite and mechanical properties of Fe–19Cr–4Ni–3Mn–0.15N–0.15C wt% austenitic stainless steel (in short Cr19NC15.15) during deformation at room temperature and cryogenic temperatures. In situ magnetic measurements of the martensite evolution during tensile tests at various temperatures are conducted. The triggering stress required for strain‐induced martensite formation is determined at the minimum in the strain hardening curve. It is found that with reducing deformation temperature in the range from 0 to –20 °C slightly decreases, whereas the triggering stress increases with further reduction of deformation temperature to −70 °C. The relation between the formed α′‐martensite fraction and the strain applied during tensile test is established. The results demonstrate that a reduced deformation temperature from room temperature (RT) to −70 °C significantly enhances the transformation rate and the total volume fraction of strain‐induced α′‐martensite. The yield and tensile strength increase whereas elongation continuously decreases due to an increasing α′‐martensite volume fraction with decreasing tensile test temperature. The α′‐martensite formation kinetic follows Olson and Cohen's model and are in good agreement between the in situ experiment and theoretical calculations.

The Practice of Christians' Spiritual Faith Viewed from Tourism in the Holy Land Israel

Recently, lots of people are talking about visiting the Holy Land — Israel especially those who believe in Jesus Christ. In this paper, I will qualitatively review the historical background of the Holy Land, introduce why people like to visit Israel (reasons) together with the religious-cultural affairs of Jews. Indeed, there are five types of travelling: (1) leisure travel; (2) pilgrimage travel; (3) experiential travel; (4) diversionary mode; (5) experimental model. I will discuss these visiting mode. In the research methodology, I will look into the web statistical survey (102 interviewees), documentary analysis of churches’ Israel visiting etc. Then I will qualitatively analyse those barriers that affect a Christian’s decision making to visit Holy Land Israel. One of the main focus is the relationship between faith and the Middle-East security risk problem between Islamic countries and Jewish Israel. Then we shall connect such faith-security barrier to the result of discovering the new Christian typology of Israel travellers — a mixed type of curiosity, depression (or anxiety) and pilgrimage that disproof Erik Cohen's travelling model. How the spiritual faith does overcome the security anxiety and hence create the corresponding experience. Thus, the motives of this type of Christian’s Israel travelling decision is because of curiosity such as they want to find the root of Christianity, daily depression like the concern about Israel-Islamic conflicts and pilgrimage from the spiritual faith practice. Hence, we may further deduce the role of faith that plays in their final decision outcome. This event will then lead to the Christians’ Israel visiting and tailor-made the respective afterwards spiritual revival follow-up scheme for such new typology discovered. Lastly, we may empirically deduce the wanted Markov Decision Process Model and prepare for the future prediction in the higher doctoral degree study.

On $\mathbb R$-embeddability of almost disjoint families and Akemann–Doner C$^*$-algebras

An almost disjoint family $\mathcal A$ of subsets of $\mathbb N$ is said to be $\mathbb R$-embeddable if there is a function $f:\mathbb N\rightarrow \mathbb R$ such that the sets $f[A]$ are ranges of real sequences converging to distinct reals for distinct $A\in \mathcal A$. It is well known that almost disjoint families which have few separations, such as Luzin families, are not $\mathbb R$-embeddable. We study extraction principles related to $\mathbb R$-embeddability and separation properties of almost disjoint families of $\mathbb N$ as well as their limitations. An extraction principle whose consistency is our main result is: every almost disjoint family of size continuum contains an $\mathbb R$-embeddable subfamily of size continuum. It is true in the Sacks model. The Cohen model serves to show that the above principle does not follow from the fact that every almost disjoint family of size continuum has two separated subfamilies of size continuum. We also construct in ZFC an almost disjoint family, where no two uncountable subfamilies can be separated but always a countable subfamily can be separated from any disjoint subfamily. Using a refinement of the $\mathbb R$-embeddability property called a controlled $\mathbb R$-embedding property we obtain the following results concerning Akemann-Doner C*-algebras which are induced by uncountable almost disjoint families: a) In ZFC there are Akemann-Doner C*-algebras of density $\mathfrak c$ with no commutative subalgebras of density $\mathfrak c$, b) It is independent from ZFC whether there is an Akemann-Doner algebra of density $\mathfrak c$ with no nonseparable commutative subalgebra. This completes an earlier result that there is in ZFC an Akemann-Doner algebra of density $\omega_1$ with no nonseparable commutative subalgebra.