Discontinuous Systems Research Articles

Quantum Inference Fuzzy Rules Network Model Free Adaptive Control for Discontinuous Derivative Discrete-Time Systems

Quantum Inference Fuzzy Rules Network Model Free Adaptive Control for Discontinuous Derivative Discrete-Time Systems

A Fixed-/Preassigned-Time Stabilization Approach for Discontinuous Systems Based on Strictly Intermittent Control

A Fixed-/Preassigned-Time Stabilization Approach for Discontinuous Systems Based on Strictly Intermittent Control

Comparative study of virgin olive oil from Moroccan Picholine cultivars in TADLA perimeter -Morocco

Olive oil, extracted from olive fruits (Olea europaea), is renowned for its distinctive flavour, nutritional richness and health benefits. The aim of this comparative study is to analyze olive oil from several TADLA perimeter units, including Province of AZILAL, FQUIH BEN SALAH, BENI MELLAL, ZAOUIT CHEIKH, and BRADIA. The oil under investigation was extracted from olives of the Moroccan Picholine variety, by a discontinuous system including grinding, pressing and decanting. Significant variations were found at the values of the studied parameters. The results of our study showed that Olive oil from FBS and BM are classified as an extra virgin olive. However, olive oils from ZC, BR and AZ are classified as virgin olive oil. Sample from FQUIH BEN SALAH province had the lowest Free Fatty Acids (FFA) and peroxide values 0.236% oleic acid and 3.434 méqO2/Kg respectively. While the highest FFA value found was the olive oil obtained from AZILAL (1.084% Oléic Acid) and the highest Peroxide value was obtained in the sample from BRADIA (8.108 méq O2/Kg). E232, E270 and delta K values of all samples were under the limit fixed by IOC for virgin olive oil. Polyphenols content of ZAOUIT CHEIKH, FQUIH BEN SALAH and BRADIA oils are relatively high with values equal to 1.347, 1.082, and 1.141mg GA/100ml extract respectively. DPPH test showed that ZAOUIT CHEIKH oil had the greater antioxidant capacity.

Fixed-Time Control and Estimation of Discontinuous Fuzzy Neural Networks: Novel Lyapunov Method of Fixed-Time Stability.

This article considers the fixed-time stability (FXTS) issue for discontinuous system described by differential equation (DE) with time-varying parameters. Using the tool of differential inclusion (DI), several improved FXTS criteria and estimation formulas of settling time (SET) are derived by employing a relaxed Lyapunov method. The special novelty of the developed Lyapunov method is that the derivative of Lyapunov function possesses indefiniteness. As an important application, the established FXTS theorems are utilized to deal with fixed-time (FXT) synchronization issue for fuzzy neural networks (FNNs) possessing state discontinuity, where the fuzzy operation is used in the synaptic law computing, and one typical time-varying switching control protocol is designed. Moreover, a series of estimations of SET for FXT synchronization are given out. Finally, the simulation examples are present to substantiate the validity of the obtained results.

Method for Finding Solution to Nonsmooth Differential Inclusion of Special Structure

The paper explores the differential inclusion of a special form. It is supposed that the support function of the set in the right-hand side of an inclusion may contain the maximum of the finite number of continuously differentiable (in phase coordinates) functions. It is required to find a trajectory that would satisfy differential inclusion with the boundary conditions prescribed and simultaneously lie on the surface given. Such problems arise in practical modeling discontinuous systems and in other applied ones. The initial problem is reduced to a variational one. It is proved that the resulting functional to be minimized is superdifferentiable. The necessary minimum conditions in terms of superdifferential are formulated. The superdifferential (or the steepest) descent method in a classical form is then applied to find stationary points of this functional. Herewith, the functional is constructed in such a way that one can verify whether the stationary point constructed is indeed a global minimum point of the problem. The convergence of the method proposed is proved. The method constructed is illustrated by examples.

Existence and uniqueness of Carathéodory and Filippov solutions for discontinuous systems of differential equations

Existence and uniqueness of Carathéodory and Filippov solutions for discontinuous systems of differential equations

Some Applications Related to Differential Inclusions Based on the Use of a Weighted Space

In this paper, we present an existence theorem for the problem of discontinuous dynamical system related to ordinary differential inclusion, based on the use of the concepts related to weighted spaces introduced by Gorka and Rybka, without using any fixed point theorem. The solution concept in this theorem is considered to belong to the weighted space. For comparison with the classical case and as an application of the theorem, we give an example problem that has such a solution but no continuously differentiable solution.

The Extended 16th Hilbert Problem for Discontinuous Piecewise Systems Formed by Linear Centers and Linear Hamiltonian Saddles Separated by a Nonregular Line

We study discontinuous piecewise linear differential systems formed by linear centers and/or linear Hamiltonian saddles and separated by a nonregular straight line. There are two classes of limit cycles: the ones that intersect the separation line at two points and the ones that intersect the separation line in four points, named limit cycles of type [Formula: see text] and limit cycles of type [Formula: see text], respectively. We prove that the maximum numbers of limit cycles of types [Formula: see text] and [Formula: see text] are two and one, respectively. We show that all these upper bounds are reached providing explicit examples.

Microbial Detoxification of Oilfield Produced Water Using Discontinuous Bio-Unit System

Microbial Detoxification of Oilfield Produced Water Using Discontinuous Bio-Unit System

Reflections on Required Competencies For Health Systems Monitoring, Evaluation, and Learning In India

The movement towards systems thinking and complexity-informed monitoring and evaluation has been ongoing for some time. Covid-19 has accelerated this shift and increased the salience of contextually aware, adaptive forms of evaluation. Drawing from our experience over three years of providing monitoring, evaluation, research and learning (MERL) to a large international philanthropic organization’s health systems portfolio of work in India, we identify three types of evaluator capacities and associated set of competencies that derive from complexity-driven practice in a developing country.
 The first type of capacity relates to deriving evidence in contexts where there are very few traditional forms of data. The MERL portfolio related to health systems outcomes of access, financial protection, and equity even as the health programs themselves were evolving in a period of rapid transformation and dynamism of policy priorities and implementation mechanisms. This required an integration of traditional performance indicators drawn from government datasets with qualitative ‘signals’ focused on drivers of change within the system. Assessment of signals in turn required synthesizing different sources of information, including informal channels of obtaining evidence such as partner meetings or government-sponsored events. The evaluating team thus consciously empowered different kinds of researchers with differential expertise with the goal of building a much more pixelated picture. The goal was not to identify a single source of truth but rather a patchwork of validated information where the relevance of different pieces of data were dependent on evolving outcomes of interest. 
 The second set of competencies related to the skills required to play a convening role for donors and implementing partners, supporting better understanding of the changing operating context and help inform decision-making by program officers and partners. This involved building and sustaining relationships across different stakeholders at different stages of the project – from proposal development to review. Competencies relating to effective dialogue and developing an understanding of the core interests of international, national and sub-national partners as well as international donors and experts could only be developed iteratively and over time, but this was crucial in a distributed health decision-making ecosystem like India.
 The third and final set of competencies relate to operational adaptiveness, while evaluating an ecosystem with few constants. This can be the hardest competency to acquire because it is the farthest from the traditional notions embedded in the training of evaluation scientists and MERL practitioners. We found that the degree of buy-in and commitment to previously agreed upon frames of reference for evaluation can be shifted by changes in personnel or internal organizational structures. These shifts can lead to chain reactions of mismatched expectations that needed to be understood and managed in real time by MERL partners. The pandemic further created a natural experiment that on the one hand required a reexamination of program priorities and on the other depended on reliability of donor support.
 Each of these three types of capacities – synthesizing nuanced evidence for adaptive action, relationship building and communication, and managing operational discontinuities are in fact inter-dependent. Building evaluator competencies isn’t simply about capacity-building but rather a recognition of the diversity of skills and worldviews that need to be encompassed within our monitoring and evaluation functions for today’s complex, discontinuous health systems.

Tight Remainder-Form Decomposition Functions With Applications to Constrained Reachability and Guaranteed State Estimation

This paper proposes a tractable family of remainder-form mixed-monotone decomposition functions that are useful for over-approximating the image set of nonlinear mappings in reachability and estimation problems. Our approach applies to a new class of nonsmooth, discontinuous nonlinear systems that we call either-sided locally Lipschitz semicontinuous (ELLS) systems, which we show to be a strict superset of locally Lipschitz continuous (LLC) systems, thus expanding the set of systems that are formally known to be mixed-monotone. In addition, we derive lower and upper bounds for the over-approximation error and show that the lower bound is achieved with our proposed approach, i.e., our approach constructs the tightest, tractable remainder-form mixed-monotone decomposition function. Moreover, we introduce a set inversion algorithm that along with the proposed decomposition functions, can be used for constrained reachability analysis and guaranteed state estimation for continuous- and discrete-time systems with bounded noise.

Size effects in the electrical conductance of discontinuous thin-film systems based on Fe (FeNi) and SiO

Size effects in the electrical conductance of discontinuous thin-film systems based on Fe (FeNi) and SiO

Enhancing Symptom Management and Coordination of Breast Cancer Care at Secondary Hospitals in Saudi Arabia

The passage highlights the complexity of integrated breast cancer care and the importance of effective communication in ensuring treatment compliance, reducing errors and complications, and managing co-morbidities. It emphasizes the need for clarity in the role of the care director to prevent patients from getting lost across different departments. Digital tools are recognized as valuable resources for improving care communication, but their directives and integration within the care team need to be clearly defined. Multidisciplinary team meetings are essential for driving care planning, establishing directives, and collecting structured data. Nurse navigators play a pivotal role in ensuring care continuity and assuming the director's role in the complex landscape of breast cancer care. While AI-driven planning can facilitate their tasks, human intervention remains crucial for providing psychosocial support and addressing unexpected urgencies. The allocation of patients across different healthcare centers is often managed manually and through phone communication, resulting in time-consuming processes and discontinuous system solutions. Privacy rules and competition among providers further limit the effectiveness of current solutions. Additionally, the collection of comprehensive outcome information is currently limited to specific collaborative networks. To address these challenges, AI tools can play a role in facilitating care allocation and predicting risks by leveraging data continuity over time. This can help identify non-compliance issues caused by factors such as limited local resources, distance, and costs. However, it is essential to conduct applied research to bring AI modeling into clinical practice and promote well-coordinated, patient-centric cancer care within the complex healthcare landscape.

Limit Cycles of Some Families of Discontinuous Piecewise Differential Systems Separated by a Straight Line

In the past years the study of continuous or discontinuous piecewise differential systems has attracted significant interest, due to their wide use to model many natural phenomena. Important questions such as finding an upper bound for the number of limit cycles of such systems and their possible configurations have been considered by many authors. These problems are known as the extension of the second part of the 16th Hilbert’s problem to the piecewise differential systems. In this paper, we solve an extension of the second part of the 16th Hilbert’s problem for two families of discontinuous piecewise differential systems separated by the straight line [Formula: see text]. The first family is formed by a linear center and a cubic Hamiltonian isochronous center, and the second family is formed by cubic Hamiltonian isochronous centers. As a result we prove that the first family can exhibit [Formula: see text] or [Formula: see text] limit cycle, for the second one there are either three limit cycles or no limit cycles. We also show that there are examples of all types of these systems with one or three limit cycles.

Periodic trajectories in planar discontinuous piecewise linear systems with only centers and with a nonregular switching line

In this paper periodic trajectories of dynamical systems presenting discontinuities are studied. The considered model consists of two distinct linear differential systems, each one containing a single equilibrium point of centre type. Each system is defined on disjoint regions of the plane, the separation line is a union of two half-straight lines contained on the coordinate axes. The obtained differential system is non-smooth, so we apply Filippov’s theory to study the transitions from one dynamical system to another. The combination of the two linear plus the Filippov system acting on the separation line generates a nonlinear regime observed by the presence of limit cycles, sliding and tangential periodic trajectories as well as the coexistence of such objects. In theorem we establish the location, stability and hyperbolicity of limit cycles for certain classes of the considered model. In theorem we perform the global analysis of a representative model through bifurcation theory to analyse the birth of limit cycles, sliding periodic trajectories and tangential ones. We also provide some results addressing the coexistence of periodic trajectories and two potential physical interpretations of the model considered in the paper, one addressing nonlinear oscillations and the other considering slow-fast systems of neuron models. The main techniques employed to obtain the results are first integrals, Poincaré half return maps, and elements of bifurcation theory.

On the number of limit cycles coming from a uniform isochronous center with continuous and discontinuous quartic perturbations

Abstract In this paper, we study the number of limit cycles bifurcated from the periodic orbits of a cubic uniform isochronous center with continuous and discontinuous quartic polynomial perturbations. Using the averaging theory of first order for continuous and discontinuous differential systems and comparing the obtained results, we show that the discontinuous systems have at least 6 more limit cycles than the continuous ones. This study needs some computations that have been verified using Maple.

Epitachophoresis – A Method for the Extraction of Biomacromolecules from Complex Biological Matrices

Epitachophoresis is a new separation preparative technique based on discontinuous electrolyte systems enabling the preconcentration of biomacromolecules from complex biological matrices. Moreover, it enables the transfer of these compounds from biological liquids, such as urine or growth medium, to a simpler solution, suitable for subsequent analyses. In our recently published papers, we focused on the use of epitachophoresis to pretreat the samples containing proteins and DNA. The technique enabled more than seventyfold preconcentration with recoveries reaching more than 90%. The preparative nature of epitachophoresis enables one to subsequently analyse the isolated biomacromolecules by various techniques including mass spectrometry, capillary electrophoresis, gel electrophoresis, ELISA analysis, or new-generation sequencing. Full text English translation is available in the on-line version.

On cyclicity in discontinuous piecewise linear near-Hamiltonian differential systems with three zones having a saddle in the central one

On cyclicity in discontinuous piecewise linear near-Hamiltonian differential systems with three zones having a saddle in the central one

Optimal partial regularity of discontinuous subelliptic systems with VMO coefficients related to Hörmander’s vector fields

In this paper, we study discontinuous subelliptic systems with VMO coefficients related to Hörmander’s vector fields. In the case of growth exponential pgeq 2 , the regularity results of the partial Hölder continuity of weak solutions are established based on the mathcal{A}-harmonic approximation method under the controllable growth condition.

Dynamic scaling design strategy of discontinuous bolted rotor systems based on bidirectional parameter mapping

Rods fastened rotor system are widely used in heavy-duty gas turbines. The contact nonlinearity and discontinuity induced by bolted rotor structures, make it difficult to design a scaled rotor system accurately. Thus, a dynamic scaling design strategy for discontinuous bolted rotor systems is proposed in this paper. An improved continuous modeling method considering rods deformation based on equivalent material layer (EML) is introduced to reflect the weakening effect of the rotor stiffness with bolted structure, and the parameter mapping relationships between the continuous and the discontinuous structure are constructed. The scaling factors of each element of the rotor system are derived by the similarity theory. Through this approach, a discontinuous rotor system can be scaled, demonstrating a high level of consistency with the prototype in terms of natural frequencies, critical speeds as well as frequency response. In addition, modal experiments under different preloads and dynamic acceleration experiment are carried out to verify of the proposed modeling method for discontinuous rotor structures. The testing and simulation results prove that the introduced equivalent material layer reflects the contact effect of prototype accurately. Compared with the experimental results, the maximum deviation of the first two natural frequencies is 4.06%, and the maximum deviation of the critical speeds is 1.36%, demonstrating the potential of small size, low-cost scaled models for predicting the complex dynamic characteristics of the prototype rotor system. Overall, the proposed scaling design strategy provides practical guidance for the design and manufacture of the discontinuous scaled rotor systems, which has broad application in testing, fault prediction and dynamic design of prototypes.