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Let \(A\) be a bounded linear operator in a complex separable Hilbert space, \(A^*\) be its adjoint one and \(A_I:=(A-A^*)/(2i)\). Assuming that \(A_I\) is a Hilbert-Schmidt operator, we investigate perturbations of the imaginary parts of the eigenvalues of \(A\). Our results are formulated in terms of the "extended" eigenvalue sets in the sense introduced by T. Kato. Besides, we refine the classical Weyl inequality \(\sum_{k=1}^\infty (\operatorname{Im} \lambda_k(A))^2 \leq N_2^2(A_I)\), where \(\lambda_k(A)\) \((k=1,2, \ldots )\) are the eigenvalues of \(A\) and \(N_2(\cdot)\) is the Hilbert-Schmidt norm. In addition, we discuss applications of our results to the Jacobi operators.

We present some sufficient conditions for the existence of positive solutions to a third order differential equation subject to nonlocal boundary conditions. Our approach is based on the Krasnosel'skiĭ-Guo fixed point theorem in cones and the properties of the Green's function corresponding to the BVP under study. The main results are illustrated by suitable examples.

The main aim of this article is to study the Poisson type problem for anisotropic \(p\)-Laplace type equation on long cylindrical domains. The rate of convergence is shown to be exponential, thereby improving earlier known results for similar type of operators. The Poincaré inequality for a pseudo \(p\)-Laplace operator on an infinite strip-like domain is also studied and the best constant, like in many other situations in literature for other operators, is shown to be the same with the best Poincaré constant of an analogous problem set on a lower dimension.

Let \(k\geq 1\) be an integer, and let \(D\) be a finite and simple digraph with vertex set \(V(D)\). A weak signed Roman \(k\)-dominating function (WSRkDF) on a digraph \(D\) is a function \(f \colon V(D)\rightarrow \{-1,1,2\}\) satisfying the condition that \(\sum_{x \in N^-[v]}f(x)\geq k\) for each \(v\in V(D)\), where \(N^-[v]\) consists of \(v\) and all vertices of \(D\) from which arcs go into \(v\). The weight of a WSRkDF \(f\) is \(w(f)=\sum_{v\in V(D)}f(v)\). The weak signed Roman \(k\)-domination number \(\gamma_{wsR}^k(D)\) is the minimum weight of a WSRkDF on \(D\). In this paper we initiate the study of the weak signed Roman \(k\)-domination number of digraphs, and we present different bounds on \(\gamma_{wsR}^k(D)\). In addition, we determine the weak signed Roman \(k\)-domination number of some classes of digraphs. Some of our results are extensions of well-known properties of the weak signed Roman domination number \(\gamma_{wsR}(D)=\gamma_{wsR}^1(D)\) and the signed Roman \(k\)-domination number \(\gamma_{sR}^k(D).\)

Abstract A growing number of social media studies in the U.S. rely on the characterization of the opinion of individual users, for example, as Democrat- or Republican-leaning, or in continuous scales ranging from most liberal to most conservative. Recent works have shown, however, that additional opinion dimensions, for instance measuring attitudes towards elites, institutions, or cultural change, are also relevant for understanding socio-informational phenomena on social platforms and in politics in general. The study of social networks in high-dimensional opinion spaces remains challenging in the US, both because of the relative dominance of a principal liberal-conservative dimension in observed phenomena, and because two-party political systems structure both the preferences of users and the tools to measure them. This article leverages graph embedding in multi-dimensional latent opinion spaces and text analysis to propose a method to identify additional opinion dimensions linked to cultural, policy, social, and ideological groups and preferences. Using Twitter social graph data we infer the political stance of nearly 2 million users connected to the political debate in the U.S. for several issue dimensions of public debate. We show that it is possible to identify several new dimensions structuring social graphs, non-aligned with the classic liberal-conservative dimension. We also show how the social graph is polarized to different degrees along these newfound dimensions, leveraging multi-modality measures in opinion space. These results shed a new light on ideal point estimation methods gaining attention in social media studies, showing that they cannot always assume to capture liberal-conservative divides in single-dimensional models.

Abstract In the paper, we investigate the uniqueness problem of a meromorphic function and its difference operator to the most general setting via two shared set problems and thus improve a recent result of Chen–Chen (Bull Malays Math Sci Soc 35(3): 765-774, 2012) .

Abstract This paper deals with some existence and uniqueness results for a class of deformable fractional differential equations. These problems encompassed nonlinear implicit fractional differential equations involving boundary conditions and various types of delays, including finite, infinite, and state-dependent delays. Our approach to proving the existence and uniqueness of solutions relied on the application of the Banach contraction principle and Schauder’s fixed-point theorem. In the last section, we provide different examples to illustrate our obtained results.

Abstract Of concern is a Cohen–Grossberg neural network (CGNNs) system taking into account distributed and discrete delays. The class of delay kernels ensuring exponential stability existing in the previous papers is enlarged to an extended class of functions guaranteeing more general types of stability. The exponential and polynomial (or power type) type stabilities becomes particular cases of our result. This is achieved using appropriate Lyapunov-type functionals and the characteristics of the considered class.

The present study examines a semi-analytical method known as the Fractional Residual Power Series Method for obtaining solutions to the non-linear, time-fractional Kawahara and modified Kawahara equations. These equations are fifth-order, non-linear partial differential equations that arise in the context of shallow water waves. The analytical process and findings are compared with those obtained from the well-known Variational Iteration Method (VIM) and Homotopy Perturbation Method (HPM). The results obtained from the Fractional Residual Power Series Method are found to be more efficient, reliable, and easier to implement compared to other analytical and semi-analytical methods.

Methicillin-Resistant Staphylococcus Aureus (MRSA) infection can occur alongside or following COVID-19, which is a concern in healthcare settings. The effectiveness of antiviral treatments for COVID-19 depends on a functioning immune response, but antibiotics used for bacterial infections like MRSA can disrupt the immune response and reduce the effectiveness of antiviral treatments. The emergence of MRSA due to excessive antibiotic usage has led to the widespread use of vancomycin as an alternative treatment. Immunomodulatory antibiotics like azithromycin may also be considered. To study the dynamics of these coinfections, a multiscale model was developed. Parameter estimation and sensitivity analysis were performed, revealing influential parameters affecting the reproduction number. Numerical simulations showed that methicillin may increase the population of co-infected cells, while azithromycin can improve the host immune response but has limited impact on MRSA proliferation. Increased efficacy of vancomycin can lead to MRSA eradication. Combination of immunomodulatory antibiotics and vancomycin has minimal effect on co-infected cell population, but increased vancomycin efficacy can reduce coinfection severity. This study emphasizes the importance of continuous research, surveillance, and the development of effective strategies to combat the complexities of COVID-19 and MRSA coinfection.

Chaos, comprehended characteristically, is the mathematical property of a dynamical system which is a deterministic mathematical model in which time can be either continuous or discrete as a variable. These respective models are investigated as mathematical objects or can be employed for describing a target system. As a long-term aperiodic and random-like behavior manifested by many nonlinear complex dynamic systems, chaos induces that the system itself is inherently unstable and disordered, which requires the revealing of representative and accessible paths towards affluence of complexity and experimental processes so that novelty, diversity and robustness can be generated. Hence, complexity theory focuses on non-deterministic systems, whereas chaos theory rests on deterministic systems. These entailments demonstrate that chaos and complexity theory provide a synthesis of emerging wholes of individual components rather than the orientation of analyzing systems in isolation. Therefore, mathematical modeling and scientific computing are among the chief tools to solve the challenges and problems related to complex and chaotic systems through innovative ways ascribed to data science with a precisely tailored approach which can examine the data applied. The complexity definitions need to be weighed over different data offering a highly extensive applicability spectrum with more practicality and convenience owing to the fact that the respective processes lie in the concrete mathematical foundations, which all may as well indicate that the methods are required to be examined thoroughly regarding their mathematical foundation along with the related methods to be applied. Furthermore, making use of chaos theory can be considered to be a way to better understand the internal machinations of neural networks, and the amalgamation of chaos theory as well as Artificial Intelligence (AI) can open up stimulating possibilities acting instrumental to tackle diverse challenges, with AI algorithms providing improvements in the predictive capabilities via the introduction of adaptability, enabling chaos theory to respond to even slight changes in the input data, which results in a higher level of predictive accuracy. Therefore, chaos-based algorithms are employed for the optimization of neural network architectures and training processes. Fractional mathematics, with the application of fractional calculus techniques geared towards the problems’ solutions, describes the existence characteristics of complex natural, applied sciences, scientific, engineering related and medical systems more accurately to reflect the actual state properties co-evolving entities and patterns of the systems concerning nonlinear dynamic systems and modeling complexity evolution with fractional chaotic and complex systems. Complexity entails holistic understanding of various processes through multi-stage integrative models across spanning scales for expounding complex systems while following actuality across evolutionary path. Moreover, Fractional Calculus (FC), related to the dynamics of complicated real-world problems, ensures emerging processes adopting fractional dynamics rather than the ordinary integer-ordered ones, which means the related differential equations feature non integer valued derivatives. Given that slight perturbation leads to a significantly divergent future concatenation of events, pinning down the state of different systems precisely can enable one to unveil uncertainty to some extent. Predicting the future evolution of chaotic systems can screen the direction towards distant horizons with extensive applications in order to understand the internal machinations of neural and chaotic complex systems. Even though many problems are solvable and have been solved, they remain to be open constantly under transient circumstances. Thus, fields with a broad range of spectrum range from mathematics, physics, biology, fluid mechanics, medicine, engineering, image analysis, based on differing perspectives in our special issue which presents a compilation of recent research elaborating on the related advances in foundations, theory, methodology and topic-based implementations regarding fractals, fractal methodology, fractal spline, non-differentiable fractal functions, fractional calculus, fractional mathematics, fractional differential equations, differential equations (PDEs, ODEs), chaos, bifurcation, Lie symmetry, stability, sensitivity, deep learning approaches, machine learning, and so forth through advanced fractional mathematics, fractional calculus, data intensive schemes, algorithms and machine learning applications surrounding complex chaotic systems.

Recent advancements in deep learning, particularly convolutional networks, have rapidly become the preferred methodology for analyzing medical images, facilitating tasks like disease segmentation, classification, and pattern quantification. Central to these advancements is the capacity to leverage hierarchical feature representations acquired solely from data. This comprehensive review meticulously examines a variety of deep learning techniques applied across diverse healthcare domains, delving into the intricate realm of medical imaging to unveil concealed patterns through strategic deep learning methodologies. Encompassing a range of diseases, including Alzheimer’s, breast cancer, brain tumors, glaucoma, heart murmurs, retinal microaneurysms, colorectal liver metastases, and more, the analysis emphasizes contributions succinctly summarized in a tabular form.The table provides an overview of various deep learning approaches applied to different diseases, incorporating methodologies, datasets, and outcomes for each condition.Notably, performance metrics such as accuracy, specificity, sensitivity, and other crucial measures underscore the achieved results. Specifically, an in-depth discussion is conducted on the Convolutional Neural Network (CNN) owing to its widespread adoption as a paramount tool in computer vision tasks. Moreover, an exhaustive exploration encompasses deep learning classification approaches, procedural aspects of medical image processing, as well as a thorough examination of key features and characteristics. At the end, we delve into a range of research challenges and put forth potential avenues for future improvements in the field.

The effectiveness of the local fractional reduced differential transformation method (LFRDTM) for the approximation of the solution related to the extended n-term local fractional Klein-Gordon equation is the main aim of this paper in which fractional complex transform and local fractional derivative have been employed to analyze the n-term Klein-Gordon equations, and Cantor sets. The proposed method, along with the existence of the solutions demonstrated through some examples, provides a powerful mathematical means in solving fractional linear differential equations. Considering these points, the paper also provides an accurate and effective method to solve complex physical systems that display fractal or self-similar behavior across various scales. In conclusion, the fractional complex transform with the local fractional differential transform method has been proven to be a robust and flexible approach towards obtaining effective approximate solutions of local fractional partial differential equations.

This research article deals with analytical solutions to two problems. The first is the (1+1)-coupled Jaulent-Miodek system of equations, which is associated with the energy-dependent Schrödinger potential, whereas the second problem, the system of coupled Konno-Oono equations relates to complexity and chaos in electromagnetic fields. Similarity reductions via Lie-symmetry analysis is performed for the systems to derive their analytical solutions. Since Lie symmetry involves arbitrary constants in the infinitesimals, this opens up more possibilities for getting a rich variety of analytical solutions for both real-life problems. The analytical solutions are supplemented graphically to understand them in a better way. Traveling wave profiles are obtained eventually. Solution for CKOEs are different from the earlier research (Kumar and Kumar 2022a; Kumar et al. 2022) as far as the authors are aware.

The present study perturbs the fractional integral of a continuous function $f$ defined on a real compact interval, say $(\mathcal{I}^vf)$ using a family of fractal functions $(\mathcal{I}^vf)^\alpha$ based on the scaling parameter $\alpha$. To elicit this phenomenon, a fractal operator is proposed in the space of continuous functions, an analogue to the existing fractal interpolation operator which perturbs $f$ giving rise to $\alpha$-fractal function $f^\alpha$. In addition, the composition of $\alpha$-fractal function with the linear fractal function is discussed and the composition operation on the fractal interpolation functions is extended to the case of differentiable fractal functions.

In this article, we investigate various Bernstein-Kantorovich variants together with their approximation properties. Nowadays, these variants of Bernstein-Kantorovich operators have been a source of inspiration for researchers as it helps to approximate integral functions also which is not feasible in the case of discrete operators. Chaos theory has also been referred to as complexity theory. Using chaos theory complexity is also reduced as in approximation theory. Thus in order to reduce complexity and to have better understanding of images in sciences and engineering field, sampling Kantorovich operators of approximation theory are widely used in this regard for enhancement of images. Thus, we discuss the important applications of Kantorovich operators depicting pragmatic and theoretical aspects of approximation theory.

In this article, we consider the Generalized Damped Forced Korteweg-de Vries (GDFKdV) equation. The forcing term considered is of the form $F(U)=U(U-v_1)(U-v_2)$, where $v_1$ and $v_2$ are free parameters. We investigate the behaviour of fixed points evaluated for the corresponding dynamical system of our model problem. With respect to these fixed points, we investigate the effects of a few significant parameters involved in the model, namely, the free parameters $v_1$ and $v_2$, the nonlinear, dispersion and damping coefficients using the tools from bifurcation analysis. We also obtain the wave plots for the critical values of the nonlinear and dispersion coefficients for which the system becomes unstable and exhibit chaotic behaviour. We confirm the chaos in our dynamical system under various conditions with the help of Lyapunov exponents.

The partial differential equation (PDE)-based models are widely used to remove additive Gaussian white noise and preserve edges, and one of the most widely used methods is the total variation denoising algorithm. Total variation (TV) denoising algorithm-based time-dependent models have seen considerable success in the field of image-denoising and edge detection. TV denoising algorithm is based on that signals with spurious detail have a high total variation and reduction of unwanted signals to achieve noise-free images. It is a constrained optimization-type algorithm. The Lagrange multiplier and gradient descent method are used to solve the TV algorithm to reach the PDE-based time dependent model. To eliminate additive noise and preserve edges, we investigate a class of weighted time-dependent model in this study. The proposed method is investigated in a well-balanced flow form that extends the time-dependent model with an adaptive fidelity element. Adaptive function is fusing into the regularization term of the classical time-dependent model which successfully enhances the intensity of the regularizer function. We maintain the ability of the time-dependent model without any oscillation effects. Furthermore, we want to prove the viscosity solution of our weighted and well balanced time-dependent model, demonstrating its existence and uniqueness. The finite difference method is applied to discretize the nonlinear time-dependent models. The numerical results are expressed as a statistic known as the peak signal-to-noise ratio (PSNR) and structural similarity index metric (SSIM). Numerical experiments demonstrate that the proposed model yields good performance compared with the previous time-dependent model.

We review some recent results of quantitative long-time convergence for the law of a killed Markov process conditioned to survival toward a quasi-stationary distribution, and on the analogous question for the particle systems used in practice to sample these distributions. With respect to the existing literature, one of the novelties of these works is the degeneracy of the underlying process with respect to classical elliptic diffusion, namely it can be a non-elliptic hypoelliptic diffusion, a piecewise deterministic Markov process or an Euler numerical scheme.

This article presents a selection of recent results in the mathematical study of physical systems described by a large number of particles, with various types of interactions (mean-field, moderate, nearest-neighbor). Limit theorems are obtained concerning either the large-scale or the long-time behavior of these systems. These results rely on the use of a large range of mathematical tools, arising from both probability theory and the analysis of partial differential equations, and thereby illustrate fruitful interactions between these two disciplines.

Electromagnetic simulations on large domains require a huge memory consumption. Domain decomposition methods, based on Trefftz methods, could be an answer to this issue. In this paper, we associate to heterogeneous three-dimensional Maxwell equations one variational formulation which can be obtained either by upwind fluxes or Riemann traces. We associate to this variational formulation an iterative Trefftz Krylov solver. The poor conditioning due to the use of plane wave basis functions is bypassed thanks to a compression strategy. Moreover, the developed iterative solver is accelerated thanks to a left preconditioner. The considered numerical cases illustrate the performance of this basis reduction, which leads to the consideration of an industrial case of more than 750 millions of degrees of freedom.

This review presents some recent works on the construction of closure relations for moment systems extracted from a kinetic equation. A rough construction of those closures and the main properties of the resulting systems are described. Especially, based on the underlying kinetic equation, the main properties desired for such moment systems are the realizability, i.e. the positivity of an underlying kinetic solution, global strong hyperbolicity and entropy dissipation.

This paper reviews the different existing Contact Dynamics schemes for the simulation of granular media, for which the discrete incremental problem is based on the resolution of convex problems. This type of discretization has the great advantage of allowing the use of standard convex optimization algorithms. In the case of frictional contacts, we consider schemes based on a convex relaxation of the constraint as well as a fixed point scheme. The model and the computations leading to the discrete problems are detailed in the case of convex, regular but not necessarily spherical particles. We prove, using basic tools of convex analysis, that the discrete optimization problem can be seen as a minimization problem of a global discrete energy for the system, in which the velocity to be considered is an average of the pre- and post-impact velocities. A numerical study on an academic test case is conducted, illustrating for the first time the convergence with order 1 in the time step of the different schemes. We also discuss the influence of the convex relaxation of the constraint on the behavior of the system. We show in particular that, although it induces numerical dilatation, it does not significantly modify the macrosopic behavior of a column collapse en 2d. The numerical tests are performed using the code SCoPI.

A solution is given to generalized backward stochastic differential equations driven by a real-valued RCLL martingale on an arbitrary filtered probability space. The existence and uniqueness of a solution are proved via the Yosida approximation method when the generators are only stochastic monotone with respect to the y-variable and stochastic Lipschitz with respect to the z-variable, with different linear growth conditions.

In this article, a non-Gaussian long memory process is constructed by the aggregation of independent copies of a fractional Lévy Ornstein–Uhlenbeck process with random coefficients. Several properties and a limit theorem are studied for this new process. Finally, some simulations of the limit process are shown.

In this paper, the asmptotics is considered for the distribution tail of a randomly stopped sum ${S_{\nu }}={X_{1}}+\cdots +{X_{\nu }}$ of independent identically distributed consistently varying random variables with zero mean, where ν is a counting random variable independent of $\{{X_{1}},{X_{2}},\dots \}$. The conditions are provided for the relation $\mathbb{P}({S_{\nu }}\gt x)\sim \mathbb{E}\nu \hspace{0.1667em}\mathbb{P}({X_{1}}\gt x)$ to hold, as $x\to \infty $, involving the finiteness of $\mathbb{E}|{X_{1}}|$. The result improves that of Olvera-Cravioto [14], where the finiteness of a moment $\mathbb{E}|{X_{1}}{|^{r}}$ for some $r\gt 1$ was assumed.

The term moderate deviations is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability to zero (governed by a large deviation principle) and a weak convergence to a centered Normal distribution. The notion of noncentral moderate deviations is used when the weak convergence is towards a non-Gaussian distribution. In this paper, noncentral moderate deviation results are presented for two fractional Skellam processes known in the literature (see [20]). It is established that, for the fractional Skellam process of type 2 (for which one can refer to the recent results for compound fractional Poisson processes in [3]), the convergences to zero are usually faster because one can prove suitable inequalities between rate functions.

The object of investigation is the mixed fractional Brownian motion of the form ${X_{t}}=\kappa {B_{t}^{{H_{1}}}}+\sigma {B_{t}^{{H_{2}}}}$, driven by two independent fractional Brownian motions ${B_{1}^{H}}$ and ${B_{2}^{H}}$ with Hurst parameters ${H_{1}}\lt {H_{2}}$. Strongly consistent estimators of unknown model parameters ${({H_{1}},{H_{2}},{\kappa ^{2}},{\sigma ^{2}})^{\top }}$ are constructed based on the equidistant observations of a trajectory. Joint asymptotic normality of these estimators is proved for $0\lt {H_{1}}\lt {H_{2}}\lt \frac{3}{4}$.

In this paper, the discontinuous dynamic behavior of a two-degree-of-freedom frictional collision system including intermediate elastic collision and unilateral elastic constraints subjected to periodic excitation is studied by using flow switching theory. In this system, given that the motion of each object might have a velocity that is either greater than or less than zero and each object experiences a periodic excitation force that has negative feedback, because the kinetic and static friction coefficients differ, the flow barrier manifests when the object's speed is zero. Based on the discontinuity or nonsmoothness of the oscillator's motion generated by elastic collision and friction, the motion states of the oscillator in the system are divided into 16 cases and the absolute and relative coordinates are used to define various boundaries and domains in the oscillator motion's phase space. On the basis of this, the G-function and system vector fields are used to propose the oscillator motion's switching rules at the displacement and velocity boundaries. Finally, some dynamic behaviors for the 2-DOF oscillator are demonstrated via numerical simulation of the oscillator's stick, grazing, sliding and periodic motions and the scene of sliding bifurcation. The mechanical system's optimization designs with friction and elastic collision will benefit from this investigation's findings.

This paper investigated the Kronecker product (KP) decomposition of the Boolean matrix and analyzed the topological structure of Kronecker product Boolean networks (KPBNs). First, the support matrix set of the Boolean matrix consisting of support matrices was defined. Second, a verifiable condition was presented for the KP decomposition of the Boolean matrix based on the support matrices. Third, the equivalence of KP decomposition between the Boolean matrix and support matrix set was established. Finally, the KP decomposition of Boolean matrix was used to analyze the topological structure of KPBNs. It was shown that the topological structure of KPBNs can be determined by that of the factor of Boolean networks (BNs).

Based on fuzzy semi-tensor product (STP) algorithms and fuzzy relation matrix (FRM) models, the design of an adaptive fuzzy controller was proposed in this paper for the multivariable nonlinear systems with uncertainty. The controlled multi-input-and-multi-output (MIMO) plants were expressed and processed first by FRM models and fuzzy STP operations, and then the indirect adaptive fuzzy control laws were designed. The tracking property of the FRM models was proved for the control objective of MIMO systems. The effectiveness of the novel matrix expression was verified by simulations of the tracking control on a two-link rigid robot manipulator. Results in simulation tests show that the proposed design of adaptive FRM control is efficient for nonlinear multivariables. Therefore, the proposed indirect fuzzy adaptive controllers can be extended to general matrix expression for MIMO nonlinear systems with fuzzy STP algorithms and FRM models and online approximate unknown parameters, according to required accuracy.

This paper mainly studied the problem of solving interval type-2 fuzzy relation equations $ \widetilde A \circ \widetilde X = \widetilde B $. First, to solve the interval type-2 fuzzy relation equations, we extend the semi-tensor product of matrices to interval matrices and give its specific definition. Second, the interval type-2 fuzzy relation equation was divided into two parts: primary fuzzy matrix equation $ {\widetilde A_\mu } \circ {\widetilde X_\mu }{\rm{ = }}{\widetilde B_\mu} $ and secondary fuzzy matrix equation $ {\widetilde A_f} \circ {\widetilde X_f} = {\widetilde B_f} $. Since all elements of $ {\widetilde X_f} $ equal to one, only the principal fuzzy matrix equation needs to be considered. Furthermore, it was proved that all solutions can be obtained from the parameter set solutions if the primary fuzzy matrix equation is solvable. Finally, with semi-tensor product of interval matrices, the primary fuzzy matrix equation was transformed into an algebraic equation and the specific algorithm for solving an interval type-2 fuzzy relation equation was proposed.

A novel closed-loop optimal controller for fractional nonlinear quadratic optimal control problems is introduced. By using a new idea, the optimality conditions for the fractional nonlinear problems are derived. The linearized Riccati fractional order differential equation is derived and a new solution method is given for the first time, which can be applied to integer order nonlinear optimal control problems. The proposed closed-loop controller is applied to illustrative examples. Novel unprecedented processes of designing a variable linear controller and of finding the optimal performance index for integer order nonlinear systems are presented.

This paper presents a neuro-adaptive finite-time control strategy for uncertain nonstrict-feedback fractional-order nonlinear systems with multiple-objective constraints. To stabilize the uncertain nonlinear fractional-order systems, neural networks (NNs) are employed to identify the unknown nonlinear functions, and dynamic surface control is used to avoid the computational complexity of the backstepping design procedure. The effect caused by the algebraic loop problem can be solved via establishing fractional-order adaptive laws. Introducing a new barrier function, the system output is always limited to the predefined time-varying acceptable range while effectively solving the multi-objective constraint problem. Utilizing fractional-order finite-time stability theory, a finite-time control scheme is constructed to drive the system output to the reference signal in finite time, which ensures better tracking performance. Two examples are given to illustrate the availability and superiority of the presented control scheme.

Anthrax is a bacterial infection caused by Bacillus anthracis, primarily affecting animals and occasionally affecting humans. This paper presents two compartmental deterministic models of anthrax transmission having vaccination compartments. In both models, a nonlinear ratio-dependent disease transmission function is employed, and the latter model distinguishes itself by incorporating fractional order derivatives, which adds a novel aspect to the study. The basic reproduction number $ \mathcal{R}_0 $ of the epidemic is determined, below which the disease is eradicated. It is observed that among the various parameters, the contact rate, disease-induced mortality rate, and rate of animal recovery have the potential to influence this basic reproduction number. The endemic equilibrium becomes disease-free via transcritical bifurcations for different threshold parameters of animal recovery rate, disease-induced mortality rate and disease transmission rate, which is validated by utilizing Sotomayor's theorem. Numerical simulations have revealed that a higher vaccination rate contributes to eradicating the disease within the ecosystem. This can be achieved by effectively controlling the disease-induced death rate and promoting animal recovery. The extended fractional model is analyzed numerically using the Adams-Bashforth-Moulton type predictor-corrector scheme. Finally, it is observed that an increase in the fractional order parameter has the potential to reduce the time duration required to eradicate the disease from the ecosystem.

This paper was concerned with the problem of filter design for the continuous-discrete system in the Takagi-Sugeno (T-S) fuzzy model. In a known finite frequency (FF) domain, an FF $ H_\infty $ performance was defined for the nonlinear continuous-discrete system. With the designed filter, sufficient conditions were then established for the filtering error system to be asymptotically stable and having a prescribed FF $ H_\infty $ performance. After that, a systematic method for the filter design was proposed. Finally, an example was provided to check effectiveness of the derived results.

Chameleon chaotic systems are nonlinear dynamical systems whose chaotic attractors can transform between hidden and self-excited types by tuning system parameters to modify equilibrium points. This paper proposes a novel family of chameleon chaotic systems, which can exhibit three types of chaotic attractors: self-excited attractors with a nonhyperbolic equilibrium, hidden attractors with a stable equilibrium, and hidden attractors with no equilibrium points. Bifurcation analysis uncovers the mechanisms by which self-excited and hidden chaotic attractors arise in this family of chameleon systems. It is demonstrated that various forms of chaos emerge through period-doubling routes associated with changes in the coefficient of a linear term. An electronic circuit is designed and simulated in Multisim to realize a hidden chaotic system with no equilibrium points. It is demonstrated that the electronic circuit simulation is consistent with the theoretical model. This research has the potential to enhance our comprehension of chaotic attractors, especially the hidden chaotic attractors.

Bacterial meningitis, which is considered a major concern by the World Health Organization, is a medical emergency that lingers as a terrifying infection in sub-Saharan Africa and other countries in the "meningitis belt" due to the frequent occurrence of the infection and its debilitating effects among survivors, even after treatment. This study presents a novel two-strain compartmental bacterial meningitis model. The disease-free equilibrium was established to be locally and globally asymtotically stable. Numerical simulations were performed to visualize the effects of various model parameters on each compartment. Sensitivity analysis was also performed and it was established that the most sensitive parameter for both strains $ 1 $ and $ 2 $ is the transmission probability, $ \beta $. It was ascertained that bacterial meningitis will not spread in the population if at least $ 25\% $ of the population are immune to the disease.

Decisions of central banks on foreign exchange rates are based on the comovement of foreign exchange (FOREX) in mature markets such as US dollar rates to the British pound, euro, Chinese yuan, Japanese yen and Australian dollar. We investigate the long-run movement and dynamic quantile connectedness of volatility among pairs of these exchange rates. The updated residual-based fractional cointegration testing framework using narrow-band frequency domain least squares estimator is used to obtain the residual series for fractional cointegration. Quantile dynamic connectedness framework for volatility spillovers at different market conditions, depicted by quantiles, are used. We find evidence of long memory cointegration in seven pairs of exchange rates involving the previously mentioned currencies. These seven cases also correspond to a higher average index of quantile connectedness, with the effect of connectedness phasing out at higher quantiles and being more visible at lower quantiles. A portfolio investment strategy using optimal portfolio weights and hedge ratios for maintaining the accrued profit at the FOREX market is also presented.

In this paper, we present an in-depth analysis of Central Bank Digital Currencies (CBDCs), focusing on their definition, purpose, design considerations and recent developments. We also delve into the potential advantages of CBDCs for Asia, such as enhancing convenience, precisely quantifying economic metrics, managing anonymity, catalyzing innovation, and promoting financial inclusion. Moreover, we examine how CBDCs can fortify monetary and fiscal policies, ensure safe distribution, reduce costs and combat corruption. We also address the risks associated with CBDC adoption in Asia and explore potential outcomes such as substitution effects, valuation fluctuations, and foreign currency dependence, while highlighting the importance of managing financial imbalances, holdings concentration and public apprehension toward digital currencies.

Our aim of this paper is to determine whether inflation targeting could improve economic growth and financial stability in 35 emerging economies of which 19 inflation-targeting and 16 non-inflation-targeting countries over the 1995–2017 period. To this end, we first determine the preconditions needed to adopt the inflation targeting regime using the Qualitative Comparative Analysis method (QCA). We then construct a Financial Stability Index (FSI) for emerging markets using a Principal Components Analysis (PCA). Finally, we determine the impact of shocks on economic growth and financial stability in inflation-targeting and non-inflation-targeting countries through a Panel VAR model estimated using the GMM method. The results show that some structural and institutional preconditions, should be set up during the pre-adoption period. In addition, the results indicate that the inflation-targeting regime allows emerging countries to control their economic growth and financial stability in the event of shocks to a greater extent than non-targeting countries, although the magnitude of the shock persists only in the short run, given that economic and financial conditions return to their normal state in the long run.

Abstract We introduce a Tseng extragradient method for solving monotone inclusion problem in Banach space. A strong convergence result of an Halpern inertial extrapolation method for solving the resolvent of sum of two monotone operators without the knowledge of the Lipschitz constant was established. Lastly, we illustrate some numerical behavior of our iterative scheme to showcase the performance of the proposed method compared to other related results in the literature.

The emergence of COVID-19 has broken the silence of humanity and people are gradually becoming concerned about pneumonia-related diseases; thus, improving the recognition rate of pneumonia-related diseases is an important task. Neural networks have a remarkable effectiveness in medical diagnoses, though the internal parameters need to be set in accordance to different data sets; therefore, an important challenge is how to further improve the efficiency of neural network models. In this paper, we proposed a learning exponential distribution optimizer based on chaotic evolution, and we optimized Resnet50 for COVID classification, in which the model is abbreviated as IEDO-net. The algorithm introduces a criterion for judging the distance of the signal-to-noise ratio, a chaotic evolution mechanism is designed according to this criterion to effectively improve the search efficiency of the algorithm, and a rotating flight mechanism is introduced to improve the search capability of the algorithm. In the computed tomography (CT) image data of COVID-19, the accuracy, sensitivity, specificity, precision, and F1 score of the optimized Resnet50 were 94.42%, 93.40%, 94.92%, 94.29% and 93.84%, respectively. The proposed network model is compared with other algorithms and models, and ablation experiments and convergence and statistical analyses are performed. The results show that the diagnostic performance of IEDO-net is competitive, which validates the feasibility and effectiveness of the proposed network.

As a typical deep learning technique, Graph Convolutional Networks (GCN) has been successfully applied to the recommendation systems. Aiming at the leakage risk of user privacy and the problem of fraudulent data in the recommendation systems, a Privacy Preserving Recommendation and Fraud Detection method based on Graph Convolution (PPRFD-GC) is proposed in the paper. The PPRFD-GC method adopts encoder/decoder framework to generate the synthesized graph of rating information which satisfies edge differential privacy, next applies graph-based matrix completion technique for rating prediction according to the synthesized graph. After calculating user's Mean Square Error (MSE) of rating prediction and generating dense representation of the user, then a fraud detection classifier based on AdaBoost is presented to identify possible fraudsters. Finally, the loss functions of both rating prediction module and fraud detection module are linearly combined as the overall loss function. The experimental analysis on two real datasets shows that the proposed method has good recommendation accuracy and anti-fraud attack characteristics on the basis of preserving users' link privacy.