Relative Degree Research Articles

Grey relational analysis model with cross-sequences and its application in evaluating air quality index

It is important to detect the internal operating regularity in system developing with poor information. To identify the real relationship among multi factors, we propose a grey relational analysis (GRA) method inspired by the characteristics of sequences variation. The proposed model considers the changes of fluctuating sequences like cross-sequences both in domain time and between time intervals. To obtain the quantitative change about sequences, relative angle change is employed to determine the variation in each interval, and the relative angle oscillation change is utilized for measuring variations between intervals. To find the optimal time lag or time intervals, the corresponding cycles are extracted by time-delay models. The reliability of the proposed models will be verified through cases in identifying crucial factors for air quality, and the final detection will then be made. To compare with existing representative GRA models clearly, the relation between two fluctuating sequences shaped in cross-sequences is examined by the proposed model. The empirical results show that the relation degree between pollutants and air quality is reasonable. The compared experiment shows that the GRA for cross-sequences can effectively identify the relationship among fluctuating sequences and the impact of time-delay is small for the proposed model with similar shapes.

Forecast of China’s natural gas demand based on the double-logarithmic model with stepwise regression method

ABSTRACT In the current world’s energy system, natural gas, as a clean energy source, is gradually becoming the main energy source. However, the volume of natural gas demand could be able to be influenced by numerous factors, in order to forecast the future trend of the requirement more precisely, it is necessary to further explore effective driving factors influencing the volume of demand and construct a brand new function model of forecasting natural gas demand. In this study, the relative gray relational degree is used to quantitatively describe the correlation among variables, diagnosing whether there are serious multicollinearity problems among these factors. According to the principle of correlation degree: first and then small, a stepwise regression analysis is adopted to refine the analysis of factors influencing natural gas demand. On the basis of statistical significance testing, in-depth studying is conducted on the effective influencing factors of natural gas demand. This helps to develop a more accurate prediction model. In this study, we find that: (1) China’s energy consumption structure and economic development influence its natural gas demand. (2) The stepwise regression double logarithmic demand function model based on the effective drivers has good forecasting performance. Researchers can use it to forecast the natural gas demand for medium- and long-term in different regions, and the forecasting results can be considered an important reference basis for scientific natural gas policy formulation. (3) Over the coming 15 years, Natural gas demand in China will continue to grow. It will reach about 6910 × 10 8 m 3 by 2035. It is concluded that the development of China’s natural gas demand would be promoted in an increasing scale trend by striving to promote China’s high-quality economic development, carefully building a new pattern of high-quality energy development, and increasing the proportion of natural gas consumption.

A multi-objective q-rung orthopair fuzzy programming approach to heterogeneous group decision making

In allusion to heterogeneous multi-criteria group decision making (MCGDM) problems with incomplete weights and q-rung orthopair fuzzy (q-ROF) truth degrees, where many kinds of criteria values, i.e., crisp values, intervals, trapezoidal fuzzy values, hesitant fuzzy values and q-ROF values (q-ROFVs), and multiple types of interactions exist, i.e., positive synergetic interactions, negative synergetic interactions and independence, a novel multi-objective q-ROF programming approach is proposed. In particular, in order to globally capture the interactions among criteria, Choquet-based relative closeness degrees are developed based on the technique for order performance by similarity to ideal solution (TOPSIS) and the Choquet integral. Then, the q-ROF Choquet-based group consistency index (q-ROFCGCI) and the q-ROF Choquet-based group inconsistency index (q-ROFCGII) are defined. Next, to derive optimal 2-additive fuzzy measures on the criteria set and optimal experts' weights, a new multi-objective q-ROF mathematical programming model is established by minimizing the q-ROFCGII and maximizing the q-ROFCGCI. Subsequently, an algorithm based on the adaptive non-dominated sorting genetic algorithm III (A-NSGA-III) is designed to solve the established model. Afterwards, the Choquet-based overall relative closeness degrees of the alternatives are used to obtain their preferred ordering. Finally, the effectiveness and advantage of the proposed approach is verified using four real cases concerning the evaluation of social commerce.

Energy cost of localization of relational quantum information

Entanglement of spatially separated quantum states is usually defined with respect to a reference frame provided by some external observer. Thus, if one wishes to localize the quantum information within a spatially separated entangled state, one must enact an entanglement extraction protocol also defined with respect to that external frame. Entanglement extraction for Gaussian ground states in such an external frame construction has been shown to require a minimum energy and is hence an interesting process for gravitational physics, where examinations of localization vs energy cost have a long history. General covariance, however, precludes dependence on external frames. In order to enact an extraction protocol in a generally covariant theory, dependence on the external reference frame must first be removed and the states made relational. We examine the implementation of an extraction protocol for Gaussian states, whose center of mass and relational degrees of freedom are entangled, in a relational toy model where translation invariance stands in for full diffeomorphism invariance. Constructing fully relational states and the corresponding extraction/localization can, in principle, be done in two ways. External frame position information can be removed through $G$-twirling over translations or one can spontaneously break the translation symmetry via the gradient of an auxiliary field, or $Z$-model. We determine the energetics of quantum information localization after the states have been made fully relational via both the $G$-twirl and $Z$-model. We also show one can obtain the $G$-twirl construction from a $Z$-model as a limit of positive operator valued measurements.

Retracted: Application of TOPSIS Method Combined with Grey Relational Degree in the Selection of Snow-Melting Agent Use Plan

Retracted: Application of TOPSIS Method Combined with Grey Relational Degree in the Selection of Snow-Melting Agent Use Plan

Making nonlinear systems negative imaginary via state feedback

This paper provides a state feedback stabilization approach for nonlinear systems of relative degree less than or equal to two by rendering them nonlinear negative imaginary (NI) systems. Conditions are provided under which a nonlinear system can be made a nonlinear NI system or a nonlinear output strictly negative imaginary (OSNI) system. Roughly speaking, an input-affine nonlinear system can be rendered nonlinear NI and nonlinear OSNI if it has a normal form with relative degree less than or equal to two after possible output transformation. In addition, if the internal dynamics of the normal form are input-to-state stable, then there exists a state feedback input that stabilizes the system. This stabilization result is then extended to achieve stability for systems with a nonlinear NI uncertainty. A numerical example is provided to illustrate the process of stabilizing an uncertain system using the proposed results.

Robust Control Barrier Functions under high relative degree and input constraints for satellite trajectories

This paper presents methodologies for constructing Control Barrier Functions (CBFs) for nonlinear, control-affine systems, in the presence of input constraints and bounded disturbances. More specifically, given a constraint function with high-relative-degree with respect to the system dynamics, the paper considers three methodologies, two for relative-degree 2 and one for higher relative-degrees, for creating CBFs whose zero sublevel sets are subsets of the constraint function’s zero sublevel set Three special forms of Robust CBFs (RCBFs) are developed as functions of the input constraints, system dynamics, and disturbance bounds, such that the resultant RCBF condition on the control input is always feasible for states in the RCBF zero sublevel set. The RCBF condition is then enforced in a switched fashion, which allows the system to operate safely without enforcing the RCBF condition when far from the safe set boundary and allows tuning of how closely trajectories approach the safe set boundary The proposed methods are verified in simulations demonstrating the developed RCBFs in an asteroid flyby scenario for a satellite with low-thrust actuators.

Tightly related sets and collective degree distribution on hypernetworks

超网络是描述真实世界事物间日趋复杂关系的最一般且无约束的数学模型，其无标度特性是重要的研究内容.超网络无标度特性的研究基础是超度的分布特征，但是超度的定义是着眼于单个节点的.为了探究超网络中广泛存在的群体的特性从而更充分地发掘超网络表示复杂系统的结构优势，本文扩展了超网络中超度和超度分布的概念.在提出的紧密相关集概念的基础之上，给出了组度的定义，进而提出了组度分布的定义.在两个不同的超网络上研究的结果表明，超网络的组度分布呈现出多样的分布特性.本文的研究结果可以充实超图理论的内容，对超网络中群体特性的研究具有借鉴意义，同时也有利于拓宽网络科学的应用范围.

The defect formula

In this paper we present a characterization for the defect of simple algebraic extensions of valued fields. This characterization generalizes the known result for the henselian case, namely that the defect is the product of the relative degrees of limit augmentations. The main tool used here is the graded algebra associated to a valuation on a polynomial ring. Let Kh be a henselization of a valued field K. Another relevant result proved in this paper is that for every valuation μh on Kh[x], with restriction μ on K[x], the corresponding map Gμ↪Gμh of graded algebras is an isomorphism.

Resilience of healthy cities in the post-pandemic era: Findings based on internet of things data and artificial intelligence algorithms

This study aims to improve urban resilience in the face of public health emergencies. Therefore, based on the urban resilience development theory, a resilience evaluation index system for healthy cities is constructed. In addition, the Back Propagation Neural Network (BPNN) algorithm and entropy method are combined to empirically evaluate 7 representative cities in the Yangtze River Delta urban agglomeration. Linear regression analysis is carried out on the index weight of the evaluation system, relative proximity degree, and score of urban resilience. The results reveal that social environment and infrastructure are two important factors in the resilience evaluation of healthy cities. Nanjing and Shanghai have relatively good resilience, while Ma'anshan has the worst resilience. It is also found that economic status is the most critical factor affecting urban resilience. Thus, this study enriches the theories related to urban resilience, expands the evaluation system of urban resilience, and opens up a new approach to the quantitative evaluation of urban resilience.

Stakeholder engagement in coastal adaptation interventions: Insights from the Southwest coast of Nigeria

Coastal areas in developing nations are in a highly precarious situation, making adaptation an urgent policy option for the region. However, since the ultimate success of many implemented adaptation decisions may only be known once the evolving impacts of climate change test them, greater attention may be devoted to the decision-making processes that shape adaptation choices. This study, therefore, focused on the stakeholder engagement process, which as an integral component of the adaptation process, unifies the efforts, commitments, and knowledge of different individuals and groups toward the implementation and success of coastal adaptation projects. The study applied an integrated approach comprising Stakeholder Analysis and Social Network Analysis tools to identify, categorize, and map stakeholders' relationships on the Southwest coast of Nigeria. The result highlights the multiplicity of stakeholders across administrative levels. Furthermore, it shows the disconsolate interest and detachment of statutory stakeholders notwithstanding their powers while portraying the high degree of local relations (autonomous communities and trade associations). The result further highlights the widespread adoption of public consultation as the approach of choice for stakeholder engagement, notwithstanding its flaws. The study's implications are evident in the prevalence of autonomously undertaken adaptation strategies that are overly narrowly focused, disjointed, and counterproductive. Addressing this issue must start with formulating a coastal zone management policy and establishing a coastal zone management agency as the coordinating body for all coastal matters across the study area.

Impact of Individual Spinopelvic Anatomy on the Localization and Severity of Symptomatic Isthmic Spondylolisthesis.

Retrospective analysis of prospectively collected data. Isthmic spondylolisthesis (iSPL) occurs most commonly in L5/S1 and L4/5. This study investigates the association between spinopelvic anatomy and the pathogenesis of iSPL. Spinopelvic parameters as well as severity of slip grade were measured in sagittal spine radiographs of symptomatic patients with iSPL in segments L4/5 and L5/S1. Means were calculated and differences between both groups were analyzed. A correlation between the analyzed parameters and degree of slippage was performed. We included 73 subjects in this study; 11 in L4/5 group and 62 in L5/S1 group. Pelvic anatomy significantly differed between L4/5 and L5/S1 iSPL (Pelvic Incidence (PI) 54.8° vs 66.3°, P value = .006; Pelvic Radius (PR) 124.4mm vs 137.4mm; P value = .005 and Sacral Table Angle (STA) 101.0° vs 92.2°, P value < .001). The relative degree of slippage was significantly higher in the L5/S1 group (L4/5 29.1% vs L5/S1 40.1%, P value .022). We also observed a significant correlation between pelvic anatomy and the severity of the slip in iSPL at the L5/S1 level. Pelvic parameters PI and STA play an important role concerning the level of occurrence and severity of iSPL. Spinopelvic anatomy determines the pathogenesis of iSPL.

The Life Course of Unemployment: The Timing and Relative Degree of Risk

We use the National Longitudinal Survey of Youth 1979 to identify group-based trajectories of unemployment risk as workers age in the United States. Our novel methodological approach reveals 73% of full-time workers spend much of their 20, 30, and 40 s with a relatively low risk of unemployment. The remaining sizable minority varies in the timing and relative degree of their unemployment risk. Eighteen percent experience early career unemployment risk into their early thirties, well after the transition to adulthood. Chronic unemployment characterizes the labor market experiences of the remaining 9%. When expanding the sample to all workers, we find two key differences: the overall prevalence of unemployment is greater each year for all groups and the distribution of respondents across groups differs, with fewer workers experiencing Lower unemployment and more workers experiencing Early Career or Higher unemployment. Unemployment risk is shaped by experiences of long-term unemployment in young adulthood and early labor market constraints. Moreover, while men and women appear equally at risk of Early career unemployment, men are particularly at risk of Higher unemployment. Black workers were significantly more likely to be at risk of Higher unemployment, but only slightly more likely to be at risk of Early career unemployment. Since Early career unemployment risk gives way to steadier work for most, this suggests that some men and some Black workers face disproportionately high levels of employment precarity. Our findings point to the importance of a life course approach for understanding the relationship between unemployment and labor market precarity.

Occurrence of characteristic defects of grinding balls from rejects of continuously cast billets of rail steel

On the basis of metallographic studies, the authors determined the characteristic defects of grinding balls rolled from the rejects of continuously cast billets of K76F rail steel. Relationship of the presence of internal defects of the balls with their impact resistance was established. Defects in the form of internal cracks with accumulations of non-metallic inclusions in the area of their localization and flocks have the greatest impact on the reduction of balls impact resistance. Such defects are the cause of balls destruction during impact resistance tests in 62 and 17 % of cases, respectively. The effect of internal cracks without significant accumulations of non-metallic inclusions and quenching microcracks located along the boundaries of the phase interface was estimated at 12 and 9 %. The regularities and mechanism of influence of the rejects chemical composition of K76F rail steel billets on the probability of destruction of the balls produced from them during impact resistance tests were established. An increase in sulfur content in the billets of the studied rail steel reduces impact resistance of the balls produced from them, as it contributes to formation of non-plastic sulfides that concentrate in the area of internal cracks. An increase in hydrogen content in rail steel naturally contributes to an increase in probability of formation of the flocks, which significantly reduce the balls stability to shock loads. An increase in carbon content in the initial billets affects the increase in probability of destruction of K76F steel balls during copra tests. It is explained by formation of cementite-type carbides when carbon content corresponding to the eutectoid steel is reached. In general, the relative degree of influence of the K76F rail steel chemical composition on impact resistance of grinding balls is 48 %.

Comparison of Antiaromatic Properties in a Series of Structurally Isomeric Naphthothiophene-fused s-Indacenes.

Fusion of aromatic subunits to stabilize an antiaromatic core allows the isolation and study of otherwise unstable paratropic systems. A complete study of a series of six naphthothiophene-fused s-indacene isomers is herein described. Additionally, the structural modifications resulted in increased π-π overlap in the solid state, which was further explored through changing the sterically blocking mesityl group to (triisopropylsilyl)ethynyl in three derivatives. The computed antiaromaticity of the six isomers is compared to the observed physical properties, such as NMR chemical shift, UV-vis, and CV data. We find that the calculations predict the most antiaromatic isomer and give a general estimation of the relative degree of paratropicity for the remaining isomers, when compared to the experimental results.

(De)unionization, trade, unemployment, and wage differentials

AbstractThis research examines the interaction of (de)unionization and trade liberalization in shaping firm productivity, market structure, trade flows, unemployment, and functional distribution (changes in the wage difference and labor income share). It introduces unemployment to the Melitz‐Ottaviano model by considering unionism in the differentiated manufacturing sector and searching frictions in the homogeneous service sector. It shows that unionization has a selection‐softening effect, leading to a non‐monotonic relationship between unionization and the number of firms and unemployment. With international trade, a unilateral increase in the degree of unionization in one country gives rise to a selection‐softening effect for domestic‐only firms and a selection‐toughening effect for exporting firms in this country, resulting in unemployment being more likely to increase relative to autarky. If openness to trade is relatively low (high), then the average wage difference for this country compared to its trading partner country rises (declines). Trade liberalization does not necessarily reduce unemployment, and depends on the relative degree of unionization between the two trading countries. In sharp contrast to the conventional notion, de‐unionization can increase, rather than decrease, the labor income share of unionized workers, provided that openness to trade is sufficiently high.

A Modified Cannulated Cancellous Bone Impactor Is a Helpful Tool During Acetabular Fractures ORIF, a Technical Note

A Modified Cannulated Cancellous Bone Impactor Is a Helpful Tool During Acetabular Fractures ORIF, a Technical Note

To Filter or Not to Filter? Impact on Stability of Delay-Difference and Neutral Equations With Multiple Delays

For control systems where the closed-loop system description is governed by linear delay-differential equations of neutral type, it is known that stability may be fragile, in the sense of sensitive to infinitesimal perturbations to parameters in the system model or arbitrarily small errors in the implementation of the controller. A natural approach to resolve this problem of ill-posedness and to break down the underlying instability mechanisms, rooted in characteristic roots moving from the left plane to the right one via the point at infinity, consists of including a low-pass filter in the control loop, provided the inclusion preserves stability. Independently of the particular control problem, the addition of a low-pass filter essentially boils down to a &#x201C;regularization&#x201D; of delay-difference equations and delay equations of neutral type in terms of parametrized delay equations of retarded type, where the parameter can be interpreted as the inverse of the filter&#x0027;s cut-off frequency. In this paper, the stability properties of these parametrized delay equations are analyzed in a general, multi-delay setting, with focus on the transition to the original delay-difference or neutral equations. It is illustrated that the spectral abscissa may not be continuous at the transition, which may impact stability. Hence, conditions for preservation of stability in terms of a robustified stability indicator called filtered spectral abscissa are presented, for which mathematical characterizations and a computationally tractable expression are provided. The application of a PD controller to a time-delay system with relative degree one is used to motivate the structure of the equations studied throughout the paper, and to explicate the implications of the presented results on control design, discussed in the last section.

Analysis of Research Publication on Logistics at the Time of COVID-19: A Scientometric Study

Abstract: Coronaviruses have a wide range of health, mobility, and economic consequences. The Coronavirus pandemic is an unprecedented incident that has drawn the attention of the general public to supply chain management. It caused severe interruptions between 2020 and 2022. Despite the importance and size of the impact of coronaviruses on research performance across time, the literature on comprehensive coronavirus-related research performance is limited. This study aimed at a scientometric evaluation of bibliographic facts associated with the supply chain during the pandemic, and data related to it was extracted from PubMed between January 2020 and December 2022. The purpose of this research is to examine scientometric methods such as frequency distribution, percentage analysis, relative growth rate, doubling time, and degree of collaboration. We have obtained a total of 116 publications during this study period, and a maximum of 26 (22.4%) contributions were made in the months of May to August 2021. The relative growth rate is declining, and the doubling time is increasing between May to August 2021. Scientifically analysing and comprehending bibliographic facts associated with the supply chain during the COVID-19 pandemic as widely as possible can also assist society in being better prepared for future pandemic breakouts, ultimately supporting informed decision-making in light of societal values. The authors highly advocate the recent COVID-19 epidemic as a call for greater collaborative, worldwide research.

Prony Analysis of Left Ventricle Pressure and Volume.

Direct measurement of cardiac pressure-volume (PV) relationships is the gold standard for assessment of ventricular hemodynamics, but few innovations have been made to "multi-beat" PV analysis beyond traditional signal processing. The Prony method solves the signal recovery problem with a series of dampened exponentials or sinusoids. It achieves this by extracting the amplitude, frequency, dampening, and phase of each component. Since its inception, application of the Prony method to biologic and medical signal has demonstrated a relative degree of success, as a series of dampened complex sinusoids easily generalizes to multifaceted physiological processes. In cardiovascular physiology, the Prony analysis has been used to determine fatal arrythmia from electrocardiogram signals. However, application of the Prony method to simple left ventricular function based on pressure and volume analysis is absent. We have developed a new pipeline for analysis of pressure volume signals recorded from the left ventricle. We propose fitting pressure-volume data from cardiac catheterization to the Prony method for pole extraction and quantification of the transfer function. We implemented the Prony algorithm using open-source Python packages and analyzed the pressure and volume signals before and after severe hemorrhagic shock, and after resuscitation with stored blood. Each animal (n=6 per group) underwent a 50% hemorrhage to induce hypovolemic shock, which was maintained for 30min, and resuscitated with 3-week-old stored RBCs until 90% baseline blood pressure was achieved. Pressure-volume catheterization data used for Prony analysis were 1s in length, sampled at 1000Hz, and acquired at the time of hypovolemic shock, 15 and 30min after induction of hypovolemic shock, and 10, 30, and 60min after volume resuscitation. We next assessed the complex poles from both pressure and volume waveforms. To quantify deviation from the unit circle, which represents deviation from a Fourier series, we counted the number of poles at least 0.2 radial units away from it. We found a significant decrease in the number of poles after shock (p=0.0072vs. baseline) and after resuscitation (p=0.0091vs. baseline). No differences were observed in this metric pre and post volume resuscitation (p=0.2956). We next found a composite transfer function using the Prony fits between the pressure and volume waveforms and found differences in both the magnitude and phase Bode plots at baseline, during shock, and after resuscitation. In summary, our implementation of the Prony analysis shows meaningful physiologic differences after shock and resuscitation and allows for future applications to broader physiological and pathophysiological conditions.