Argument Principle Research Articles

Cauchy’s Residue Theorem and Its Application

One of the key theorems in complex analysis, Cauchy’s Residue Theorem, which refers to the integral value of an analytic function along any simple closed contour surrounding an isolated singularity in a certain ring domain divided by 2πi, will greatly simplify the process of computing integrals on contour surrounding singularities. In the field of basic mathematics, the Cauchy’ Residue Theorem plays a key role in the integral calculation of analytic functions, nonuniform complex functions and the argument principle, which establishes a connection between a curve’s winding number and the quantity of zeros and poles inside the curve. Furthermore, Residue Theorem can combine with various subjects, including electromagnetism. This paper gives an overview of the Cauchy’s Residue Theorem and its application. Firstly, it talks about the definition and proof of the Cauchy’ Residue Theorem, along with the definition of residue. Then two examples of using Residue Theorem to integrate functions will be given. Finally, this paper involves application of Residue Theorem in trigonometric sum identities and a remark on the method.

On the structure of the matrix in Sturm algorithm for determining the number of zeros in the open unit disk for a real polynomial

In 1984, C.W Schelin presented a numerical method for calculating the number of zeros of a real polynomial inside the unit disk using the argument principle and Cauchy index on [-1, 1] inspired by sturm’s algorithm [3], this method is based on calculation of the generalized Sturm sequence in Chebyshev form, however in some cases this algorithm does not efficient for this reason, it has been modified in another works [1], [2]. There are other numerical algorithms for calculating the number of zeros of a polynomial in the unit disk like shur -Cohn and Marden-Cohn but the numerical method presented in this study [1] is more efficient in cost of elementary operations (o (n2)). In this paper, we propose to improve this algorithm [1], to do this we study the matrix structure involved in the calculation of chebychev polynomials, for there on we prove that is a Toeplitz matrix which is known for their important properties in the complexity of calculations and we calculate its last line which is necessary to define the whole matrix to solve the linear system for calculating polynomials which are necessary to obtain Chebyshev sequence, this result will reduce calculation steps in this method [1]. This numerical algorithm may operate to study the stability of dynamical systems [2].

226. PHILOSOPHICAL CONSIDERATIONS IN SURGICAL INNOVATION

Abstract Background Innovation in surgery has been viewed as synonymous with progress. This is not always the case as many new innovative processes, devices and techniques do not yield same results in "real world" as they do in the experimental stage. The purpose of this presentation is to discuss the role of philosophical experiment in the process of appraisal of surgical innovation. Methods A thought experiment was conducted analysing past surgical innovations. Introduction of electrosurgery, laparoscopic cholecystectomy, surgical safety checklist and laparoscopic aortic aneurysm repair were tested. All consequences (known and hypothetical) of these innovations were considered in attempt to establish a more holistic metric of success. Results Significant limitations exist in the current assessment methods of innovation "success" which is commonly defined based on the results of a study of chosen pre-set metrics (main outcome). The utility of key metric used to assess innovation (e.g. lengths of hospital stay or visual pain scores) is limited by the choice of these outcomes. This reduces the changes of detecting rate, but possibly, much more significant unintended effects both advantageous and harmful (e.g. discovery of insulin vs thalidomide). The magnitude of detectable change is dictated by practicality of powering controlled studies and exposes results to the sensitivity bias. Unanticipated effects of the innovation are frequently not discovered until it is adopted on a large scale. Various outcomes of innovation are non-commensurable and further complicate the definition of "success". A novel innovation outcome assessment process is proposed: net global utility, a composite outcome measure which considers all potential effects of innovation (clinical, social, economic, ethical and other). Net global utility is a subjective measure that allows observer to compare non-commensurable values by not using them in isolation. One of the main advantages of net global utility is that it only requires knowledge of available metrics and principles of logical argument, providing an easy assessment tool to boost local oversight of introduction of innovation and policy-making. It includes calculation of risk (probability x consequence) which allows to account for improbable but highly consequential outcomes. Net global utility is compared to the best available alternative and derives internal face validity from this. Net global utility encompasses potential incidental future benefits as well as assessment of innovation against the test of justice. Conclusion Defining success in surgical innovation can be challenging. The use of thought experiment and logical argument is described to introduce a novel metric "net global utility" allowing for composite assessment of innovation success. Various previous surgical innovations used to demonstrate the application of the net global utility.

An optimization‐based method for robust stabilization of linear delay systems

AbstractThis paper investigates the robust stabilization problem of linear delay systems with parametric uncertainty. First, by means of the argument principle, a delay‐dependent sufficient condition is derived for designing a feedback controller, with which the closed‐loop system can achieve robust stability. Then, based on the fundamental matrix of the linear delay systems, a constrained optimization problem is formulated for solving the feedback gain matrices. The effectiveness of the proposed method is verified by some simulation results.

A global argument-based algorithm for finding complex zeros and poles to investigate plasma kinetic instabilities

Root-finding is a common problem in various fields of physics and mathematics. The basic version of this problem can be formulated as an equation f(z)=0 where z∈ℂ and f is a meromorphic function on a complex plane ℂ. In some cases, a conjugated problem has to be solved as well to investigate the properties of the inspected system: f(z)−1=0. Iterative Householder-like methods show high convergence rate, however, the convergence itself is strongly dependent on the input parameters such as an initial guess. If the function f is complicated enough, there can be no prior information about its zeros and poles, and thus, no way to correctly pick the initial guess. The aim of the algorithm proposed in this article is to find all zeros and poles inside a selected region without any information about the local behavior of the function f. Additionally, the method is generalized to a parametric problem with continuous solutions: f(z)→f(z;p) where p∈Rd, d∈N∪{0}. The basis of the algorithm consists of a triangulation process and an implementation of the Cauchy’s argument principle to inspect the constructed subregions. The refinement process is accompanied by an absolute value gradient ∇ln|f| analysis that significantly decreases the number of points needed to correctly identify the locations of all zeros and poles. The algorithm is presented as a hybrid class for d∈{0,1} that can be directly used to solve corresponding problems.

Algebraic winding numbers

In this paper, we propose a new algebraic winding number and prove that it computes the number of complex roots of a polynomial in a rectangle, including roots on edges or vertices with appropriate counting. The definition makes sense for the algebraic closure C=R[i] of a real closed field R, and the root counting result also holds in this case. We study in detail the properties of the algebraic winding number defined in [3] with respect to complex root counting in rectangles. We extend both winding numbers to rational functions, obtaining then algebraic versions of the argument principle for rectangles.

Analytical solution of fractional oscillation equation with two Caputo fractional derivatives

Analytical solution of initial value problem for the fractional oscillation equation with two Caputo fractional derivatives , where the coefficients and orders satisfy and , is investigated by using the Laplace transform and complex inverse integral method on the principal Riemann surface. It is proved by using the argument principle that the characteristic equation has a pair of conjugated simple complex roots with a negative real part on the principal Riemann surface under the assumption that and are not both integers. Then three fundamental solutions, the unit impulse response, the unit initial displacement response, and the unit initial rate response, are derived analytically. Each of these solutions is expressed into a superposition of a classical damped oscillation decaying exponentially and a real Laplace integration decaying in a negative power law. Finally, the asymptotic behaviors of these analytical solutions for sufficiently large are determined as monotonous decays in a power of negative exponent.

Teach the Crisis: arguments for teaching the Cartoon Crisis in primary school

ABSTRACT The proposal to turn the so-called Cartoon Crisis into the obligatory history curriculum of the primary school system has been debated publicly over the years. Pros and cons regarding its integration into a teaching environment have been put forward. Since 2021, the proposal has also been formally debated as a bill and put to vote in the Danish parliament two times – each time voted down by the current government. Despite the bill’s defeat, I present here a number of principled arguments for making the so-called Cartoon Crisis (including the actual drawings) an obligatory teaching subject in the Danish school system. The arguments can be summed up as an encouragement to ‘Teach the Crisis’. Choosing not to include the Crisis and its primary sources in the teaching will only instal the proverbial elephant in the classroom and is probably a short-term solution for the cultural, social, and political challenges that Denmark will meet in the future.

An adaptive feature mode decomposition based on a novel health indicator for bearing fault diagnosis

In this paper, a novel scheme for detecting bearing defects is proposed utilizing single-valued neutrosophic cross-entropy (SVNCE). Initially, the artificial hummingbird algorithm (AHA) is used to make the feature mode decomposition (FMD) adaptive by optimizing its parameter based on a novel health indicator (HI) i.e. sparsity impact measure index (SIMI). This HI ensures full sparsity and impact properties simultaneously. The raw signals are decomposed into different modes by adaptive FMD at optimal values of its parameters. The energy of these modes is calculated for different health conditions. The energy interval range has been decided based on energy eigen which are then transformed into single-valued neutrosophic sets (SVNSs) for unknown defect conditions. The minimum argument principle employs the least SVNCE values between SVNSs of testing samples and SVNSs of training samples to recognize the different defects in the bearing. The proposed methodology is applied to bearing from industrial mechanical systems.

Revisit Impedance-Based Stability Analysis of VSC-HVDC System

According to different partitioning styles, there exist different impedance-based stability analysis methods for complex systems such as voltage source converter (VSC)-based high-voltage direct current (HVDC) systems. Thus, the determination of the partitioning method is of importance in impedance-based stability analysis. However, how to partition a complex system is not paid much attention in the past. In this paper, the partitioning problems are revisited and a set of practical partitioning principles are proposed. Based on the principles, the VSC-HVDC system is partitioned into five parts, satisfying simplicity and integrity. In addition, the methods to form the equivalent circuits of the sub-systems are given and the equivalent circuits of the sub-systems are built, which is helpful to obtain the input-output models of the sub-systems. Furthermore, a stability criterion by directly applying the argument principle is used instead of the generalized Nyquist criterion (GNC), which could avoid the calculation of eigenvalue transfer functions, especially when a large number of sub-systems are involved. Finally, the correctness of the impedance-based stability analysis method is verified by control hardware-in-loop (CHIL) experimental results.

Consensus control of multi-agent systems with delays

<p>This paper concerns the consensus problem of linear time-invariant multi-agent systems (MASs) with multiple state delays and communicate delays. Consensus control is widely applied in spacecraft formation, sensor networks, robotic manipulators, autonomous vehicles, and others. By introducing a linear transformation, the consensus problem of the delayed MAS under an undirected network was converted into a robust asymptotic stability problem associated with the eigenvalues of the normalized Laplacian matrix of the network. By means of the argument principle and optimization technologies, a numerical controller design method was presented for the delayed MAS to reach consensus. The effectiveness of the proposed approach was illustrated by some numerical examples. The proposed approach may be applied to multi-agent systems with distributed delays.</p>

The development of pre-service teachers’ argumentation self-efficacy through argumentation-based chemistry instruction

This research aimed to examine the impact of argumentation-based chemistry instruction on the argumentation self-efficacy of pre-service teachers' (PSTs’) and their perceptions regarding the effectiveness of this instruction on their argumentation self-efficacy. This exploratory study involved a cohort of PSTs who actively participated in a series of argumentation-based chemistry activities facilitated by their classroom teacher over an 11-week period, with each activity spanning 1 or 2 weeks. The introduction of argumentation preceded the exploration of chemistry topics, including heat and temperature, gas laws, physical and chemical change, solubility, distinctive properties of matter, chemical reactions, and acids-bases. Data sources comprised the self-efficacy scale for argumentation, the evaluation of instruction for enhancing self-efficacy survey, and semi-structured interviews. The findings revealed an increase in PSTs' self-efficacy for argumentation after 11 weeks of argumentation-based chemistry instruction. These results suggest that PSTs can significantly enhance their self-efficacy for argumentation when provided with instruction tailored to incorporate argumentation principles.

Quantitative homogenization of principal Dirichlet eigenvalue shape optimizers

AbstractWe apply new results on free boundary regularity to obtain a quantitative convergence rate for the shape optimizers of the first Dirichlet eigenvalue in periodic homogenization. We obtain a linear (with logarithmic factors) convergence rate for the optimizing eigenvalue. Large scale Lipschitz free boundary regularity of almost minimizers is used to apply the optimal homogenization theory in Lipschitz domains of Kenig et al. A key idea, to deal with the hard constraint on the volume, is a combination of a large scale almost dilation invariance with a selection principle argument.

Comparison results for a nonlocal singular elliptic problem

We provide symmetrization results in the form of mass concentration comparisons for fractional singular elliptic equations in bounded domains, coupled with homogeneous external Dirichlet conditions. Two types of comparison results are presented, depending on the summability of the right-hand side of the equation. The maximum principle arguments employed in the core of the proofs of the main results offer a nonstandard, flexible alternative to the ones described in (Arch. Ration. Mech. Anal. 239 (2021) 1733–1770, Theorem 31). Some interesting consequences are L p regularity results and nonlocal energy estimates for solutions.

The Non Instrumental Value of Abilities: The Argument and Difficulties of Aristotelian Principle in A Theory of Justice

The Non Instrumental Value of Abilities: The Argument and Difficulties of Aristotelian Principle in A Theory of Justice

ROAD2H: Development and evaluation of an open-source explainable artificial intelligence approach for managing co-morbidity and clinical guidelines.

Clinical decision support (CDS) systems (CDSSs) that integrate clinical guidelines need to reflect real-world co-morbidity. In patient-specific clinical contexts, transparent recommendations that allow for contraindications and other conflicts arising from co-morbidity are a requirement. In this work, we develop and evaluate a non-proprietary, standards-based approach to the deployment of computable guidelines with explainable argumentation, integrated with a commercial electronic health record (EHR) system in Serbia, a middle-income country in West Balkans. We used an ontological framework, the Transition-based Medical Recommendation (TMR) model, to represent, and reason about, guideline concepts, and chose the 2017 International global initiative for chronic obstructive lung disease (GOLD) guideline and a Serbian hospital as the deployment and evaluation site, respectively. To mitigate potential guideline conflicts, we used a TMR-based implementation of the Assumptions-Based Argumentation framework extended with preferences and Goals (ABA+G). Remote EHR integration of computable guidelines was via a microservice architecture based on HL7 FHIR and CDS Hooks. A prototype integration was developed to manage chronic obstructive pulmonary disease (COPD) with comorbid cardiovascular or chronic kidney diseases, and a mixed-methods evaluation was conducted with 20 simulated cases and five pulmonologists. Pulmonologists agreed 97% of the time with the GOLD-based COPD symptom severity assessment assigned to each patient by the CDSS, and 98% of the time with one of the proposed COPD care plans. Comments were favourable on the principles of explainable argumentation; inclusion of additional co-morbidities was suggested in the future along with customisation of the level of explanation with expertise. An ontological model provided a flexible means of providing argumentation and explainable artificial intelligence for a long-term condition. Extension to other guidelines and multiple co-morbidities is needed to test the approach further.

Non-stability of a bogie moving along a specific infinite complex flexibly beam-layer structure

A comprehensive investigation was conducted to analyze the vibration stability of a bogie that moves uniformly along a complexly modeled flexibly supported infinite Reddy-Bickford coupled beam system situated on a viscoelastic base. The bogie was simulated as a non-deformable body of finite length, connected through a specific system of two springs and two dampers with identical stiffness and damping, interacting with masses within a complex beam-layer system commonly encountered in technical practice. These masses, through which the bogie interacts with the high-order shear deformable beam-layer system, form part of a mechanical system consisting of a double oscillator in constant contact with the infinitely long flexible structure. As it is well-known that when the velocity of masses, such as the bogie or any other complex oscillator, exceeds the minimum velocity at which waves propagate in the beam, the system's oscillation may become unstable, it is crucial to determine the conditions and stable regions of motion that involve specific combinations of system parameters. The region of instability is identified within the parameter space of the system using the D-decomposition technique and the argument principle. A comprehensive analysis was conducted to investigate the impacts of the viscous damping in the supports of the bogie, the mass of the bogie bar, and the wheelbase on the stability of the model. The derived conclusions, focused on determining the stable regions of motion based on the considered parameters, represent a significant novelty and contribution to the research previously unknown for the motion system of a bogie along a complexly modeled flexibly supported infinite high-order shear deformable coupled beam-layer system on a viscoelastic base.

Legal argumentation in the court: native experience and foreign practice

The article is devoted to highlighting domestic experience and foreign practice of legal argumentation in court proceedings. The Great Legal Encyclopedia defines legal argumentation as the process of giving arguments legal meaning and establishing relationships between them, which acquires jurisprudence. forms when harmonizing logical rules with legal norms.
 It is stated that legal reasoning in court decisions is mandatory, since the acceptability of legal decision- making depends on the procedures of argumentation and the desire to achieve the truth in law. Therefore, the justice of court decisions is determined by their compliance with the requirements of legality, reasonableness and motivation.
 It is established that an argument is a statement containing premises and a conclusion, not all of which are expressed in real arguments. In legal argumentation, evidence is an auxiliary tool of argument.
 In practical discourse, in order to achieve the criteria of rationality and correctness, there is often a need to apply special knowledge, the bearers of which are experts. Opinions of experts provided within the limits of the examination appointed by the court are sources of evidence.
 Evidence must be proper, admissible, reliable, sufficient. That is why forensic experts involved in the judicial process must possess the skills of argumentation and oral communication, be professional, authoritative, and their conclusions substantiated and impartial. That is, the rules of legal discourse and the principles of legal argumentation necessarily apply to the judicial expert, who appears as one of the subjects of argumentation.
 It was found that domestic courts do not always trust the conclusions provided by experts. The results of a psychophysiological diagnosis of a person using a polygraph do not provide advantages in proof, but «are taken into account, along with other evidence».
 Involvement of experts in the legal process does not always provide grounds to include the conclusions they provide in the evidence base, let alone consider them as real arguments. There is a need for legislative regulation of the issue of the possibility of the participation of a polygraph specialist in the legal process.
 The evidence practice was outlined and the role of expert witnesses in Italy was clarified. Thus, in Italian civil proceedings there are two types of experts: the judicial technical expert appointed by the judge (CTU) and the expert appointed by the parties (CTP). The expert should not have any interests related to the proceedings. The appointed expert must agree to his own appointment and can reject it only for valid reasons assessed by the judge.

Dynamics of moving coupled objects with stabilizers and unconventional couplings

A comprehensive investigation was carried out to analyze the vibration stability of a coupled bogie system moving uniformly along a complexly modeled flexibly supported infinite high-order shear deformable coupled beam system on a viscoelastic base. The main contribution of this study involves a comparative analysis of the specific coupling of the bogie system with and without the proposed additional stabilizer, in comparison to conventional cases. The study demonstrates significant benefits of the newly proposed options of dual coupling and additional stabilizers in terms of stability. Another contribution of the study is the feasibility of the proposed unconventional models in technical practice. A phenomenon has been discovered that increasing the viscous damping in a special coupling leads to the occurrence of motion instability in the mechanical system. The paper also presents a novel technical solution for connecting moving objects at high speeds. The benefits of the additional oscillator as a stabilizer are extensively illustrated through numerous different examples. It is well-known that when the velocity of masses, such as the bogie or any other complex oscillator, exceeds the minimum velocity at which waves propagate in the beam, the oscillation of the system may become unstable. Therefore, it is crucial to determine the conditions and stable regions of motion that involve specific combinations of system parameters. The region of instability is identified within the parameter space of the system using the D-decomposition technique and the argument principle. The bogie is specifically connected to another bogie in two new ways: with an additional stabilizer allowing double transverse displacement and providing an additional contact with the base, or with a specific coupling that enables simultaneous rotational and transverse displacement at the contact point. The analysis reveals two key findings. First, the additional mechanical stabilizer allows for the widest range of permissible suspension stiffness (largest stability region) when the connection is conventional. Second, enabling transverse displacement in the couplings results in a stable regime of motion at much lower suspension stiffness compared to other cases.

Physician Ownership for the Virtuous Practice of Medicine.

The shift from physicians as owners or shareholders of practices to being employees of corporations is now a widespread trend with over 50% of physicians now considered employees. If continued, this trend will have profound effects on the medical profession and on physicians' personal lifestyles and sense of agency. However, ownership is not a morally neutral consideration but is important for safeguarding the traditions of virtue in the medical profession. Virtue develops within localized communities of practice and thrives in settings that embody principles such as solidarity, subsidiarity, and participation found in Catholic social teaching. Ownership increases physicians' investment in moral communities where they practice, affording physicians greater agency to benefit these communities according to their best judgment. This ownership can vary by type of organization and degree of shareholding. Because moral communities are the settings in which physicians form virtue, and ownership increases physicians' commitment and investment in communities, I make a principled argument that physicians who value developing virtue should consider having ownership of their practices when planning their careers. Ownership will be an important aspect of any medical ethics based on virtue rather than on principlism.