Theoretical Conditions Research Articles

New method to predict porosity loss during sandstone compaction based on packing texture

The grain packing texture of underground sandstone tends to be a major controlling factor in porosity loss during compaction when the effective stress and buried depth increase. However, existing models used to predict porosity loss during sandstone compaction mostly disregard the grain packing texture of sandstone. Based on the micromechanical parameters of discrete element method (DEM) numerical simulation reported in literature, we designed one-component, binary, and ternary packing textures with different grain size distributions and subsequently performed compaction under triaxial servo simulation. We monitored the porosity loss, grain displacement, and force acting on the grain contact point during compaction. Based on the packing texture in sandstone, we propose a new method that considers varying grain sizes, grain size contents, and packing texture types to determine porosity loss during compaction without grain crushing and plastic deformation. The applicability of the method under theoretical conditions was evaluated with 5, 31, and 53 types of one-component, binary, and ternary packing textures. The correlation coefficient between the predicted and simulated values of the void ratio change (△e) was 0.999 and 0.985 for the binary and ternary packing textures, respectively. The reliability of the proposed method was verified using nine groups of physical experimental data derived from literature. The results showed a correlation coefficient of 0.88 between the measured and predicted values of △e and porosity loss (△ϕ). Errors in physical experimental data were derived mainly from grain shape and the crushing of coarse grains. Although the predicted physical experimental data △e and △ϕ were inferior to DEM simulation data, our model was deemed reliable since it showed high correlation between predicted and measured values of △e and △ϕ. Furthermore, the proposed method characterized the influence of the micromechanical process of grain rotation and grain packing texture on reservoir quality during compaction, thereby establishing its importance in predicting reservoir quality of underground sandstone.

Quality of the strain state in simple shear testing using field measurement techniques

Shear testing holds a peculiar place in sheet metal characterization for multiple reasons. Indeed, as opposed to tension or bi-axial expansion, the principal strains of such a deformation change their direction, non-linearly, as a test proceeds. It is, in general, also impossible for an experimental setup to reproduce theoretical conditions. The kinematics assumptions are therefore not verified in absolute, but satisfied up to a certain level that often remains subjective. Fortunately, field measurement methods provide comprehensive data that can be used for assessing and improving experimental processing. In this work, digital image correlation is applied to different types of shear testing performed on a dual phase steel. Results are used to construct quantitative estimators to assess the quality of measurement as well as to decrease the number and weight of assumptions. A method is also proposed to separate the measured kinematics into the expected theoretical ones and the unwanted experimental deviations. It is quantitatively shown that, for the considered material and sample types, translational simple shear testing achieves kinematics that are closer to theory than pseudo-simple shear testing. The other major finding of this work is a method to identify shear strains independently of experimental biases.

Synthesis of pure potassium pentaborate (KB5) from potassium dihydrogen phosphate (KH2PO4) and colemanite

In this study, after specifying theoretical reaction conditions required for the chemical reaction, potassium pentaborate (KB5) was synthesized from the potassium dihydrogen phosphate ( $${\text{KH}}_{2} {\text{PO}}_{4}$$ ) solution and raw colemanite ( $${\text{Ca}}_{2} {\text{B}}_{6} {\text{O}}_{{11}} \cdot 5{\text{H}}_{2} {\text{O}}$$ ) ore. The slow evaporation solution method was used at 25 °C. The effect of time (6–18 h) on crystallization was studied. Synthesized minerals were characterized by X-ray diffraction (XRD), Fourier transform infrared (FT-IR), RAMAN spectroscopy, and scanning electron microscopy (SEM). The results according to XRD, FT-IR, RAMAN, and SEM analyses proved that the synthesized product was potassium pentaborate ( $${\text{KB}}_{5} {\text{O}}_{8} \cdot 4{\text{H}}_{2} {\text{O}}$$ ) mineral with ICSD: 96-026-1927 pdf code. As a result, the cost was reduced by using raw boron ore, colemanite, and KB5 was obtained in a shorter time and at a lower temperature.

Rewarding Good Taxpayers, an Effective Mechanism?

In this paper, I examine the conditions under which rewarding honest taxpayers is an optimal mechanism to reduce tax evasion and improve collection. My theoretical model suggests that when it is expensive to audit contributors, and moral (or pecuniary) evasion cost is high enough, rewarding tax compliance is an effective strategy to increase collection. I provide empirical evidence from Argentina’s province variation of rewards policies and tax collection. Where the data suggests that theoretical conditions hold, I find a positive effect in real estate per capita tax collection between 0.4 and more than 2 standard deviations.

EWOLUCJA MODELU HELISY JAKO KONCEPCJI ROZWOJOWEJ WE WSPÓŁCZESNEJ GOSPODARCE ŚWIATOWEJ

The purpose of this article is to analyze the conditions of the functioning of the helix model in a dynamic approach, as well as to synthetically present how changes in the de­velopment conditions of the modern world economy, including primarily technological changes as well as the processes of globaliza­tion, integration and regionalization as well as a qualitative subjective change, affect the evolution of the helix model and its applica­tion abilities. The main research hypothesis was formulated as follows: “The development concept based on a helix evolves towards the expansion of planes and groups of entities dynamising development processes and also increasing the quality of this development, mainly in the innovative plane.” The article uses the descriptive method and the methods of non-reactive research, especially the his­torical-comparative method, e.g. in order to present the differences in the construction of the helix models as well as to show the evo­lution of the entire model concept, a critical analysis of scientific publications relating to the theoretical conditions of the model as well as the analysis of documents and reports relating to the subject matter described. The analysis shows that knowledge plays a fun­damental role both in the theoretical layer of the helix models and in their application aspects. However, in order to be able to draw from knowledge resources, a flexible and dy­namic approach to the subjective structure in the created models of the helix is necessary. It is mainly manifested by the necessity to engage new groups of entities to cooperate as well as to change the attitudes of partici­pants and implement modern forms of both cooperation and communication based on Industry 4.0

재원조달 방법을 고려한 재정지출 효과 분석 : 미국의 사례를 중심으로 (Estimating Fiscal Multiplier: Do Financing Methods Matter?)

Korean Abstract: 본고에서는 재정 확대 정책 시행 시 재원조달 방법이 달라짐에 따라 정책 효과에 차이가 발생하는지 분석하였다. 기존 실증분석 연구는 재원조달 방법을 정의할 때 이론적인 조건을 엄밀하게 충족하지 못하는 경우가 많고 체계적인 분석이 다소 부족하며, 정의가 각기 달라서 분석결과 비교에 어려움이 있다. 이에 본고에서는 실증분석 연구에서 사용할 수 있는 이론적으로 엄밀한 재원조달 방법의 정의와 반사실적(counterfactual) 분석 방법론을 제시하고 미국 자료를 이용하여 분석하였다. 구조 VAR모형을 이용한 실증분석 결과 추정치의 불확실성 정도를 고려할 때 재원조달 방법 변경에 따라 재정지출의 상대적 효과가 다르다고 단정 짓기는 어렵다. 충격 초기에는 부채로 재원을 조달(debt-financing)할 때의 재정지출승수가 증세로 조달(tax-financing)할 때의 재정지출승수보다 최대 0.31가량 더 큰 것으로 추정되었으나, 충격 5년 이후에는 부채 조달 방법(debt-financing)을 이용한 재정지출승수가 조세 조달 방법(tax-financing)을 이용한 재정지출승수와 비슷하거나 더 작았다. 하지만 확률적으로 이러한 차이가 명확히 나타나지 않았다. 이러한 결과는 모형의 형태, 분석방법의 변경에도 불구하고 대체로 지지되었다. 한편 재원조달 방법의 변경이 GDP외 다른 경제 변수에 미치는 영향을 분석한 결과 재원조달 방법이 변경되면서 소비, 투자, 순수출의 반응이 달라지는 것을 확인하였다. 또한 기존의 연구 방법대로 분석하는 경우 증세의 반응이 정부의 기간 간 예산제약을 충족시킬 만큼 충분히 이루어지지 않아 증세로 조달할 때 재정지출승수가 과대 추정될 가능성이 있음을 보였다. English Abstract: This paper analyzes whether there is a difference in the effectiveness of the fiscal policy used as the method of financing is changed. Existing literature often fails to strictly meet theoretical conditions when defining financing methods and lacks systematic analysis. Therefore, we present theoretically rigorous counterfactual analysis methodologies and definitions of financing methods. We show that the fiscal multiplier is likely to be overestimated when analyzed using existing research methods. We find evidence that the debt-financed government spending multiplier is estimated to be up to 0.31 larger than when tax-financed government spending multipliers are used, up until five years after a government spending shock. However, five years after the shock, the debt-financed government spending multiplier is similar to or smaller than the tax-financed government spending multiplier. However, the difference between the two multipliers is not statistically supported. These results are generally supported by various changes in the pattern of government spending and the time difference between any tax increase and government expenditure. On the other hand, an analysis of the impact of a change in financing methods on other economic variables other than GDP confirms that a change in funding methods results in a different response to consumption, investment, net exports, and real wages.

Theoretical and experimental investigation of the sources of error in stochastic parallel gradient descent-based digital modal decomposition technique

A detailed systematic investigation of the accuracy of digital modal decomposition process that uses stochastic parallel gradient descent (SPGD) algorithm is presented in this paper. Composite beams of known weights and phases corresponding to the eigenmodes of a three-mode fiber are generated theoretically and through experiments using a spatial light modulator (SLM). The weights and phases of the constituent scalar modes are extracted from the intensity profile of the composite beam using the SPGD method, for both theoretical and experimental conditions. Detailed analysis of the sources of error in such SPGD based digital modal decomposition method is carried out by generating composite beams of various modal ratios and phase combinations theoretically. Impact of the experimental errors such as effect of background noise, nonlinearity, misalignment of the camera and that due to the cumulative propagation phase, on the extracted weights and relative phase values are quantified. We find that any ambiguity at phase angles closer to 90 deg among the constituent modes especially when the modal weights are non-uniform, cannot be corrected easily and hence is a fundamental limitation of the intensity-based modal decomposition technique. The methodology used in this manuscript to identify the systemic errors in modal decomposition can be potentially extended to any digital decomposition technique.

Escalating commitment to a failing course of action — A re-examination

We report the results from an experiment inspired by a seminal study (Staw, 1976) that introduced the notion of “escalation of commitment”, a variant of the sunk cost fallacy. This topic has received much attention outside of economics, and we investigate whether the escalation phenomenon can be reproduced using standard protocols established in experimental economics. The focus is on how decision makers respond to a signal about a previous investment depending on (i) whether or not they were responsible for that investment, (ii) whether the signal is positive or negative, and (iii) whether or not the signal is associated with a loss or gain. We characterize theoretical conditions under which escalation—increased follow-up investments after receiving a negative signal—may occur. Our data indicates that subjects react differently to negative feedback when this feedback is linked to a financial loss and when they have been responsible for the initial investment. We also observe gender effects.

Population dynamic regulators in an empirical predator-prey system

Capelin (Mallotus villosus) is a short-lived (1–4 years) fish species, that plays a crucial role by dominating the intermediate trophic level in the Barents Sea. Several episodes of extreme biomass decline (collapse) have been observed during the last three decades. We postulate that these collapses might be regulated by food availability (bottom-up effect) and/or by time discrepancy between capelin feeding and abundance of its prey (match-mismatch hypothesis). This paper investigates our postulate using a model consisting of a set of coupled differential equations to describe the predator-prey system, with a single delay term, τ, in description of the predator dynamics. We derive theoretical conditions on τ, as well as determine how changes in these conditions define different stability regimes of the system. Unconstrained optimization is used to calculate optimal model parameters by fitting the predator-prey model to empirical data. The optimization results are combined with those from the theoretical analysis, to make inference about the empirical system stability. Our results show that Hopf bifurcation occurs in the predatory-prey system when τ exceeds a theoretically derived value τ∗>0. This value represents the critical time for prey availability in advance of the optimal predator growth period.Set into an ecological context, our findings provide mathematical evidence for validity of the match-mismatch hypothesis and a bottom-up effect for capelin.

SVARs Identification Through Bounds on the Forecast Error Variance

This article identifies structural vector autoregressions (SVARs) through bound restrictions on the forecast error variance decomposition (FEVD). First, the article shows FEVD bounds correspond to quadratic inequality restrictions on the columns of the rotation matrix transforming reduced-form residuals into structural shocks. Second, the article establishes theoretical conditions such that bounds on the FEVD lead to a reduction in the width of the impulse response identified set relative to only imposing sign restrictions. Third, this article proposes a robust Bayesian approach to inference. Fourth, the article shows that elicitation of the bounds could be based on DSGE models with alternative parameterizations. Finally, an empirical application illustrates the potential usefulness of FEVD restrictions for obtaining informative inference in set-identified monetary SVARs and remove unreasonable implications of models identified through sign restrictions.

Θεραπευτική σχέση: δυναμικές αλληλεπιδράσεις και ο ρόλος του φύλου

The article emphasizes, first of all, the importance of various aspects of the psychotherapeutic relationship -such as the therapeutic alliance, the cooperation, the empathy, the goal agreement-, which have been proven to influence the therapeutic outcome and are consistently linked with the mental health improvement of the patient, regardless of the different theoretical conditions and principles of the psychotherapeutic approaches. On the other hand, it is recognized that identifying the quality characteristics that contribute to and influence the psychotherapeutic relationship and process is a difficult task, as it depends on the therapeutic boundaries of this relationship, the characteristics of the therapist, but also on factors related with the patient, such as his/her attitudes, expectations, motivations and commitment to a process of change. One element that seems to characterize the identity of each member individually, but also the dynamic processes of interaction between the therapeutic dyad, is gender. For this reason, the article underlines the importance of gender in shaping the communication and cooperation between therapists and patients, while stating also that awareness of the gender dynamics, in combination with other identity characteristics, is a prerequisite for an effective and ethical practice.

When it really counts: Investigating the relation between trait mindfulness and actual prosocial behavior

Meta-analytical findings suggested a positive link between trait mindfulness and prosociality. However, most correlational studies on mindfulness and prosociality have relied on self-report measures. The present work aimed to address this serious limitation by investigating actual prosocial behavior. We further focused on mindfulness as a multi-dimensional personality trait to disentangle effects of different mindfulness aspects. In addition, we tested whether the relation between trait mindfulness and prosocial behavior emerges under a theoretical meaningful experimental boundary condition (i.e., feelings of guilt). In two studies (using four different samples; N = 1240), we did not find support for a positive link between trait mindfulness and (a) charitable donation and (b) behavior in an incentivized economic game, respectively. Evidence for manipulated guilt-level as a moderator was inconclusive. Taken together, the findings point to a more complex role of trait mindfulness for prosocial behavior. Limitations and ideas for further research are discussed.

Roy Bhaskar on Scientific Progress and the Fallibility of Cognition: A Critique of Four Approaches

So far, various approaches have been proposed to explain the progress of science. These approaches, which fall under a fourfold classification, are as follows: semantic, functional, epistemic, and noetic approaches. Each of these approaches, based on the intended purpose of science, defines progress on the same basis. The semantic approach defines progress based on the approximation to the truth, the functional approach based on problem-solving, the epistemic approach based on knowledge accumulation, and the noetic approach based on increased understanding. With a stratified description of the world, Roy Bhaskar sees science as the movement toward deeper layers aimed at discovering productive mechanisms. He also explains progress based on the layering and acquisition of knowledge of the underlying layers. But because he believes in the social nature of science and considers knowledge a social product and subject to change, he acknowledges the fallibility of cognition. Hence, it is believed that moving to a new layer does not necessarily lead to the progress of science. However, it is possible that by acquiring knowledge about the new layer, our previous knowledge will be revised and corrected. In this article, while expressing the Bhaskar theory of scientific progress and explaining its contingency with respect to the fallibility of cognition, we pursue a basic goal. This goal is summarized in the review of all four approaches in order to show their lack of attention to the fallibility of cognition and its effect on explaining progress. What has been done in this article is based on two phases: explaining the contingency of the progress of science for Bhaskar and examining the four approaches to the progress of science in order to show their inattention to the fallibility of cognition. In his philosophy, referring to the two dimensions of transitive and intransitive, Roy Bhaskar considers the purpose of science to be the acquisition of knowledge about intransitive objects, and this knowledge is achieved through a social activity. Since this cognition is a social product and belongs to the transitive dimension of science, it will be fallible and subject to change. Bhaskar concludes with philosophical arguments that the world contains generative mechanisms, but that it is the task of science to discover their nature and exactly what mechanisms are at work. This requires work in two theoretical dimensions, namely the use of conceptual tools and a practical dimension, that is, the use of experimental tools. Now, as the theoretical and technical conditions under which cognition is formed and evaluated are themselves expanding and subject to change and modification, our knowledge may also be expanded or corrected. In this study, it was found that the semantic approach is unaware of the effect of fallibility on the evidence used to estimate the approximation to the truth and, consequently, progress. The functional approach ignores this effect in solving the problems posed by theories. The epistemic approach does not take into account the fallibility of evidence used to justify and validate the evidence, and finally, the noetic approach neglects the effect of the fallibility on what the explanation and prediction are based on. These have led to these approaches, which consider the satisfaction of the criteria in question necessarily leads to progress.

Professional training of students for the organization of cognitive and research activities of preschool children: theoretical foundations and conditions for improving quality

Professional training of students for the organization of cognitive and research activities of preschool children: theoretical foundations and conditions for improving quality

Career-computer simulation increases perceived importance of learning about rare diseases

BackgroundRare diseases may be defined as occurring in less than 1 in 2000 patients. Such conditions are, however, so numerous that up to 5.9% of the population is afflicted by a rare disease. The gambling industry attests that few people have native skill evaluating probabilities. We believe that both students and academics, under-estimate the likelihood of encountering rare diseases. This combines with pressure on curriculum time, to reduce both student interest in studying rare diseases, and academic content preparing students for clinical practice. Underestimation of rare diseases, may also contribute to unhelpful blindness to considering such conditions in the clinic.MethodsWe first developed a computer simulation, modelling the number of cases of increasingly rare conditions encountered by a cohort of clinicians. The simulation captured results for each year of practice, and for each clinician throughout the entirety of their careers. Four hundred sixty-two theoretical conditions were considered, with prevalence ranging from 1 per million people through to 64.1% of the population. We then delivered a class with two in-class on-line surveys evaluating student perception of the importance of learning about rare diseases, one before and the other after an in-class real-time computer simulation. Key simulation variables were drawn from the student group, to help students project themselves into the simulation.ResultsThe in-class computer simulation revealed that all graduating clinicians from that class would frequently encounter rare conditions. Comparison of results of the in-class survey conducted before and after the computer simulation, revealed a significant increase in the perceived importance of learning about rare diseases (p < 0.005).ConclusionsThe computer career simulation appeared to affect student perception. Because the computer simulation demonstrated clinicians frequently encounter patients with rare diseases, we further suggest this should be considered by academics during curriculum review and design.

Why do managers disclose risks accurately? Textual analysis, disclosures, and risk exposures

I provide an economic model that justifies using bag-of-words, topic modeling, and machine learning techniques to measure firms’ risk exposures using the percentage they allocate to each risk in their financial statements. The model provides a theoretical set of sufficient conditions under minimal assumptions that make managers optimally disclose risk accurately and give more space to the most critical risks. I document that the SEC Regulation satisfies this set of sufficient theoretical conditions and induces rational managers to disclose risks truthfully.

Collective De-Anonymization of Social Networks With Optional Seeds

As Internet users interacting with their different friends in different social networks, the de-anonymization problem has been raising improving concern. Since the assailants may de-anonymize a social network by matching it with a correlated sanitized network and identifying anonymized user identities, multifarious arts study on the theoretical conditions or practical algorithms for correctly de-anonymizing a social network. Except for the structural information of these social networks, there has also been bounteous works taking advantage of some pre-identified seed nodes for reference in the anonymized network. In this paper, we systematically probe the theoretical conditions and algorithmic approaches for correctly matching two different-sized social networks by leveraging the multi-hop neighborhood relationships. A limited number of seeds are also taken into consideration as auxiliary information. To this end, we introduce the de-anonymization problem with the aid of the collectiveness and the collective adjacency disagreements, which are the collection of disagreements of different multi-hop adjacency matrices. We theoretically demonstrate that minimizing the collective adjacency disagreements can help match two social networks even in a very sparse circumstance, as it significantly enlarges the difference between the mismatched node pairs and the correctly matched pairs. Besides, the seeds is proved to bring positive influence in improving the de-anonymization accuracy. Algorithmically, we relax the domain of the matching function to continuum and adopt the conditional gradient descending method on the collective-form objective, to efficiently minimize the collective adjacency disagreements of two networks. We conduct tremendous experiments on different networks with or without seeds, the results of which return desirable de-anonymization accuracies and reveal the advantages of the collectiveness: the collectiveness manifests rich structural information, thereby most nodes can be correctly matched with their correspondences even in some sparse networks, where merely utilizing the 1-hop adjacency relationships might fail to work.

The Potential Scope of the Ultrasonic Surface Reflection Method Towards Mechanical Characterisation of Isotropic Materials. Part 2. Experimental Results

This paper is Part 2 of a study on the scope of the ultrasonic Surface Reflection Method (SRM). Part 1 deals with the theoretical conditions for a satisfactory usage of this method. This second part validates the practical feasibility and reliability of the SRM method by comparison with the conventional Transmission Method (TM) in cases where the latter is applicable. Two experimental devices (one for SRM and one for TM) are developed and measurements of shear and bulk moduli are carried out at ultrasonic frequency (610 kHz) and at room temperature. The experimental conditions in terms of sample geometry, pulse characteristics and interfacial transmission required to obtain a given accuracy on the measurement are stated. The SRM is then validated against other experimental methods and is used to determine the shear modulus of a carbon black filled neoprene at ambient temperature (T = 21 °C) and ultrasonic frequency. The benefit brought by this method is well demonstrated: a unique measurement allows the determination of all the moduli of a highly damping isotropic material (carbon black filled neoprene) not achievable by other methods.

The Potential Scope of the Ultrasonic Surface Reflection Method Towards Mechanical Characterisation of Isotropic Materials. Part 1. A Theoretical Analysis

This paper deals with the possible field of application of ultrasonic Surface Reflection Method (SRM) to achieve the mechanical characteristics of isotropic materials. This method is based on the measurement of the amplitude of the reflected wave at the interface between reference material and the material to be characterised. Objective: The purpose of Part 1 of this paper is to establish the theoretical conditions for the applicability of SRM. First, the theoretical formulas necessary to obtain the mechanical properties of the material to be tested will be established. Then, on the basis of these analytical formulas, the validity of the results for the material to be studied will be discussed according to the choice of the mechanical properties of the reference material through uncertainty calculations. The measurand error of SRM is then compared to that of traditional methods (transmission, transmission in water bath, pulse-echo). The analytical solution to the inverse problem (the mechanical characteristics of the tested medium based on those of the reference medium and the waves’ amplitude) will be given. From this analytical solution, an analysis of the measurand error will be performed and a method for choosing the reference material will be proposed. It appears that SRM is better suited than traditional methods in two specific cases: measurement of small deviations of mechanical properties from a reference material or characterisation of high damping materials. In Part 2 of this paper, the practical conditions of applicability of the method are described and then applied to different kinds of materials.

Dilogarithm and higher ℒ-invariants for 𝒢ℒ₃(𝐐_{𝐩})

The primary purpose of this paper is to clarify the relation between previous results in [Ann. Sci. Éc. Norm. Supér. 44 (2011), pp. 43–145], [Amer. J. Math. 141 (2019), pp. 661–703], and [Camb. J. Math. 8 (2020), p. 775–951] via the construction of some interesting locally analytic representations. Let E E be a sufficiently large finite extension of Q p \mathbf {Q}_p and ρ p \rho _p be a p p -adic semi-stable representation G a l ( Q p ¯ / Q p ) → G L 3 ( E ) \mathrm {Gal}(\overline {\mathbf {Q}_p}/\mathbf {Q}_p)\rightarrow \mathrm {GL}_3(E) such that the associated Weil–Deligne representation W D ( ρ p ) \mathrm {WD}(\rho _p) has rank two monodromy and the associated Hodge filtration is non-critical. A computation of extensions of rank one ( φ , Γ ) (\varphi , \Gamma ) -modules shows that the Hodge filtration of ρ p \rho _p depends on three invariants in E E . We construct a family of locally analytic representations Σ m i n ( λ , L 1 , L 2 , L 3 ) \Sigma ^{\mathrm {min}}(\lambda , \mathscr {L}_1, \mathscr {L}_2, \mathscr {L}_3) of G L 3 ( Q p ) \mathrm {GL}_3(\mathbf {Q}_p) depending on three invariants L 1 , L 2 , L 3 ∈ E \mathscr {L}_1, \mathscr {L}_2, \mathscr {L}_3 \in E , such that each representation in the family contains the locally algebraic representation A l g ⊗ S t e i n b e r g \mathrm {Alg}\otimes \mathrm {Steinberg} determined by W D ( ρ p ) \mathrm {WD}(\rho _p) (via classical local Langlands correspondence for G L 3 ( Q p ) \mathrm {GL}_3(\mathbf {Q}_p) ) and the Hodge–Tate weights of ρ p \rho _p . When ρ p \rho _p comes from an automorphic representation π \pi of a unitary group over Q \mathbf {Q} which is compact at infinity, we show (under some technical assumption) that there is a unique locally analytic representation in the above family that occurs as a subrepresentation of the Hecke eigenspace (associated with π \pi ) in the completed cohomology. We note that [Amer. J. Math. 141 (2019), pp. 611–703] constructs a family of locally analytic representations depending on four invariants ( cf. (4) in that publication ) and proves that there is a unique representation in this family that embeds into the Hecke eigenspace above. We prove that if a representation Π \Pi in Breuil’s family embeds into the Hecke eigenspace above, the embedding of Π \Pi extends uniquely to an embedding of a Σ m i n ( λ , L 1 , L 2 , L 3 ) \Sigma ^{\mathrm {min}}(\lambda , \mathscr {L}_1, \mathscr {L}_2, \mathscr {L}_3) into the Hecke eigenspace, for certain L 1 , L 2 , L 3 ∈ E \mathscr {L}_1, \mathscr {L}_2, \mathscr {L}_3\in E uniquely determined by Π \Pi . This gives a purely representation theoretical necessary condition for Π \Pi to embed into completed cohomology. Moreover, certain natural subquotients of Σ m i n ( λ , L 1 , L 2 , L 3 ) \Sigma ^{\mathrm {min}}(\lambda , \mathscr {L}_1, \mathscr {L}_2, \mathscr {L}_3) give an explicit complex of locally analytic representations that realizes the derived object Σ ( λ , L _ ) \Sigma (\lambda , \underline {\mathscr {L}}) in (1.14) of [Ann. Sci. Éc. Norm. Supér. 44 (2011), pp. 43–145]. Consequently, the locally analytic representation Σ m i n ( λ , L 1 , L 2 , L 3 ) \Sigma ^{\mathrm {min}}(\lambda , \mathscr {L}_1, \mathscr {L}_2, \mathscr {L}_3) gives a relation between the higher L \mathscr {L} -invariants studied in [Amer. J. Math. 141 (2019), pp. 611–703] as well as the work of Breuil and Ding and the p p -adic dilogarithm function which appears in the construction of Σ ( λ , L _ ) \Sigma (\lambda , \underline {\mathscr {L}}) in [Ann. Sci. Éc. Norm. Supér. 44 (2011), pp. 43–145].