Congruent Transformation Research Articles

Supplemental Stability Criteria with New Formulation for Linear Time-Invariant Fractional-Order Systems

In this paper, new stability criteria for linear time-invariant fractional-order systems (LTIFOSs) based on linear matrix inequalities (LMIs) are derived. The solved variable of the existing LMI formulations is generalized to a complex one. In addition, based on the congruent transformation, a new LMI formulation is obtained, which is different from those in the existing literature. To deal with the above LMIs more conveniently with simulation software, the complex LMIs are converted to equivalent real LMIs. Finally, numerical examples are presented to validate the effectiveness of our theoretical results.

A socially constructed framework for culturally congruent nursing curriculum transformation in Lesotho: A Multi-Methods approach

BackgroundImplementing a transformative nursing curriculum is strategic for a country’s population health outcomes. However, transforming a nursing curriculum is challenging due to the lack of investigation into cultural influences impacting such transformation.Therefore, in order to implement a transformative nursing curriculum, educators need support to explore what a culturally congruent framework would look like. PurposeTo socially construct a framework for culturally congruent nursing curriculum transformation in Lesotho. Methodological approachThis study used a descriptive, qualitative, multiple-method research approach. The transformative learning theory was the theoretical context within the social constructivism research paradigm. The Mmogo-MethodTMand the KAWA technique were methods used for data collection during the study’s two empirical phases. The Mmogo-MethodTM was used to describe cultural influences on curriculum implementation, while the KAWA technique was used to describe the congruency between culture and transformative curriculum implementation. Out of a population of 11, a convenience sample of seven midwifery educators was used for the Mmogo-MethodTM and a criterion purposive samplingselection of 14 nursing educatorsfrom a population of 64 for the KAWA technique. Additionally, a narrative literature review was systematically performed to establisha relationship between culture and transformative curriculum implementation. Findings and interpretationsEmpirical findings from the Mmogo-MethodTM, KAWA technique, and the narrative literature review confirmed that culture might well influence the implementation of a transformative nursing curriculum. The findings were used to draft a framework validated by nursing educators. The three emergent framework concepts were: transformative learning; educators; and students. These three concepts were inter-related throughout the learning process.

H∞ filtering for continuous fractional‐order 2D Roesser model: The 0<α≤1 case

AbstractThis paper investigates the filtering for the continuous fractional‐order (FO) two‐dimensional (2D) Roesser model with the FO between 0 and 1. Firstly, a sufficient condition to ensure the stability and bounded realness in the sense of ‐norm for the continuous FO 2D Roesser model is given in the form of linear matrix inequalities (LMIs). Secondly, based on the bounded real lemmas proposed above, the filtering problem for continuous FO 2D Roesser model is addressed through some congruent transformation and matrix transformation. The results are given in LMI form, and the parameters of the continuous FO 2D filters can be achieved from the LMIs easily. In the end, the effectiveness of the proposed results is verified by two numerical examples.

Cryptosystems Based on Tropical Congruent Transformation of Symmetric Matrices

Recently, public-key cryptography based on tropical semi-rings have been proposed. However, the majority of them are damaged. The main reason is that they use a public matrix to construct commutative matrix semi-rings. New public-key cryptosystems are proposed in this paper. They are based on tropical congruent transformation of symmetric matrix by circular matrix. The NP-hard problem of solving a tropical system of nonlinear equations underlies the cryptosystem’s security. Since a known matrix cannot express the used commutative subsemi-rings of circular matrices and there is no tropical matrix addition operation and power of matrix, the cryptosystems can withstand known attacks, including the KU attack, RM attack, and IK attack. The length of the public key and private key of the new cryptosystems is half that of those described in the literature.

Experimental determination of phase equilibria and phase stability in the Al-U system by using DSC, spot-technique and XRD

The solid-state phase transition, phase stability, invariant equilibria, and liquidus in the system Al-U were investigated experimentally by using DSC, spot-technique, and XRD. The liquidus of the alloys in the composition range from 20 to 100 at.% U were measured for the first time. The measured congruent melting transformation of UAl2 was 1890 ± 2 K. The temperature pertaining to peritectic transformation P1 and P2 were determined to be 1002 ± 8 K and 1604 ± 10 K, respectively. The polymorphic transformation of order α-UAl4 to disorder β-UAl4 was found to be 897 ± 2 K. These values are notably different from previous measurements and are more accurate. Rietveld refinement of the XRD for the alloy composition 18 and 19 at.% U suggests UAl4 is a non-stoichiometric compound with U0.9Al4 stoichiometry. The maximum composition uncertainty estimated by Davies and Gray technique was ± 0.78 at.% U.

Fast Time-Domain Analysis of Darwin Model of Maxwell’s Equations Using Arnoldi-Based Model Order Reduction

The quasi-static approximation that considers inductive–capacitive–resistive effects is referred to as the Darwin model of Maxwell’s equation. However, numerical analysis of the Darwin model is computationally expensive on account of large ill-conditioned equations. In this article, we proposed a new model order reduction technique for the Darwin model of Maxwell’s equations to drastically reduce the computational cost. In this method, four symmetric non-gauged equations were solved to obtain the basis vectors and avoid solving the non-symmetric equations. The reduced-order model (ROM) was obtained through congruent transformation, and time-domain analysis was performed using the time-difference method. We observed that the symmetric ROM was superior to the asymmetric ROM, in terms of accuracy and stability of the time-domain analysis.

Construction and analysis of the quadratic finite volume methods on tetrahedral meshes

A family of quadratic finite volume method (FVM) schemes are constructed and analyzed over tetrahedral meshes. In order to prove the stability and the error estimate, we propose the minimum V-angle condition on tetrahedral meshes, and the surface and volume orthogonal conditions on dual meshes. Through the technique of element analysis, the local stability is equivalent to a positive definiteness of a 9 × 9 element matrix, which is difficult to analyze directly or even numerically. With the help of the surface orthogonal condition and congruent transformation, this element matrix is reduced into a block diagonal matrix, and then we carry out the stability result under the minimum V-angle condition. It is worth mentioning that the minimum V-angle condition of the tetrahedral case is very different from a simple extension of the minimum angle condition for triangular meshes, while it is also convenient to use in practice. Based on the stability, we prove the optimal H1 and L2 error estimates, respectively, where the orthogonal conditions play an important role in ensuring the optimal L2 convergence rate. Numerical experiments are presented to illustrate our theoretical results.

Intermetallic compounds of the Cr–Mn system investigated using in situ powder neutron diffraction: The reported order-disorder transformation of the σ phase elucidated

Cr–Mn system is very important for many applications. In the present work, the reported intermetallic compounds have been studied using in situ high temperature neutron powder diffraction. For the first time, site occupancies in a σ phase are obtained as a function of temperature by Rietveld analysis. They are compared with calculated data obtained from DFT. The previously reported order-disorder transition in the σ phase around 1000 °C is shown to be in fact a congruent phase transformation to the bcc Cr–Mn solid solution. This solid solution is probably continuous between pure Cr and δ-Mn. The second reported intermetallic α’ phase (Cr2Mn3) phase is shown to be in fact a ternary nitride of the Cr–Mn–N system that should not appear in the binary phase diagram. The present work clarifies and explains all the features of the previous literature on this system and brings major revisions to the phase diagram. General conclusions are drawn concerning mistakes that can be done in the evaluations of phase diagrams.

On Smith normal forms of q-Varchenko matrices

In this paper, we investigate q-Varchenko matrices for some hyperplane arrangements with symmetry in two andthree dimensions, and prove that they have a Smith normal formover Z[q]. In particular, we examine the hyperplane arrangement forthe regular n-gon in the plane and the dihedral model in the spaceand Platonic polyhedra. In each case, we prove that the q-Varchenko matrix associated with the hyperplane arrangement has a Smith normal form over Z[q] and realize their congruent transformation matrices over Z[q] as well.

The Cartesian elastodynamics linear model of mechanical systems with flexible links

The linearized Cartesian elastodynamics model of mechanical systems with flexible links is introduced in this paper to simplify its counterpart n-dof generalized model. The stiffness is represented by means of Lončarić’s 6 × 6 Cartesian stiffness matrix (CSM), the inertia by what von Mises termed the inertia dyad, i.e., the 6 × 6 Cartesian mass matrix (CMM). This model applies to a mechanical system with compliant components. Furthermore, the Cartesian frequency matrix (CFM) is defined as a congruent transformation of its stiffness counterpart, the transformation matrix being the inverse of the square root of the positive-definite CMM. The CFM thus defined is dimensionally-homogeneous, symmetric and at least positive-semidefinite. Upon the eigenvalue decomposition of the same matrix, the natural frequencies and the corresponding natural modes, i.e., the eigenscrews of the system, are obtained. The physical meaning of the CFM, together with that of its eigenvalues and eigenscrews, are given due interpretation in the paper, within the context of screw theory. This matrix is intended to serve as a useful tool for the elastodynamics analysis and design of a large class of multibody systems with flexible components, especially at the early design stages.

Dynamic output-feedback control for singular interval-valued fuzzy systems: Linear matrix inequality approach

This paper introduces an admissibilization condition for singular interval-valued fuzzy systems with a dynamic output-feedback controller using a linear matrix inequality approach. The derivation of the admissibility criterion (satisfying regularity, non-impulsiveness and stability) for the closed-loop system of the singular interval-valued fuzzy systems using the dynamic output-feedback controller is concerned. Here, the derived criterion is represented as the parameterized matrix inequalities depending on the membership functions of the system and the controller. To relax the derived parameterized matrix inequalities, this paper proposes a relaxation lemma based on the properties of the membership functions and their relations. By using this lemma, the parameterized matrix inequalities are converted into the matrix inequalities independent of the membership functions but not convex. Therefore, by introducing the structures of the variables and the congruent transformation matrix, a sufficient condition for the admissibility criterion is successfully given in terms of strict linear matrix inequalities. Two numerical examples are given to show the effectiveness of the proposed control.

A Systematic Review: Location-Limited SNSs Research and Psychological Well-Being

The turn of the 21st century witnessed an unprecedented surge in the use of Social Network Sites (SNSs). The developing world also experienced a similar congruent networking transformation in terms of employment of the emerging SNN tools. Correspondingly, research magnitude on the implication of SNSs use has also grown exponentially with recommendations for conducting studies in less privileged countries. The present systematic review is based on doctoral research aimed to present the status of SNSs studies and psychological well-being in both developing and developed countries. The review analyzed thirty-two location-limited articles–conducted in developed countries like the USA—published from 2005 to 2018 and focused on the relationship between SNSs usage and users’ psychological well-being. Given the limitations of the available literature, the review also recommended suggestions for future directions in investigations and studies on the subject.

ETNOMATEMATIKA PADA KELENTENG TJOE TIK KIONG PASURUAN SEBAGAI BAHAN PAKET TES SISWA SMP KELAS VIII

The purpose of this study was to determine what ethnomatematics in the Tjoe Tik Kiong Temple and produce a test package related to ethnomatematics in the Tjoe Tik Kiong Temple. This temple is a place of worship for the Tri Dharma people in Pasuruan City. This type of research is qualitative research with an ethnographic approach. The subjects of this study were one religious leader and one handyman. Data collection methods used are observation and interviews. In this study focused on several objects of building and carving shapes. Mathematical concepts that emerged in the Tjoe Tik Kiong Temple building were geometric, congruent, similarity and geometric transformation. The product made is a test package related to ethnomatematics at the Tjoe Tik Kiong Temple in Pasuruan. This test package is intended for junior high school grade VIII

Modeling of Complex Planetary Gear Sets Using Power-Oriented Graphs

In this paper, a systematic approach for the dynamic modeling of complex planetary gear sets is presented. The approach relies upon a set of rules for building the system matrices and vectors of the system full dynamic model for any planetary gear set. A congruent state-space transformation is applied to obtain a reduced-order rigid model of the system, which allows for faster simulations. The behavior of the tangential forces accounting for the gears interactions is proven to be obtained from the reduced-order model. Furthermore, the kinematic relations of the considered planetary gear set are automatically generated when developing the reduced-order rigid model. As an example, two systems of interest in the vehicle industry are then modeled with the proposed approach and simulated in Matlab/Simulink: a Ravigneaux planetary gear set and a double-stage planetary gear set.

지식의 구조로서 변환기하를 다루기 위한 성취기준 방향 탐색

While Korean students learn more about Euclidean geometry earlier than other countries, they learn transformation geometry less. Therefore, in this study, we proposed a way to find consistency and systematicness of the geometric curriculum in Korea, focusing on transformation geometry. For this reason, the importance of transformation geometry was discussed in terms of the structure of knowledge. Also, we analyzed the transformation-based perspective expressed in the curriculum standards of the Common Core State Standards for Mathematics(CCSSM) and the Korean 2015 revised mathematics curriculum in terms of curriculum articulation. As a result, the topics of transformation geometry that can be dealt with in school geometry were “congruent transformation”, “symmetry”, “similar transformation”, and “analytic approach to transformation”. In the case of CCSSM, the standards for each topic were structured to have a curriculum articulation, but in the case of Korea, the curriculum articulation of each topic was insufficient. Among the topics of transformation, 'similar transformation' was selected, which is important but not emphasized in Korea, and suggested what can be changed when the relevant standards are systemized into a transformation-based perspective.

Event-Triggered Distributed State Estimation for Cyber-Physical Systems Under DoS Attacks.

This article investigates the event-triggered distributed state estimation problem for a class of cyber-physical systems (CPSs) with multiple transmission channels under denial-of-service (DoS) attacks. First, an observer-based event-triggered transmission scheme is proposed to improve the transmission efficiency, and the corresponding distributed Kalman filter is designed to estimate the system states. Under the collective observability condition, a relationship between estimation error covariance, attack intensity, and transmission efficiency is established by utilizing the covariance intersection fusion method and the property of matrix congruent transformation rank. The important features that distinguish our work from others are that the considered DoS attacks compromise each channel independently and do not have to satisfy the probabilistic property of the packet loss process. Furthermore, an event-triggered communication scheme is considered to improve the utilization of network resources between filters, and a sufficient condition for the parameter design is given which takes into account the influence of DoS attacks. Finally, simulation results are provided to verify the effectiveness of the proposed methods.

Non-conventional transformation pathways and ultrafine lamellar structures in γ-TiAl alloys

The mechanical properties of two-phase γ-TiAl alloys depend strongly on the scale of their lamellar microstructures. In this study, we investigate the effect of alloy composition on lamellar thickness in Ti100-xAlx by simulating microstructural evolution during the α2′ → α2 + γ phase transformation using the phase field method. From both existing experimental data and our simulation results we find that the average thickness of γ lamellae first decreases and then increases with increasing Al content. Further analyses reveal that this unique composition-dependence of the lamellar thickness could be associated with non-conventional pseudospinodal decomposition and congruent structural transformation mechanisms that generate ultra-high densities of nuclei at the initial stage, which impacts the later growth processes. The interplay between the number density of nuclei and the number of coalescence events during growth results in the non-monotonic dependence of the lamellar thickness on the alloy composition. These findings may offer new insights on the design of ultrafine lamellar microstructures for γ-TiAl alloys.

Fault detection filter design for interval type-2 fuzzy systems under a novel adaptive event-triggering mechanism

ABSTRACTThis study is concerned with the problem of event-based fault detection (FD) filter design for interval type-2 fuzzy systems in a network environment. Firstly, by employing the properties of exponential function, a novel adaptive event-triggering mechanism (AETM) where the boundedness of threshold function is guaranteed and the size of threshold function is inversely proportional to the size of 2-norm of the sampled-output-error is proposed to dynamically adapt the variation of the system and to reduce the unnecessary information communication between the sensor and the filter. Secondly, in the framework of time-delay systems, the FD system with a networked filter and an AETM is modelled as an interval time-varying delayed system. Then, a sufficient condition to implement co-design of the parameters of filter and trigger is obtained by applying a simple Lyapunov–Krasovskii functionals, combined with recently developed Wirtinger-based integral inequality and reciprocally convex inequality, and utilising congruent transformation method. Thirdly, based on the obtained co-design condition, an optimisation algorithm subject to convex constraints for the tradeoffs between resource utilisation and performance of the FD system is further developed. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed scheme.

Decentralized Finite-time [formula omitted] tracking control for a class of interconnected Markovian jump system with actuator saturation

An observer-based decentralized tracking control technique is developed for a saturated interconnected Markovian jump system in the sense of finite-time stability (FTS). To improve tracking performances, a L2−L∞ performance criterion which is relevant to both estimated error and estimated tracking error is proposed. A sufficient condition for finite-time bounded (FTB) is established. In view of the obtained condition, a method with the one-step procedure to seek the gains of observer and controller is investigated. By virtue of this procedure, the problem of the decentralized tracking stabilization is transformed into a convex optimization problem subject to constraints in the form of linear matrix inequalities (LMIs). Furthermore, the tracking control problem of interconnected Markovian jump system without saturation is also investigated, and the results are obtained directly to avoid taking congruent transformation. Simulation is presented to show the effectiveness and applicability of the obtained results.

Mixed [formula omitted] state estimation for switched genetic regulatory networks subject to packet dropouts: A persistent dwell-time switching mechanism

In this work, a kind of switched gene regulatory networks with packet dropout and uncertainties are constructed by switched coupled nonlinear difference equations. In comparison, a more comprehensive switching regulation, persistent dwell-time, is employed to it. The aim is to construct a mixed mode-dependent and mode-independent estimator for the before-mentioned gene regulatory networks with a view to the loss of system modal information. Thereafter, the augmented system is established. After that, the sufficient conditions of the exponential stability and mixed H∞/l2−l∞ performance for the augmented system are deduced by the switching Lyapunov theory. Finally, a numerical example is employed to elucidate the validity of the estimator gains decoupled by the congruent transformation.