Equal Rank Research Articles

Intersection of Race and Gender in the Cardiothoracic Workforce: Study of Representation and Salary

Cardiothoracic surgery lacks gender and racial/ethnic diversity. Recent studies highlighted disparities based on gender and race/ethnicity among academic cardiothoracic surgeons. The impact of the intersection of these factors on representation and salary is unknown. A cross-sectional analysis of Accreditation Council for Graduate Medical Education and Association of American Medical Colleges data was performed on the number of trainees and clinical faculty stratified by race/ethnicity and gender using Chi-square testing. The number of women and underrepresented minorities was low in cardiothoracic surgery compared to other specialties, with lowest representation at the intersection of race/ethnicity and gender. Among trainees, 8% were Asian, 2% were Black/African American , and 1.5% were Hispanic/Latina women. Among cardiothoracic faculty, 3.4% were Asian, 0.8% were Black/African American, and 0.4% were Hispanic/Latina women. Women in academic medicine, surgery and cardiothoracic surgery earned 80-87% the salary of men of equal academic rank. White assistant professors earned more than their colleagues (all clinical faculty, surgeons and cardiothoracic surgeons), this difference was further compounded by gender. Salary disparities exist among cardiothoracic surgeons at the intersection of gender and race/ethnicity. Women experience salary disparity across all academic ranks and specialties. When considering the intersection of gender and race/ethnicity, gender is the predominant factor driving salary inequity.

Efficiency of coronavirus testing from a spatial perspective: the Israeli case

ABSTRACT A prominent characteristic of. COVID-19 is the long incubation period, the lack of symptoms during that period, and significant geographic variation in prevalence and testing. This article investigates the relationship between testing and infection based on an Israeli sample of 193 municipalities and a report from 11 May 2020. Results support an exponential rise in the fraction of positive. COVID-19 outcomes with the fraction of tests. Finally, under conditions of equal socioeconomic ranking, population density and income inequality, the projected efficiency of tests rises with population density and the Gini index and drops with socioeconomic ranking.

The Unproductive “Overconstitutionalization” of EU Copyright and Trademark Law – Fundamental Rights Rhetoric and Reality in CJEU Jurisprudence

In EU copyright and trademark law, the protection of the right to intellectual property is the rule, and breathing space for competing fundamental rights, such as freedom of expression and the right to a healthy environment, is the exception. While formally recognizing the need to balance protection interests against other fundamental rights and values, the Court of Justice of the European Union (CJEU) fails to use competing fundamental rights productively. Instead, the Court has developed a meaningless fundamental rights rhetoric that produces the false impression that there is sufficient room for all competing rights and interests within the existing copyright and trademark systems. However, the current configuration of EU copyright and trademark law fails to offer users the chance of meeting right holders as equals, even if their fundamental rights are of equal ranking in the Charter. By adding fundamental rights cosmetics to imbalanced protection systems, the CJEU only cements and further stabilizes the existing rule/exception edifice that is strongly in favour of right holders. Introducing the mantra of internal balancing – requiring the reconciliation of competing rights and interests within the confines of secondary copyright and trademark legislation – the Court has even created a considerable risk of sacrificing competing fundamental rights on the altar of the EU harmonization agenda. By letting the harmonization objective reign supreme, the CJEU has also given the three-step test in copyright law and the honest practices proviso in trademark law a quasi-constitutional status. As a result, these open-ended provisions undermine limitations of exclusive rights that could support competing fundamental rights. To remove the imbalances in current EU copyright and trademark law, it would be necessary to introduce upfront gatekeeper requirements that prevent illegitimate infringement claims from the outset when competing fundamental rights are at stake.

Older women’s constructions of equality over the lifecourse

Abstract Gender and age are central organising principles of social relations, with socially constructed gendered and age-based norms influencing patterns of social behaviour, power and inequality. Despite recent literature highlighting the importance of subjective measures of equality, including as a significant predictor of wellbeing, there is a gap in studies focused on subjective equality in research on ageing. Drawing on an equality ranking exercise and life herstory interviews with 20 older-aged women (65+) in Aotearoa New Zealand, this article focuses on the intersectionality of age and gender, analysing the ways in which participants constructed their experiences of equality over the lifecourse from their standpoint as older-aged women. The analysis reveals a significant rise in subjective equality from childhood to older age, with more varied responses in childhood and a convergence of responses from adolescence onwards. Participants’ constructions of equality differed: age was the dominant construct of equality women ascribed to their childhood years, while gender inequality came to the fore during their teenage years. In early to mid-adulthood, women found ways to navigate gendered inequality in various life domains, while in older adulthood equality was constructed as freedom and life satisfaction. This trajectory suggests that the frames individuals use to make sense of equality and their personal experiences are not fixed; they are fluid and shift throughout the lifecourse.

Nonlinear Optics Through the Field Tensor Formalism

AbstractThe “field tensor” is the tensor product of the electric fields of the interacting waves during a sum‐ or difference‐frequency generation nonlinear optical interaction. It is therefore a tensor describing light interacting with matter, the latter being characterized by the “electric susceptibility tensor.” The contracted product of these two tensors of equal rank gives the light‐matter interaction energy, whether or not propagation occurs. This notion having been explicitly or implicitly present from the early pioneering studies in nonlinear optics, its practical use has led to original developments in many highly topical theoretical or experimental situations, at the microscopic as well macroscopic level throughout a variety of coherent or non‐coherent processes. The aim of this review article is to rigorously explain the field tensor formalism in the context of tensor algebra and nonlinear optics in terms of a general time‐space multi‐convolutional development, using spherical tensors, with components expressed in the frame of a common basis set of irreducible tensors, or Cartesian tensors. A wide variety of media are considered, including biological tissues and their imaging, artificially engineered by various combinations of optical and static electric fields, with the two extremes of all‐optical and purely electric poling, and also bulk single crystals.

Equal rank local theta correspondence as a strong Morita equivalence

Let (G, H) be one of the equal rank reductive dual pairs Mp2n,O2n+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left( Mp_{2n},O_{2n+1} \\right) $$\\end{document} or Un,Un\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left( U_n,U_n \\right) $$\\end{document} over a nonarchimedean local field of characteristic zero. It is well-known that the theta correspondence establishes a bijection between certain subsets, say G^θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widehat{G}_\ heta $$\\end{document} and H^θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widehat{H}_\ heta $$\\end{document}, of the tempered duals of G and H. We prove that this bijection arises from an equivalence between the categories of representations of two C∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^*$$\\end{document}-algebras whose spectra are G^θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widehat{G}_\ heta $$\\end{document} and H^θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widehat{H}_\ heta $$\\end{document}. This equivalence is implemented by the induction functor associated to a Morita equivalence bimodule (in the sense of Rieffel) which we construct using the oscillator representation. As an immediate corollary, we deduce that the bijection is functorial and continuous with respect to weak inclusion. We derive further consequences regarding the transfer of characters and preservation of formal degrees.

A Cauchy Harish-Chandra integral for a dual pair over a p-adic field, the definition and a conjecture

For a real irreducible dual pair there is an integral kernel operator which maps the distribution character of an irreducible admissible representation of the group with the smaller or equal rank to an invariant eigendistribution on the group with the larger or equal rank.The purpose of this article is to transfer this construction to the p-adic case. We provide the precise definition of the integral kernel operator and formulate a conjecture.

Sensitivity of Multi-Criteria Analysis Methods in Rural Land Consolidation Project Ranking

Decisions around distributing available funds among potential land consolidation projects require a thorough analysis in order to maximize the effects of land consolidation. In order to avoid choosing the wrong land consolidation projects, different methods can be used. Generally, there are two possible groups of methods: one based on a qualitative approach (DELPHI; SWOT) and one based on a quantitative approach (AHP, VIKOR, SAW, TOPSIS, etc.). In this research, the focus was on the sensitivity of the resulting rankings affected by varying the input data in multi-criteria analysis methods, with an emphasis on the variation in the weight and the choice of criteria. This research was motivated by the subjective character of the choice of criteria and their weighting before applying the multi-criteria analysis methods. Four methods were included (AHP, TOPSIS, VIKOR, and SAW) for the multi-criteria analysis, with three ways of defining weights (consistent, modified, or quasi-consistent and freely determined without taking consistency into account), in order to determine the influence of the different methods on the final ranking. The weights were defined only by an acceptable interval of values. The sensitivity of the methods was investigated using the differences in the obtained rankings between each method. A case study is provided on real data, and the results are discussed. The results showed a relatively small variance and possible equal rankings of projects by means of statistical analyses. This finding opens up the possibility of the valuation of projects instead of simple rankings.

A novel landslide susceptibility prediction framework based on contrastive loss

ABSTRACT Recently, the positive unlabeled (PU) learning algorithms have proven highly effective in generating accurate landslide susceptibility maps. The algorithms categorize samples exclusively into positive samples (landslides) and unlabeled samples for training, eliminating random or subjective selection of non-landslide samples. However, existing PU learning algorithms face limitations in capturing correct negative samples in multi-genesis landslide areas, leading to lower prediction accuracy. To address this issue, the PU-pullbaggingDT algorithm was proposed in this study. This integrated method combines the strengths of two techniques: the superior ranking performance of the PU-baggingDT algorithm and the low bias of the contrastive learning approach. The contrastive learning introduces a new contrastive loss of PU learning (PUpull loss), which pulls the distance of similar landslide samples in the projection space closer based on the validation accuracy threshold, without the need for data augmentation and class probability. The PUpull loss relaxes the tightness toward unlabeled samples, reducing the impact of incorrectly defined non-landslide samples on prediction results in multi-genesis landslide areas. The proposed algorithm outperforms existing PU-learning and machine learning methods (support vector machine, decision tree, logistic regression, AdaBoost, and XGBoost) with random selection of negative samples for predicting landslide susceptibility in China’s Zigui County, as demonstrated by comprehensive evaluation metrics. The landslide susceptibility mapping utilizes equal interval division and ranking, achieving approximately a 90% landslide percentage in areas with very high and high susceptibility in Zigui County. This demonstrates the capability of the proposed algorithm to effectively predict landslide susceptibility in complex geological settings.

External R&D Supplier Evaluation and Selection: A Three-Stage Integrated Funnel Model

Rapidly changing market demand has seen more and more companies pay attention to external R&D, to make full use of external resources, improve competitiveness, and promote innovation. The suitability of external R&D suppliers directly impacts the success of R&D. However, existing research in this topic has limitations. First, few existing studies have examined the evaluation and selection of external R&D suppliers, quantitatively. Second, there are few studies on the evaluation of effectiveness of R&D suppliers from the perspective of customer demand. Third, the evaluation of prototypes involves heterogeneous data for different technical criteria. As yet, there is no specific suitable model. To bridge abovementioned gaps, this article proposes a comprehensive three-stage integrated funnel model for external R&D supplier evaluation and selection. Specifically, it evaluates the effectiveness of suppliers from the perspective of customer demand and improves the nonradial superefficiency Pythagorean fuzzy DEA methodology. In addition, it proposes a novel fuzzy MA-VIKOR submodel based on heterogeneous data, which can evaluate suppliers from two perspectives: group utility and individual regret, while avoiding the potential problem of equal ranking. Finally, the effectiveness of the proposed model is illustrated by an external R&D supplier selection case of Company J, an international communication equipment company.

Les relations transphrastiques à la frontière entre la phrase et le texte

Interclausal relations are traditionally studied within the framework of the complex sentence of endocentric subordinative form. However, there is no essential correlation between interclausal linkage and complex sentence. Interclausal relations are not meanings of subordinate clauses but conceptual relations that bridge saturated processes of equal rank. According to this premise, complex sentence is only one option for the expression of interclausal relations, along with text. Moreover, if we compare the competing structures, it turns out that the unmarked form of expression is not complex sentence but text. While a complex sentence imposes a hierarchic syntactic structure on a symmetric conceptual structure, the structure of the text and the conceptual structure of interclausal relations are isomorphic. As a marked option, the choice of complex sentence requires a specific functional motivation, which does not involve the ideation of the link itself but the communicative perspective: its function is to impose a layered communicative perspective on the connexion, which is distributed between foreground and background information.

The Fatigue Response’s Fingerprint of Composite Materials Subjected to Constant and Variable Amplitude Loadings

This paper discusses the theoretical and experimental correlations between fatigue and static strength statistical distributions. We use a two-parameter residual strength model that obeys the qualitative strength-life equal rank assumption (SLERA) for guidance. The modeling approach consists of recovering the model’s parameters by best fitting the constant amplitude (CA) fatigue data at a given stress ratio, R, and the experimental Weibull parameters of the static strength distribution function. An extensive set of fatigue life and residual strength data for AS4 carbon/epoxy 3k/E7K8 Plain Weave Fabric with [45/−45/90/45/−45/45/−45/0/45/−45]S layups, obtained at different stress ratios, R, have been analyzed. The modeling approach consists of recovering the model’s parameters from pure tension or compression fatigue data at R = 0.1 and R = 5, respectively. Once the parameters are fixed, the model’s capabilities, potential, and limits are discussed by comparing its predictions with residual strength and fatigue life data obtained at stress ratios with mixed tension/compression loadings, namely R = −0,2 and R = −1. Moreover, from a preliminary analysis, the theoretical extension of the model’s capabilities to variable amplitude loadings is conceptualized. The application of Miner’s rule is also discussed and compared with a new damage rule to analyze the fatigue responses under variable amplitude loadings.

The Cost of Being a Woman in Academic Cardiothoracic Surgery: Joint Collaboration of The Society of Thoracic Surgeons Workforces on Diversity, Equity, and Inclusion and Cardiothoracic Surgery Practice Models

BackgroundGender disparity in the cardiothoracic surgery workforce is challenging to enumerate and quantify. The purpose of our work is to use the most current data to quantify the percentage of women in academic cardiothoracic surgery and salary disparity between women and men. MethodsWe performed a cross-sectional analysis of data collected by the Accreditation Council for Graduate Medical Education Data Resource Book 2021 and Association of American Medical Colleges Faculty Data for U.S. Medical School Faculty 2019, 2020, and 2021. We used descriptive analysis of the number of faculty and mean salaries of academic cardiothoracic surgeons according to academic rank and gender. Salary disparity in cardiothoracic surgery was compared with salary disparities seen among surgical specialties and academic clinicians. ResultsOver the past 3 years, women comprised 11.5% of the cardiothoracic workforce. In 2021, cardiothoracic surgeons who were women earned $0.71 to $0.86 for every $1.00 earned by cardiothoracic surgeons who were men. Ascending academic rank correlated with greater gender salary disparity; women professors earned less than men of equal and lower academic rank. From 2019 to 2021, women of the academic ranks of associate professor, professor, and chief of cardiothoracic surgery experienced a decrease in mean salaries, whereas men of equivalent academic ranks experienced an increase in mean salaries. ConclusionsGender disparity in cardiothoracic surgery persists, with low representation of women and salary disparity at every academic rank.

Soil–pile interaction in vertical vibration in inhomogeneous soils

AbstractThis paper develops a novel reference analytical solution for axially loaded piles in inhomogeneous soils, extending the pioneering elastodynamic model of Nogami and Novak (1976) to piles embedded in vertically inhomogeneous soils. Following the classical earlier model, the pile is modelled as a rod, using the strength‐of‐materials solution, and the soil layer as an approximate continuum, which rest on rigid rock. The approximation lies in reducing the number of dependent variables by eliminating certain stresses and displacements in the governing elastodynamic equations: the vertical normal and vertical shear stresses in the soil are controlled exclusively by the vertical component of the soil displacement. Soil inhomogeneity is introduced via a power law variation of shear modulus with depth, and perfect bonding is assumed at the soil–pile interface. The proposed generalized formulation treats two types of inhomogeneity by employing pertinent eigen expansions of the dependent variables over the vertical coordinate. The response is expressed in terms of generalized Fourier series and includes: (i) displacements and stresses along the pile and the pile–soil interface; and (ii) displacement and stress in the soil. Contrary to available models for homogeneous soils, the associated Fourier coefficients are coupled, obtained as solutions to a set of simultaneous algebraic equations of equal rank to the number of modes considered.

Assessment and Ranking of the Behavioural Leadership Model in the Process of Implementing Reforms in Public Sector of the Republic of Serbia Using the PIPRECIA Method

The establishment of sustainable leadership is essential for the process of implementing reforms in public sector. Sustainable leadership implies effective leadership capable of responding to changes that come from both the internal and external environment. To achieve this, it is necessary to apply multi-criteria decision-making methods. In this paper, the new multi-criteria decision-making method PIPRECIA was used to assess the criteria and five models of leader behaviour that are significant for the process of implementing reforms in the public sector of the Republic of Serbia. In essence, the paper aims to emphasise the simplicity of the practical application of the PIPRECIA method, which was discussed through a numerical illustration on the basis of which the conclusions were drawn. The research results indicate that the criterion Individual competence of the leader (C4-0.24) has the greatest weight. By ranking the alternatives, it was estimated that the Charismatic model of behaviour (A5-0.219) is the leader’s behaviour model that can have the greatest importance in the process of implementing public sector reforms. The Directive model of behaviour (A3-0.197) was derived as the second most important, which is understandable if we consider the fact that this model of leader’s behaviour traditionally dominates the work of the public sector. Furthermore, Participatory behaviour model (A1-0.193), Supportive behaviour model (A2-0.193) and Transformational behaviour model (A4-0.193) have equal rank, which means that they have the same importance for the decision-maker. The findings provide significant information to leaders of public organisations on how to implement reforms and manage human resources more effectively.

Information Equivalence among Transformations of Semi‐parametric Nonlinear Panel Data Models*

AbstractThis paper considers transformations of nonlinear semi‐parametric mean functions that yield moment conditions for estimation. Such transformations are said to be information equivalent if they yield the same asymptotic efficiency bound. I derive a unified theory of algebraic equivalence for moment conditions created by a given linear transformation. The main equivalence result states that under standard regularity conditions, transformations that create conditional moment restrictions in a given empirical setting need only to have an equal rank to reach the same efficiency bound. I compare feasible and infeasible transformations of both nonlinear models with multiplicative heterogeneity and linear models with unobserved factor structures.

Defect extensions and a characterization of tame fields

We study the relation between two important classes of valued fields: tame fields and defectless fields. We show that in the case of valued fields of equal characteristic or rank one valued fields of mixed characteristic, tame fields are exactly the henselian valued fields for which all algebraic extensions are defectless fields. In general tame fields form a proper subclass of henselian valued fields for which all algebraic extensions are defectless fields. We introduce a wider class of roughly tame fields and show that every algebraic extension of a given valued field is defectless if and only if its henselization is roughly tame. Proving the above results we also present constructions of Galois defect extensions in positive as well as mixed characteristic.

Konsep Lembaga Negara Indonesia dalam Perspektif Teori Trias Politica Berdasarkan Prinsip Checks and Balances System

There have been many constitutional law experts who have made studies and at the same time thoroughly investigated various legal studies and have been used as a reference for a world figure named Baron Secondat de Montesquieu (hereinafter known as Montesquieu) with his famous theory built and developed, namely the Triassic Theory Politica. The theory of Trias Politica in its implementation, if applied, is still relevant in the development of the constitutional era and is one of the pillars of democracy. Based on the Theory of Trias Politica, in principle, dividing state political power into three State Institutions, namely: 1. Legislature; 2. Executive; and 3. Judiciary. In order to realize the three types of State Institutions that are independent of each other and are in an equal rank (horizontal) to one another. The equality and independence of these three types of State Institutions is and is necessary so that the three state institutions can or are willing and able to supervise and control each other based on the principle of a checks and balances system in practice. The separation and division of the three authorities in three different State Institutions, it is hoped that the running of the state government will not be unequal and at the same time not overlapping, and can avoid Collusion, Corruption and Nepotism (KKN) government by one Institution and at the same time will bring up a checks mechanism and balances system (correcting and balancing each other). Power according to the Theory of Trias Politica into three parts can be explained in this study.

Handlungsempfehlungen für SARS-CoV-2-Testkonzepte für asymptomatische Beschäftigte im Gesundheitswesen

ZusammenfassungHintergrund und ZielsetzungBei der Umsetzung von SARS-CoV‑2-Testkonzepten in Einrichtungen des Gesundheitswesens kommen ranggleiche Gesetze und Verordnungen zur Anwendung. Vor dem Hintergrund erlebter Hindernisse bei einer adäquaten Umsetzung gesetzlicher Vorgaben in regelkonforme und rechtssichere Prozesse auf betrieblicher Ebene war das Ziel der vorliegenden Arbeit, dafür konkrete Handlungsempfehlungen zu entwickeln.MethodikIn einer Fokusgruppe mit Vertreter*innen aus Behörden, Fachschaften und Interessenvertretungen wurden auf Basis von Leitfragen aus zuvor identifizierten Handlungsfeldern in einem holistischen Ansatz kritische Aspekte der Umsetzung diskutiert. Die transkribierten Inhalte wurden anhand deduktiv-induktiver Kategorienbildung qualitativ analysiert.ErgebnisseAlle Diskussionsinhalte konnten den identifizierten Kategorien Gesetzliche Hintergründe von, Anforderungen an und Zielrichtungen für Testkonzepte in Gesundheitseinrichtungen, Zuständigkeiten für Umsetzung in betrieblichen Entscheidungsketten sowie Implementierung von SARS-CoV-2-Testkonzepten/Testprozessen zugeordnet werden.ImplikationenDie Umsetzung gesetzlicher Vorgaben in regelkonforme und rechtssichere SARS-CoV-2-Testkonzepte in Einrichtungen des Gesundheitswesens setzt bereits sowohl die Einbeziehung von Ministerien, Fachschaftsvertretungen, Berufsverbänden, Arbeitgeber(AG)- und Arbeitnehmer*innenvertretungen, Datenschutzexpert*innen, Vertretungen möglicher Kostenträger als auch eine integrative und vollzugstaugliche Formulierung von Gesetzen und Verordnungen voraus. Die Definition von Zielrichtungen für Testkonzepte ist maßgeblich für nachfolgend im Betrieb etablierte Prozessabläufe, bei denen Aspekte des Beschäftigtendatenschutzes genauso berücksichtigt werden müssen wie die Bereitstellung zusätzlicher personeller Ressourcen für die Bewältigung der Aufgaben. Zudem muss es in Zukunft ein zentrales Anliegen der Betriebe sein, IT-Schnittstellenlösungen für eine datenschutzkonforme Informationsweitergabe zu Beschäftigten zu finden.

Ext-multiplicity theorem for standard representations of $$(\textrm{GL}_{n+1},\textrm{GL}_n)$$

Let $\pi_1$ be a standard representation of $\mathrm{GL}_{n+1}(F)$ and let $\pi_2$ be the smooth dual of a standard representation of $\mathrm{GL}_n(F)$. When $F$ is non-Archimedean, we prove that $\mathrm{Ext}^i_{\mathrm{GL}_n(F)}(\pi_1, \pi_2)$ is $\cong \mathbb C$ when $i=0$ and vanishes when $i \geq 1$. The main tool of the proof is a notion of left and right Bernstein-Zelevinsky filtrations. An immediate consequence of the result is to give a new proof on the multiplicity at most one theorem. Along the way, we also study an application of an Euler-Poincar\'e pairing formula of D. Prasad on the coefficients of Kazhdan-Lusztig polynomials. When $F$ is an Archimedean field, we use the left-right Bruhat-filtration to prove a multiplicity result for the equal rank Fourier-Jacobi models of standard principal series.