Complex-valued Systems Research Articles

Homotopy Perturbation Method for Semi-Bounded Solution of the System of Cauchy-Type Singular Integral Equations of the First Kind

In this paper, we introduce the standard Homotopy Perturbation Method (HPM) for obtaining semi-bounded solutions of the first kind of system of Cauchy-type singular integral equations (CSIEs) with constant coefficients. We use the Gauss elimination technique to reduce the system of CSIEs to a diagonal triangle system of algebraic equations. We then apply the HPM to solve the resulting equations. By applying the theory of semi-bounded solutions of CSIEs, we can determine the inverse operators for the first kind of CSIEs. We demonstrate that the proposed method is exact for the system of characteristic SIEs, regardless of the choice of initial guesses (in the Holder class of functions). To illustrate the validity and accuracy of our proposed method, we supply and analyse three examples. We compare the results obtained using our method with those obtained using the Chebyshev collocation and Galerkin methods. Our method includes the ability to solve the complex-valued system of CSIEs. Based on the numerical results, we conclude that the HPM is more dominant than the other methods.

Almost Sure Stability of Complex-Valued Complex Networks: A Noise-Based Delayed Coupling Under Random Denial-of-Service Attacks.

This article is concerned with stability for stochastic complex-valued delayed complex networks under random denial-of-service (RDoS) attacks. Different from the existing literature on the stability of stochastic complex-valued systems that concentrate on moment stability, we investigate almost sure stability (ASS), where noise plays a stabilizing role. It is noted that, besides the vertex systems influenced by noise, the interactions among vertices are also at the mercy of noise. As a consequence, an innovative noise-based delayed coupling (NDC) in the presence of RDoS attacks is proposed first to accomplish the stability of complex-valued networks, where the RDoS attacks have a certain probability of triumphantly interfering with communications at active intervals of attackers. Namely, RDoS attacks considered are randomly launched at active periods, which is more realistic. In terms of the Lyapunov method and stochastic analysis theory, an almost sure exponential stability (ASES) criterion of the system discussed straightforwardly is developed by constructing a delay-free auxiliary system, while removing the traditional assumption of moment stability. The criterion strongly linked with topological structure, RDoS frequency, attack successful probability, and noise intensity reveals that the higher the noise intensity, the faster the convergence rate is for the stability of the network. In light of the criterion established, we present an algorithm that can be employed to analyze the tolerable attack parameters and the upper bound of the coupling delays, under the prerequisite of guaranteeing the stability of the network. Eventually, the theoretical results are applied to inertial complex-valued neural networks (ICNNs) and an illustrative example is presented to substantiate the efficiency of the theoretical works.

A novel adaptive synchronization algorithm for a general class of fractional-order complex-valued systems with unknown parameters, and applications to circuit realization and color image encryption

This article proposes an adaptive synchronization (AS) algorithm to synchronize a general class of fractional-order complex-valued systems with completely unknown parameters, which may appear in physical and engineering problems. The analytical and theoretical concepts of the algorithm rely on the mathematical framework of the Mittag-Leffler global stability of fractional-order systems. A specific control system is established analytically based on the fractional-order adaptive laws of parameters, and the corresponding numerical results are executed to verify the accuracy of the AS algorithm. The proposed synchronization method is evaluated using the fractional-order complex Rabinovich system as an attractive example. The electronic circuits of the new system with different fractional orders are designed. By utilizing the Multisim electronic workbench software, various chaotic/hyperchaotic behaviors have been observed, and a good agreement is found between the numerical results and experimental simulation. In addition, the approximation of the transfer function for different fractional-order are presented. And the corresponding resistor and capacitor values in the chain ship model (CSM) are estimated, which can be utilized in designing electronic circuits for other fractional-order systems. Furthermore, two strategies for encrypting color images are proposed using the AS algorithm and fractional-order adaptive laws of parameters. In the first strategy, the color image is treated as a single package and divided into two vectors. The first vector is embedded into transmitter parameters, while the second vector is injected into the transmitter state signals. In the second strategy, the primary RGB channel components of the original color image are extracted and separated into two vectors, and the same process is followed as in the first strategy. These strategies complicate the decryption task for intruders. Different scales of white Gaussian noise are added to color images to examine the robustness of the proposed color images encryption strategies.

Quasi-projective and finite-time synchronization of fractional-order memristive complex-valued delay neural networks via hybrid control

<abstract><p>We focused on the quasi-projective synchronization (QPS) and finite-time synchronization (FNTS) for a class of fractional-order memristive complex-valued delay neural networks (FOMCVDNNs). Rather than decomposing the complex-valued system into its real and imaginary components, we adopted a more streamlined approach by introducing a lemma associated with the complex-valued sign function. This innovative technique enabled us to design a simpler discontinuous controller. Then, based on the finite-time Lemma, measurable selection theorem, Lyapunov function theory, properties of the Mittag-Leffler function, and the fractional-order Razumikhin theorem, various substantial results were derived using a novel hybrid control scheme. In conclusion, we presented numerical simulations to illustrate the practical effectiveness of our theoretical findings.</p></abstract>

RETROSPECTIVE PHENOMENON OF PHILOSOPHY OF EDUCATION AT THE CURRENT STAGE OF DEVELOPMEN

The modern era has posed radically new important problems for education and philosophical principles, the philosophy of education is considered the most effective theoretical basis for changes in the field of education which creates conditions for the most complete realization of the spiritual potential of a person. The retrospection of the phenomenon of education and its separation from philosophy, the stages of formation of its conceptual and categorical apparatus and the formation of its institutional forms are traced. The main directions of development of the philosophy of education in the world and in Ukraine are analyzed. The position of reviewing the fundamental principles of the university and university education, which consists in the transformation of the entire system of higher education and its adaptation to the realities of today, is very relevant today. Different approaches and views on the system of modern university transformation, the ambivalent nature of modern higher education and the retrospection of the phenomenon of the philosophy of education at the current stage of development are analyzed. Changes in the philosophy of the functioning of the educational system, ideological reorientations, reproduction of the humanistic nature, which contribute to the transition of higher education educational processes into sustainable innovative trends, have been clarified. The article examines the philosophy of education in the general system of university knowledge in connection with pedagogical theory and practice. Also, the methodology of changing the world's values and goals in the interests of the sustainable development of Ukrainian society and the harmonious development of the individual and the further transformation of a modern university is especially relevant in today's globalized world. Education has always been an objectively necessary condition for the formation of a personality developed in professional, spiritual and general cultural directions. Undoubtedly, any person is characterized by the ability for self-development, self-education, but his life definition, professional, civil and moral formation in different historical eras has its own characteristics, largely due to changes in the education system. In our opinion, the theoretical basis of such changes in education as a complex system of civilizational values has always been and continues to be the philosophy of education, since it lays down the mechanism of self-development and maximizes the inner spiritual potential of every person.

Finding hope and fulfillment in meaningful work: An interpretative phenomenological analysis of conservation and stewardship practitioners’ experience, values, and motivations

Values and motivations can shape natural resource management decision-making as individuals set conservation goals based on diverse, unique backgrounds, histories, and experiences. Recent literature points to the need to understand, evaluate, and articulate practitioner values to make explicit how experiences shape their work. Our research responds to calls to explore a diverse range of values and motivations among conservation practitioners. We used a qualitative approach grounded in phenomenology to advance an in-depth understanding of how conservation and stewardship practitioners experience, acknowledge, and make sense of conservation decision-making in Maine, USA. We interviewed 21 conservation and stewardship practitioners. Our results indicate the presence of complex value systems, including strong biospheric, altruistic, eudaimonic, as well as egoistic values. These values interact and intersect with motivations for participants’ careers in conservation in unique ways, driving participant actions and decision-making. Within Maine specifically, our results highlight the many areas for convergence of broad values among seemingly diverse groups that can inform opportunities for collaboration. Participants expressed various pathways to careers in conservation, where their work enables them to make a meaningful contribution to the environment and society. However in situations where personal and organizational values are misaligned, the role of organizational transparency, employee empowerment, and agency are key. Our results have implications for conservation groups seeking to achieve high employee satisfaction, as well as researchers, policymakers, and practitioners who hope to inspire individuals to take on conservation careers to create sustainable and transformative action for the future. Fostering early experiences in place, including interactions with the non-human world and local community, are important for influencing and reinforcing values and motivations for conservation action.

A Hybrid Method for All Types of Solutions of the System of Cauchy-Type Singular Integral Equations of the First Kind

In this note, the hybrid method (combination of the homotopy perturbation method (HPM) and the Gauss elimination method (GEM)) is developed as a semi-analytical solution for the first kind system of Cauchy-type singular integral equations (CSIEs) with constant coefficients. Before applying the HPM, we have to first reduce the system of CSIEs into a triangle system of algebraic equations using GEM, which is then carried out using the HPM. Using the theory of the bounded, unbounded and semi-bounded solutions of CSIEs, we are able to find inverse operators for the system of CSIEs of the first kind. A stability analysis and convergent of the proposed method has been conducted in the weighted Lp space. Moreover, the proposed method is proven to be exact in the Holder class of functions for the system of characteristic SIEs for any type of initial guess. For each of the four cases, several examples are provided and examined to demonstrate the proposed method’s validity and accuracy. Obtained results are compared with the Chebyshev collocation method and modified HPM (MHPM). Example 3 reveals that the error term of the MHPM is slightly superior to that of the HPM. One of the features of the proposed method is that it can be solved as a complex-valued system of CSIEs. Numerical results revealed that the hybrid method dominates others.

Fixed/Preassigned-Time Stabilization for Complex-Valued Inertial Neural Networks with Distributed Delays: A Non-Separation Approach

This article explores complex-valued inertial neural networks (CVINNs) with distributed delays (DDs). By constructing two new feedback controllers, some novel results on fixed-time stabilization (FTS) and preassigned-time stabilization (PTS) of CVINNs are established. Unlike most of the previous works, FTS and PTS obtained here are explored without dividing the original complex-valued system into two separate real valued subsystems. Eventually, to verify the effectiveness and reliability of the results of this article, we provide several numerical examples. The FTS and PTS of CVINNs are successfully implemented at T = 6, 5.5, and 5, and the settling time is not affected by system parameters and initial values.

Dissipative Sliding-Mode Synchronization Control of Uncertain Complex-Valued Inertial Neural Networks: Non-Reduced-Order Strategy

This study investigates the dissipative synchronization of uncertain complex-valued inertial neural networks with external disturbances using sliding mode control (SMC). In the absence of both variable substitution as well as the equivalent transformations of real- and complex-valued systems, this study focuses directly on the original complex-valued inertial system. First, a suitable integral switching surface (SS) function is proposed. Second, by constructing innovative Lyapunov-Krasovskii functionals and applying the Wirtinger-based integral inequality and reciprocally convex approach, a synchronization criterion is derived on the basis of the linear matrix inequality technique to ensure that the sliding mode dynamics are stable and dissipative. Then, an SMC law and an adaptive SMC law are designed, and the accessibility analysis of the predefined SS is provided. Numerical verifications as well as the superiority and practicality analysis of the proposed approach are provided through four examples.

First integral blow-up solutions to complex-valued KdV equations

We apply Lie theory to determine the aone-parameter point transformations which leave complex-valued Korteweg-de Vries equations invariant. The conserved vectors of the systems are constructed. We provide travelling wave reductions that lead to third-order ordinary differential equations. These equations are highly nonlinear to solve directly and, therefore, we establish their first integrals. The latter is of second-order and facilitates the analysis of the complex-valued system, as well as some interesting blow-up solutions.

Dynamic Synchrophasor Estimation Based on Weighted Real-Valued Sinc Interpolation Method

Phasor measurement units (PMUs) are the cornerstone of intelligent sensing and monitoring of power systems. The superiority of the sinc interpolation function-based least squares (SLS) method, a signal processing algorithm for PMUs, has been proven in harmonic phasor estimation. However, the SLS-based estimators suffer from spectral interferences and heavy computational burden. To this end, a real-valued sinc weighted least squares (SWLS-R) method is proposed to track the dynamic synchrophasor accurately and quickly. First, the weighted vector, i.e., window function, is introduced to enhance the SLS estimator’s behavior by mitigating the impact of spectral interference. Then, the complex-valued system matrix is transformed into the real-valued system matrix to lower the computational burden by avoiding complex matrix multiplication. Finally, an explicit and fast solution is designed to calculate the pseudoinverse matrix of the SWLS-R, which aims to further improve computational efficiency. The accuracy and effectiveness of the proposed method are validated by simulations. These are designed, under steady and dynamic conditions, according to the M-class requirements of the Standard IEC/IEEE 60255-118-1.

МЕТОДОЛОГІЯ ДОСЛІДЖЕННЯ ОСОБЛИВОСТЕЙ СТАНОВЛЕННЯ ТА РОЗВИТКУ ІНСТИТУТУ ЮВЕНАЛЬНОЇ ПРОБАЦІЇ В УКРАЇНІ

In the article, the author considers the methodology of researching the peculiarities of the establishment and development of the juvenile probation institute in Ukraine. It is indicated that the methodology of juvenile probation research should be based on a dialectical approach, which should be represented by the researcher’s rationalism, his ability to draw parallels between different points of view on the same phenomenon and single out the “core”, that can provide an opportunity to establish the universality of the studied phenomenon and its authenticity. From the point of view of dialectical materialism, juvenile probation should be investigated in the context of its effectiveness and timeliness within the existing development and mentality of Ukrainian society, with subsequent forecasting of its transformation over time. It is noted that the legislator’s perception of the forms and limits of human existence, the legal and social needs of the country’s citizens, gives him the opportunity not only to find ways to respond to any illegal actions of individuals, but also to warn them, correcting the deviant tendencies of the offender. That is why, considering juvenile probation through the prism of epistemology, it is possible to reproduce the symbiosis of sensual and rational, preserving the principle of humanism of criminal legislation and rationalism when working with a criminal offender. It is concluded that the methodology of the study of the peculiarities of the formation and development of the juvenile probation institute is a complex system of values, philosophical principles and guidelines on which the legislative representation of the phenomenon of juvenile delinquency and the single unified structure of humane interaction with deviant adolescents are based. To date, this methodology is almost no different from similar ones in the science of criminal law and has the main task of simplifying the process of researching individual phenomena with the subsequent integration of this kind of understanding into legislative initiatives and practices. Key words: methodology, juvenile, juvenile justice, juvenile probation, criminal offense, criminal offender, criminal legislation, repression.

Observer-based sliding mode synchronization control of complex-valued neural networks with inertial term and mixed time-varying delays

In this paper, the synchronization problem of complex-valued inertial neural networks is studied via sliding mode control (SMC). Both mixed time-varying delays and unknown control disturbances are considered. In the absence of the equivalent transformations of real- and complex-valued systems, the systems are analyzed as an entirety form in complex domain. A disturbance observer is designed to estimate the unknown control disturbance. By constructing suitable integral switching surface function and innovative Lyapunov–Krasovskii functionals, a delay-dependent synchronization criterion is proposed on the basis of linear matrix inequality technique. An efficient SMC law based on the disturbance observer is designed, and the accessibility analysis of the predefined switching surface is provided. Eventually, numerical verification based on two types of activation functions, as well as the superiority and practicability analysis are provided.

Iterative solution methods for 3D controlled-source electromagnetic forward modelling of geophysical exploration scenarios

We develop an efficient and robust iterative framework suitable for solving the linear system of equations resulting from the spectral element discretisation of the curl-curl equation of the total electric field encountered in geophysical controlled-source electromagnetic applications. We use the real-valued equivalent form of the original complex-valued system and solve this arising real-valued two-by-two block system (outer system) using the generalised conjugate residual method preconditioned with a highly efficient block-based PREconditioner for Square Blocks (PRESB). Applying this preconditioner equates to solving two smaller inner symmetric systems which are either solved using a direct solver or iterative methods, namely the generalised conjugate residual or the flexible generalised minimal residual methods preconditioned with the multigrid-based auxiliary-space preconditioner AMS. Our numerical experiments demonstrate the robustness of the outer solver with respect to spatially variable material parameters, for a wide frequency range of five orders of magnitude (0.1-10’000 Hz), with respect to the number of degrees of freedom, and for stretched structured and unstructured as well as locally refined meshes. For all the models considered, the outer solver reaches convergence in a small (typically < 20) number of iterations. Further, our numerical tests clearly show that solving the two inner systems iteratively using the indicated preconditioned iterative methods is computationally beneficial in terms of memory requirement and time spent as compared to a direct solver. On top of that, our iterative framework works for large-scale problems where direct solvers applied to the original complex-valued systems succumb due to their excessive memory consumption, thus making the iterative framework better suited for large-scale 3D problems. Comparison to a similar iterative framework based on a block-diagonal and the auxiliary-space preconditioners reveals that the PRESB preconditioner requires slightly fewer iterations to converge yielding a certain gain in time spent to obtain the solution of the two-by-two block system.

Evaluating Jesus and other “heroes”

AbstractThe appraisal framework developed by Martin and White and others working within systemic functional linguistics has been applied in a wide variety of contexts. However, to our knowledge, it has been little used in the interpretation of ancient written documents. We believe that it may have value, amongst other things, in determining the genre of such literature and we see this as particularly relevant in the area of biography, where the author’s presentation of the subject is a key factor. So, in this study, we apply aspects of the appraisal framework to three Hellenistic Greek texts often categorised with the genre “Lives”. Selected passages from these texts were divided into short units for quantitative analysis that focused on theJudgementthat the texts’ authors make of their central characters (their “heroes”), how this isamplifiedand how theyengagewith different “voices”. These passages were also compared with the rest of the texts in a more qualitative study. Our results show notable differences in theJudgementthe authors make and presumably wish their readers to share in terms of the positive/negative portrayal of their “heroes”, the degree of amplification and the interaction with other “voices”. We consider the appropriateness of the “Lives” genre for one of these texts, theGospel of John, and also a number of methodological issues arising from an area of application that has not previously received attention. These include the difficulty of making clear-cut evaluation choices where authors themselves may be ambivalent about those they are describing and the need to take account of the differing and complex value systems of ancient cultures. We suggest that our findings may have wider relevance for other applications of appraisal.

Narrative and Gendered Identities: A Feminist Narratological Reading of Chinua Achebe’s Things Fall Apart and D.H Lawrence’s The Fox

The significant role that narrative strategy, plot structure, characterization, perspectivity and language, precisely, metaphors and metanarratives can play as textual sites of gendered identities has been recognized within feminist narratology which is an interdisciplinary sub-domain within narrative theory. Although the central role that narrative might proffer in the analysis of gender has over the last twenty years featured as a crucial area of research in feminist narratology, over-trodden data like Chinua Achebe’s Things Fall Apart and D. H. Lawrence’s The Fox, seem to have received less attention in the light of categories or narrative strategies which can serve as sites of gender. In privileging feminist narratology as a suitable theoretical framework for locating, interpreting and analyzing sites of gendered identity construction in Things Fall Apart and The Fox, this study argues that the two text teem with narrative structures and strategies as well as linguistic evidences like metaphors and folkloric metanarratives, that may encourage a categorization of people into male and female; masculinities, femininities, and the subaltern. Gender markers: sexuality, characterization (psychological and biological elements), male-centered or “masculinist” plot structure, folkloric metanarratives, linguistic elements like metaphors and images in general as well as social codes that are gender-specific and that play a huge role in the context of the cultural construction/transmission and memory of gender are largely represented in the chosen texts. These textual devices have a highly ideological function: they are creative medial elements that play an important role in constructing and passing on the complex system of values, norms and ideas which constitute a society’s patriarchal mentality.

Finite-Time Synchronization Control of Networked Chaotic Complex-Valued Systems With Adaptive Coupling

In the present paper, the finite-time synchronization control problem is addressed for the networked complex-valued dynamical systems with directed and undirected topologies. By combining the two-phase method with delayed impulsive control and designing adaptive coupling weights, several finite-time synchronization results and the corresponding settling times are obtained by using the complex-valued states directly. In particular, the delayed impulsive control is introduced in the first phase to guarantee that the controlled system can globally exponentially converge to the inner of the unit ball, while the finite-time control term is used only in the second phase to ensure the finite-time stability. Finally, two numerical examples are used to show the validity of our control strategy.

Finite-time Mittag–Leffler synchronization of fractional-order complex-valued memristive neural networks with time delay

Without dividing the complex-valued systems into two real-valued ones, a class of fractional-order complex-valued memristive neural networks (FCVMNNs) with time delay is investigated. Firstly, based on the complex-valued sign function, a novel complex-valued feedback controller is devised to research such systems. Under the framework of Filippov solution, differential inclusion theory and Lyapunov stability theorem, the finite-time Mittag–Leffler synchronization (FTMLS) of FCVMNNs with time delay can be realized. Meanwhile, the upper bound of the synchronization settling time (SST) is less conservative than previous results. In addition, by adjusting controller parameters, the global asymptotic synchronization of FCVMNNs with time delay can also be realized, which improves and enrich some existing results. Lastly, some simulation examples are designed to verify the validity of conclusions.

Investigation of Controllability and Observability for Linear Quaternion-Valued Systems from Its Complex-Valued Systems

Investigation of Controllability and Observability for Linear Quaternion-Valued Systems from Its Complex-Valued Systems

Inter-Layer Noise-Based Topology of Complex-Valued Multi-Layer Networks: Almost Sure Stability via Time-Varying Hybrid Intermittent Pinning Control

This paper concentrates on stability of complex-valued multi-layer networks via time-varying hybrid intermittent pinning control (THIPC). A noise-based coupling that contains time-varying and nonlinear features is introduced first into complex-valued multi-layer networks. Different from existing literature on stochastic complex-valued systems that focus on moment stability, almost sure stability is explored in which noise can improve the stability of systems. Additionally, a novel THIPC strategy is proposed to achieve stability for a portion of nodes in the networks where the control gain is a sign-indefinite function and the control strategy designed integrates both stabilizing control and destabilizing input. For conquering the difficulties caused by time-varying gain, we develop the concept "average intermittent control gain" to quantify the control gain. Then the stability of remaining nodes is realized by virtue of the stability for pinning nodes and the conductive contribution by inter-layer noise-based topology. For the multi-layer networks we addressed, a stability analysis framework is constructed and we show the selection procedure of pinning nodes. Under this framework, employing Lyapunov method, stochastic analysis technique, almost sure stability criteria of complex-valued multi-layer networks are acquired. Finally, theoretical results are applied to inertial neural networks and cusp catastrophe models with numerical examples being provided.