In this paper, we introduce two subclasses of analytic and Spirallike functions and investigate convolution properties, the necessary and sufficient condition, coefficient estimates and inclusion properties for these classes .

This study explores the properties and behavior of bi-close-to-convex functions, introducing new subclasses defined by their relationship with fractional differential operator and bi-univalent functions. Using the Faber polynomial technique, we derive upper bounds for the n^{th} coefficient of functions in these classes. We also investigate the erratic behavior of initial coefficients in bi-close-to-convex functions, as characterized by the (λ,q)-fractional differintegral operator. Furthermore, we address Fekete-Szegö problems and present notable findings from our investigation, contributing to the continued growth and refinement of geometric function theory, yielding new insights and practical uses.

In this paper, we investigate a new subclass of univalent functions defined by a generalized differential operator, and obtain some interesting properties of functions belonging to the class R^m λµ ( α, β, γ, υ ).

In this paper, a multi-operator differential evolution algorithm (MODE) is proposed to solve the Optimal Power Flow (OPF) problem and is called MODE-OPF. The MODE-OPF utilizes the strengths of more than one differential evolution (DE) operator in a single algorithmic framework. Additionally, an adaptive method (AM) is proposed to update the number of solutions evolved by each DE operator based on both the diversity of population and quality of solutions. This adaptive method has the ability to maintain diversity at the early stages of the optimization process and boost convergence at the later ones. The performance of the proposed MODE-OPF is tested by solving OPF problems for both small and large IEEE bus systems (i.e., IEEE-30 and IEEE-118) while considering the intermittent solar and wind power generation. To prove the suitability of this proposed algorithm, its performance has been compared against several state-of-the-art optimization algorithms, where MODE-OPF outperforms other algorithms in all experimental results and thereby improving a network's performance with lower cost. MODE-OPF decreases the total generation cost up to 24.08%, the real power loss up to 6.80% and the total generation cost with emission up to 8.56%.

The methods for constructing solutions to integro-differential equations of the Volterra type are considered. The equations are related to fractional conformable derivatives. Explicit solutions of homogeneous and inhomogeneous equations are constructed and a Cauchy-type problem is studied. It should be noted that the considered method is based on the construction of normalized systems of functions with respect to a differential operator of fractional order.

Fractional differential mathematical model unfolding the dynamics of the COVID-19 pandemic in India is presented and explored in this paper. The purpose of this study is to estimate the future outbreak of disease and potential control strategies using mathematical models in India as a whole country as well as in some of the states of the country. This model is calibrated based on reported cases of infections over the month of April 2020 in India. We have used iterative fractional complex transform method to find approximate solutions of the model having modified Riemann Liouville fractional differential operator. We have also carried out a comparative analysis between actual and estimated cumulative cases graphically, moreover, most sensitive parameters for basic reproduction number$(R_0)$ are computed and their effect on transmission dynamics of COVID-19 pandemic is investigated in detail.

In this article, we are interested in a new generic class of nonlocal fractional impulsive differential inclusions with linear sectorial operator and Lipschitz multivalued function in the setting of finite dimensional Banach spaces. By modifying the definition of PC-mild solutions initiated by Shu, we succeeded to determine new conditions that sufficiently guarantee the existence of the solutions. The results are obtained by combining techniques of fractional calculus and fixed point theorem for contraction maps. We also characterize the topological structure of the set of solutions. Finally, we provide a demonstration to address the applicability of the theoretical results.

We investigate the existence and representation of the generalized core-EP inverse of some triangular matrices over a Banach algebra. Further, the general representations of the generalized core-EP inverse of a triangular matrix over a $C^*$-algebra are presented. As applications, the generalized core-EP inverses of some block operator matrices over Hilbert spaces are given.

In this work, an operator superquadratic function (in operator sense) for positive Hilbert space operators is defined. Several examples with some important properties together with some observations which are related to the operator convexity are pointed out. Equivalent statements of a non-commutative version of Jensen's inequality for operator superquadratic function are established. A generalization of the main result to any positive unital linear map is also provided.

Major limitations in the effective treatment of neurological cancer include systemic cytotoxicity of chemotherapy, inaccessibility, and inoperability. The capability to successfully target a drug to the tumor site(s), without incurring serious side effects, especially in the case of aggressive tumors, such as glioblastoma and neuroblastoma, would represent a significant breakthrough in therapy. Orthotopic systems, capable of storing and releasing proteins over a prolonged period at the site of a tumor, utilising nanoparticles, liposomes, and hydrogels have been proposed. One candidate for drug delivery is Micro-Fragmented Adipose Tissue (MFAT). Obtained easily from the patient by abdominal subcutaneous liposuction (autologous), and with a high content of Mesenchymal Stem Cells (MSC), mechanically derived nanofat is a natural tissue graft with a structural scaffold organization. It has a well preserved stromal vascular fraction, and a prolonged capacity to secrete anti-tumorigenic concentrations of pre-absorbed chemotherapeutics within extracellular vesicles. This review discusses current evidence supporting the potential of drug modified MFAT for the treatment of neurological cancer with respect to recent preclinical and in vitro studies. Possible limitations and future perspectives are considered.

The unified Mittag-Leffler (ML) function is important factor in formulation of compact form of fractional integrals. In this paper estimations of integral operators, with the unified ML function as kernel are given. The Hadamard inequality in the form of fractional integrals is proved by considering refinement of convexities. These estimations provide various inequalities as refinements of recently published results.

The intense motion of a ship can greatly impacts the comfort of crew members and the safety of the vessel. Therefore, accurately estimating and predicting ship attitudes has become an important issue. This paper introduces the latest development in functional deep learning model called DeepOnet. It takes wave height as input and ship motion as output, using a cause-to-result prediction approach. The modeling data used in this study is sourced from publicly available experimental data from the Iowa Institute of Hydraulic Research. Firstly, parameters system tuning was conducted for the neural network's hyperparameters to determine the appropriate combination of parameters. Secondly, the DeepOnet model for wave height and multi-degree-of-freedom motion was established, and the influence of increasing time steps on prediction accuracy was examined. Finally, a comparison was made between the DeepOnet model and the classical time series model LSTM. It was found that the DeepOnet model had a 10-fold improvement in accuracy for roll and heave attitudes. Moreover, as the forecast duration increased, the advantage of DeepOnet showed a trend of strengthening. As a functional prediction model, DeepOnet provides a new promising tool for very short-term prediction of ship motion.

In this paper we investigate the differential topological properties of a subclass of singular space--subcarteisan spaces. First, we get further result on partition of unity for differential spaces. Second, we establish the tubular neighborhood theorem for subcartesian spaces with constant structural dimension. Third, we generalize the concept of Morse functions on smooth manifolds to differential spaces. For subcartesian space with constant structural dimension, we provide examples of Morse functions; With the assumption that the subcartesian space can be embedded as a bounded subset of an Euclidean space, we prove that smooth bounded functions on this space can be approximated by Morse functions; We study the infinitesimal stability of Morse functions on subcartesian spaces. Classical results on Morse functions on smooth manifolds can be treated directly as corollaries of our results here.

By utilizing the Fourier transform, we present a practical method for evaluating a function of a derivative applied to any other arbitrary function of a single complex variable. As an illustration of this approach, we compute the actions of the displacement and squeeze operators on an arbitrary function, as well as the propagation of paraxial fields, Airy and number states, without the need for algebraic quantum operator techniques or the Fresnel integral.

In this paper, the transmutation operator method is used to construct an exact solution to the initial boundary value problem for the equation of multidimensional free transverse vibration of a thin elastic plate with a singular Bessel operator acting on geometric variables. We emphasize that multidimensional Erdélyi–Kober operators of fractional order have the property of a transmutation operator, allowing one to transform more complex multidimensional partial differential equations with singular coefficients acting over all variables into simpler ones. If formulas for solutions are known for a simple equation, then we also obtain representations for solutions to the first complex partial differential equation with singular coefficients. In particular, it is successfully applied to the singular differential equations, especially with Bessel-type operators. Using this operator, the considered problem is reduced to a similar problem without the Bessel operator. Based on the solution to the auxiliary problem, an exact solution to the original problem is constructed and analyzed.

In the dynamic and complex environment of industrial control rooms, operators are often inundated with a multitude of tasks and alerts, which can lead to an overwhelming situation known as task overload. This state can precipitate decision fatigue and a heavier reliance on cognitive biases, potentially compromising the decision-making process. To mitigate such risks, the implementation of decision support systems becomes crucial. These systems are designed to assist operators in making swift and well-informed decisions, particularly when they sense their own judgment may be faltering. Our research introduces an AI-based framework that leverages dynamic influence diagrams and reinforcement learning to construct an effective decision support system. The cornerstone of this framework is the creation of a robust, interpretable, and efficient tool that supports control room operators during critical process disturbances. By integrating expert knowledge, the dynamic influence diagram forms a comprehensive model that captures the uncertainties inherent in complex industrial processes. It is adept at anomaly detection and recommending optimal actions. Moreover, this model is enhanced through a strategic partnership with reinforcement learning algorithms, which fine-tune the recommendations to be more context-specific and precise. The ultimate goal of our framework is to provide operators with a live, reliable decision support system that can significantly improve their response during process upsets. This paper outlines the development of our AI framework and its application within a simulated control room environment. Our findings indicate that the use of decision support systems can lead to improved operator performance and reduced cognitive workload. However, it also reveals a trade-off with situation awareness, which tends to diminish as operators may become overly reliant on the system’s guidance. Trust emerges as a critical factor in the adoption and effectiveness of decision support systems. Our research underscores the importance of balancing the benefits of decision support with the need for maintaining operator engagement and comprehension during process operations.

The validity of our universe as a three-dimensional space (3+1 in relativity) is considered a fundamental fact in physics. In this study, we show that our observed world is thus the output of a prior fundamental operator referred to as an organizer. The organizer is an expansion of projecting operators. It is been shown that identical weighted projecting operators, which are associated with identical particles, generate subspaces of entangled states, whereas groups of unequal weighted coefficients are responsible for finite-size subspaces that are associated with unidentical particles. Considering 3D-subspaces as evidence of the coefficients’ arrangement in our universe, we implement our formalism to describe the implacable vectors, location, momentum, and force within each 3D subspace. By implementing the Heisenberg relation, we drive both the classical and quantum expressions for the laws of motion.

We show that if $f$ is a non-negative superquadratic function, then $A\mapsto\mathrm{Tr}f(A)$ is a superquadratic function on the matrix algebra. In particular, \begin{align*} \tr f\left( {\frac{{A + B}}{2}} \right) +\tr f\left(\left| {\frac{{A - B}}{2}}\right|\right) \leq \frac{{\tr {f\left( A \right)} + \tr {f\left( B \right)} }}{2} \end{align*} holds for all positive matrices $A,B$. In addition, we present a Klein's inequality for superquadratic functions as $$ \mathrm{Tr}[f(A)-f(B)-(A-B)f'(B)]\geq \mathrm{Tr}[f(|A-B|)] $$ for all positive matrices $A,B$. It gives in particular improvement of Klein's inequality for non-negative convex function. As a consequence, some variants of the Jensen trace inequality for superquadratic functions have been presented.

In this paper, we propose a new covering-based set in which the lower and the upper approximation operations are defined by neighborhood systems. We discuss this new type of covering-based set systematically in two steps. First, we study the basic properties of this covering-based set, such as the properties of normality, contraction, and monotone. Second, we discuss the relationship between the new type of covering-based set and the other ten sets proposed.

In this paper, we propose a new covering-based set in which the lower and the upper approximation operation are defined by neighborhood systems. We discuss this new type of covering-based set systematically in two steps. First, we study the basic properties of this covering-based set, such as the properties of normality, contraction, and monotone. Second, we discuss the relationship between the new type of covering-based set and the other ten sets proposed.

The main objective of this present paper is to introduce further extension of extended Caputo fractional derivative operator and establish the extension of an extended fractional derivative of some known elementary functions. Also, we investigate the extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and generating relations for extension of extended hypergeometric functions.

The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to k-hypergeometric and k-Appell's functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.

Data security and user privacy concerns are increasingly gaining attention. Federated learning models based on differential privacy offer a distributed machine learning framework that protects data privacy; however, the added noise can impact the model's utility, making performance evaluation crucial. To optimize the balance between privacy protection and model performance, we propose the Adaptive Weight-Based Differential Privacy Federated Learning (AWDP-FL) framework. This framework processes model parameters from the perspectives of neural network layers and model weights. Initially, each participant trains the model locally. During iterative training, the clipping threshold is determined by selecting an adaptive weight coefficient, followed by adaptive gradient clipping to control the gradient magnitude. Subsequently, adaptive gradient updates are applied to the model, and dynamic Gaussian noise is introduced when uploading the parameters to protect participant privacy. The server aggregates these noise-perturbed parameters to update the global model. This framework ensures strong privacy protection while maintaining model accuracy. Theoretical analysis and experimental results validate the effectiveness of this framework under stringent privacy constraints.

This work aims to introduce a novel concept: the Riesz-Dunkl fractional derivatives, within the context of Dunkl type operators. A particularly noteworthy revelation is that when a specific parameter $\kappa$ equals zero, the Riesz-Dunkl fractional derivative smoothly reduces to both the well-known Riesz fractional derivative and the fractional second-order derivative. Furthermore, we introduce a new concept: the fractional Sobolev space. This space is defined and characterized using the versatile framework of the Dunkl transform.

Partial Differential Equations (PDEs) constitute a fundamental framework for modeling various physical phenomena across diverse fields such as physics, engineering, and finance. Solving PDEs accurately and efficiently remains a significant challenge, particularly when dealing with complex systems or high-dimensional data. In this paper, we present a novel approach based on deep learning techniques to investigate the effective factors in solving PDEs. Our methodology leverages the expressive power of deep neural networks to learn and represent the underlying relationships between input parameters and the solutions of PDEs. By incorporating domain knowledge into the network architecture and training process, our approach aims to provide insights into the key factors influencing the solution of PDEs. We demonstrate the effectiveness of our method through numerical experiments on various PDEs, showcasing its capability to identify important features and improve predictive accuracy. Our findings suggest that deep learning techniques offer a promising avenue for understanding and analyzing the complex dynamics inherent in PDEs, paving the way for enhanced computational methods in scientific and engineering applications.

This article aims to explore the existence and stability of solutions to differential equations involving a regularized ψ−Hilfer fractional derivative, which, compared to standard ψ−Hilfer fractional derivatives, provide a clear physical interpretation when dealing with initial conditions. We discovered that the regularized ψ−Hilfer fractional derivative can be represented as the inverse operation of the ψ−Riemann–Liouville fractional integral, and used this property to prove the existence of solutions for linear differential equations with a regularized ψ−Hilfer fractional derivative. Additionally, we applied the Mönch’s fixed-point theorem and knowledge of non-compactness measures to demonstrate the existence of solutions for nonlinear differential equations with a regularized ψ−Hilfer fractional derivative, and further discussed Ulam-Hyers-Rassias stability and semi-Ulam-Hyers-Rassias stability of these solutions. Finally, we illustrated our results through case studies.

Abstract. This paper proposes a Second Order Terminal Sliding Mode (2TSM) approach to the trajectory tracking of Differential Drive Mobile Robot (DDMR). Within this cascaded control scheme, the 2TSM dynamic controller, at the inner most loop, tracks the robot’s velocity quantities; while a kinematic controller, at the outer most loop, regulates the robot’s positions. In this manner, chattering is greatly attenuated and finite time convergence is guaranteed by the second order TSM manifold which involves higher order derivatives of the state variables, resulting in inherently robust as well as fast and better tracking precision. The simulation results demonstrate the merit of the proposed control methods.

Existing one-shot neural architecture search (NAS) methods have to conduct a search over a giant super-net, which leads to the huge computational cost. To reduce such cost, in this paper, we propose a method, called FTSO, to divide the whole architecture search into two sub-steps. Specifically, in the first step, we only search for the topology, and in the second step, we search for the operators. FTSO not only reduces NAS’s search time from days to 0.68 seconds, but also significantly improves the found architecture's accuracy. Our extensive experiments on ImageNet show that within 18 seconds, FTSO can achieve a 76.4% testing accuracy, 1.5% higher than the SOTA, PC-DARTS. In addition, FTSO can reach a 97.77% testing accuracy, 0.27% higher than the SOTA, with nearly 100% (99.8%) search time saved, when searching on CIFAR10.

A new low-pass filter (LPF) circuit with independent adjustment of various, incl. digitally controlled, pole frequency resistors, pole quality factor and transmission coefficient. The proposed low-pass filter is based on the use of the properties of a multi-differential operational amplifier that performs the functions of a signal adder. The peculiarity of the filter is that it has three inputs, with respect to which different transmission coefficients are implemented, incl. inverting (-1) and non-inverting (+1). To check these properties of a low-pass filter in the Micro-Cap environment, computer simulation of a specific circuit was performed on a multi-differential operational amplifier AD 8130. Mathematical expressions are given for the main parameters of the proposed low-pass filter, which allow parametric synthesis of elements of a specific circuit under given restrictions on the used element base.

Keywords: Linear differential arrays; beam steering; frequency-invariant beamforming.

Local polynomial smoother (LPS) is a weighted local least-squares nonparametric method. It provides a local Taylor series fit of the data at any location and can be directly used in a differential equation to provide a numerical scheme. In this article, we introduce this new nonparametric idea based on local polynomial smoother, for acquiring the numerical solution of the Bagley-Torvik fractional-order differential equations. Furthermore, this paper will present a numerical comparison with some methods, such as legendre operational matrix and pseudo-spectral method. The efficiency and accuracy of the LPS method are demonstrated by two numerical examples.

Baijiu is popular with its long history and balanced flavor, and flavor type was the most widely used classification mode for Baijiu. However, the evolution relationship of Baijiu flavor types and the differential markers between flavor types are still unclear, which has greatly affected the development of Baijiu industry. In this study, a total of 319 trace components were identified by gas chromatography-olfactometry-mass spectrometry and gas chromatography-mass spectrometry. Among them, 91 trace components with high odor active values or taste active values were recognized as flavor components. Then random forests were conducted to screen differential markers between derived and basic flavor types, and principal component analysis was carried out to evaluate their effectiveness in distinguishing the flavor types of Baijiu. Finally, 19 differential markers were screened and proved to effectively reveal the evolution Baijiu flavor types, and were further verified as key differential markers by addition test and correlation analysis.

The sexual reproduction of ascomycetes is controlled by the mating-type(MAT) locus. (Pseudo)homothallic reproduction has been hypothesized based on genetic data from Hirsutella sinensis (Genotype #1 of Ophiocordyceps sinensis). In this study, the differential occurrence of the mating-type genes in the MAT1-1 and MAT1-2 idiomorphs, which constitute the genetic control of O. sinensis reproduction, was analyzed in 237 strains and 5 genomes of H. sinensis. The mating-type genes were differentially transcribed in H. sinensis Strain L0106, and the MAT1-2-1 transcript in H. sinensis Strain 1229 was alternatively spliced, with an unspliced intron I containing stop codons; these findings constitute O. sinensis reproduction controls at the transcriptional and coupled transcriptional-translational levels. The occurrence of the mating-type genes and a-/α-pheromone receptor genes differed among the 5 H. sinensis genomes. The differential occurrence and transcription of these genes are inconsistent with self-fertilization under (pseudo)homothallism but suggest self-sterility of H. sinensis, which therefore needs a mating partner to achieve sexual outcrossing under heterothallism or hybridization. Consistent occurrence and transcription of the mating-type genes of both the MAT1-1 and MAT1-2 idiomorphs have been reported in natural and cultivated Cordyceps sinensis, but these findings are insufficient to determine the reproduction mode(s) because of the co-occurrence of >90 fungal species and multiple genomically independent genotypes of O. sinensis. The mutant MAT1-1-1 and α-pheromone receptor transcripts in natural C. sinensis result in the N-terminus or middle-truncated proteins, with changes in hydrophobicity and secondary structures of the proteins, suggesting heterogeneous fungal source(s) of the proteins and hybridization reproduction.

In the past two decades, metaheuristic optimization algorithms (MOAs) have been increasingly popular, particularly in logistic, science, and engineering problems. The fundamental characteristics of such algorithms are that they are dependent on a parameter or a strategy. Some online and offline strategies are employed in order to obtain optimal configurations of the algorithms. Adaptive operator selection is one of them, and it determines whether or not to update a strategy from the strategy pool during the search process. In the filed of machine learning, Reinforcement Learning (RL) refers to goal-oriented algorithms, which learn from the environment how to achieve a goal. On MOAs, reinforcement learning has been utilised to control the operator selection process. Existing research, however, fails to show that learned information may be transferred from one problem-solving procedure to another. The primary goal of the proposed research is to determine the impact of transfer learning on RL and MOAs. As a test problem, a set union knapsack problem with 30 separate benchmark problem instances is used. The results are statistically compared in depth. The learning process, according to the findings, improved the convergence speed while significantly reducing the CPU time.

There are many criterion to generalize the concept of numerical radius; one of the most recent interesting generalization is what so called the generalized Euclidean operator radius. Simply, it is the numerical radius of multivariable operators. In this work, several new inequalities, refinements and generalizations are established for this kind of numerical radius.

Recently, different extensions of the fractional derivative operator are found in many research papers. The main aim of this paper is to establish an extension of the extended Caputo fractional derivative operator. The extension of an extended fractional derivative of some elementary functions derives by considering an extension of beta function which includes the Mittag-Leffler function in the kernel. Further, an extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and the generating relations for extension of extended hypergeometric functions also presented in this study.

In this study, we consider a Lambert series whose coefficients are the sum of divisors function. Utilizing the Lambert series in the sequel we introduce a normalized linear operator JR_(α,β) (z) by applying the convolution with Rabotnov function. We then, acquire sufficient conditions for JR_(α,β) (z) to be Univalent, Starlike and Convex respectively. In each component of this study, we expand the derived results by applying two Robin's inequalities, one of which is equivalent to the Riemann hypothesis.

The introduction of Maritime Autonomous Surface Ship (MASS) through the development of autonomous navigation technologies is expected to bring about new technologies, new vessel types, and new job roles such as remote operation center (ROC) and remote operator (RO). The MASS Code are currently being discussed through Maritime Safety Committee (MSC) of International Maritime Organization (IMO). This code is expected to be adopted in the form of non-mandatory guidelines until 2025, with the goal of establishing mandatory requirements by 2028. Additionally, revisions to the International Convention on Standards of Training, Certification and Watchkeeping for Seafarers (STCW) related to crew training and qualifications are planned for adoption by 2027, which will include requirements for MASS operators. This paper aims to examine the fundamental competencies required for safe MASS operation by remote operators using the Analytic Hierarchy Process (AHP) method, considering the emergence of the new profession of RO. Building upon the 66 Knowledge, Understanding & Proficiencies (KUPs) outlined for marine officer in the STCW Convention, the study seeks to identify the additional competencies necessary for RO and contribute to the development of a training model for the future.

Cholera is a diarrheal disease prevalent in populations without access to clean water. Cholera is caused by Vibrio cholerae, which colonizes the upper small intestine in humans once ingested. A growing number of studies suggests the gut microbiome composition modulates animal behavior. Zebrafish are an established cholera model that can maintain a complex, mature gut microbiome during infection. Larval zebrafish, which have immature gut microbiomes, provide the advantage of high-throughput analyses for established behavioral models. We identified the effects of V. cholerae O1 El Tor C6706 colonization at 5 days post-fertilization (dpf) on larval zebrafish behavior by tracking startle responses at 10 dpf. We also characterized the larval gut microbiome using 16S rRNA sequencing. V. cholerae-infected or uninfected control groups were exposed to either an alternating light/dark stimuli or a single-tap stimulus, and average distance and velocity were tracked. While there was no significant difference in the light/dark trial, we report a significant decrease in distance moved for C6706-colonized larvae during the single-tap trial. This suggests that early V. cholerae colonization of the larval gut microbiome has a dampening effect on sensorimotor function, supporting the idea of a link between the gut microbiome and behavior.

We primarily investigate the existence of solutions for fractional neutral integro-differential equations subjected to Neumann-type boundary conditions, which is crucial for understanding natural phenomena. Taking into account factors such as neutral type, fractional-order integrals, and fractional-order derivatives, we employ probability density functions, Laplace transforms, and resolvent operators to formulate a well-defined concept of a mild solution for the specified equation. Following this, by integrating fixed point theorems, we establish the existence of mild solutions under more relaxed conditions.

This paperfocusesontheoscillatorypropertiesofthesemi-canonicalnonlineardelaydifferential equation ofthird-order (δ2(t)(δ1(t)ζ′(t))′)′ + η(t)ζα(τ(t))= 0, t ≥ t0, under theconditions ∞t01δ2(t)dt = ∞ andZ ∞t01δ1(t)dt < ∞. Using the new canonical transform method, we transformed the studied equation into a canonical type equation and then we find the conditions for the oscillation of the studied equation from the canonical equations. The obtained results are new and complement to the existing results mentioned in the literature. Examples are provided to illustrate the importance and novelty of the main results.

Tumid Lupus Erythematosus has been the subject of heated debate as to its correct nosographic classification. In particular, its definition has changed over time, depending on the different studies performed. In this review we address the initial definition of TLE, the changes that have taken place in the understanding and placement within the classification of Lupus Erythematosus (LE), and focus on clinical, histopathological, immunophenotypical and differential diagnosis aspects.

In the paper, we develop some numerical schemes including finite difference scheme and finite volume scheme for the fractional Laplacian operator, and apply the resulted numerical schemes to solve some fractional diffusion equations. First, the fractional Laplacian operator can be characterized as the weak singular integral by a integral operator with zero boundary condition. Second, because of the solution of fractional diffusion equation is usually singular near the boundary, we apply finite difference scheme to discrete fractional Laplacian operator and fractional diffusion equation by fractional interpolation function. Moreover, it is find that the differential matrix of the above scheme is symmetric matrix, and strictly row-wise diagonally dominant in special fractional interpolation function. Third, we show finite volume scheme to discrete fractional diffusion equation by fractional interpolation function, and analyze the properties of differential matrix. Finally, the numerical experiments are given, and verify the correctness of theoretical results and the efficiency of the schemes.

Robotic systems are increasingly being used in healthcare to improve patient care and support healthcare professionals. These robots are especially effective at performing repetitive tasks. In complex cancer cases, robots can enhance surgical precision and efficiency, resulting in reduced pain for patients and a lower risk of complications. Robot-assisted surgery offers high-quality 3D imaging, improved clarity, and increased efficiency. This review paper examines the application of Artificial Intelligence (AI) and robotic systems in the healthcare domain, specifically focusing on the interaction among operators, patients, and robots. The goal is to promote collaboration and improve healthcare provision through human-robot interaction. We considered already published articles by relevance, to identify the primary safety issues that need addressing for the integration of AI and robots in hospitals. Concluding with insights into understanding the focal points of social errors in Human-Robot Interaction (HRI) is crucial for mitigating these errors. While current technologies have reached a certain level of maturity, there are still numerous challenges in utilizing robot-assisted clinical practice, including technological, safety, clinical, financial, insurance, psychological, social, ethical, and legal issues. In addition, there is an urgent issue that needs to be addressed: the alignment of values in artificial intelligence, ensuring that AI systems reflect ethical principles and human values is crucial to avoid negative consequences such as bias, discrimination, and prejudicial decisions. Resolving this complex issue requires collaboration among clinical staff, researchers, programmers, and political decision-makers from various fields.

Advances in technology have introduced remarkable capabilities, particularly in the realm of gathering and accessing vast amounts of data, which has led to the emergence of the "Big Data" era, presenting exciting opportunities to harness the wealth of the generated information. Traffic management centers comprise a stakeholder that can exploit such data towards improving road network operation. This research, explores the utilization of real traffic data, collected by distinct sources on an interurban motorway: static location based aggregate traffic data and probe vehicle data. The first is collected by traffic detectors, while the second involves patrol vehicles’ GNSS data. The traffic quantity analysed is vehicle speed, while specific emphasis has been given on the ap-plication of heatmaps to represent daily traffic patterns and the utilization of k-means clustering. The performed analysis demonstrates the importance of considering spatiotemporal variables as a unified entity when analysing speed in transportation networks. The limitations of using patrol vehicles as estimators of ambient speed, especially in low and heavy traffic conditions, are deline-ated, while the dual purpose of data gathered from these vehicles towards enhancing driving performance and enabling detector maintenance is emphasized. Valuable traffic insights are offered through comprehensive spatiotemporal speed behavior analysis and data combination. The inte-gration of these techniques enhances decision-making for a streamlined and secure transportation system

The main objective of this present paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. Also, we give some results related to the newly defined fractional operator such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.

In this paper, we define the cohomology of a modified $\lambda$-differential left-symmetric algebra with coefficients in a suitable representation. We also introduce the notion of modified $\lambda$-differential left-symmetric 2-algebra. We classify linear deformations and abelian extensions of modified $\lambda$-differential left-symmetric algebras using the second cohomology group and classify skeletal modified $\lambda$-differential left-symmetric 2-algebra using the third cohomology group as our propose cohomology applications. Moreover, we prove that strict modified $\lambda$-differential left-symmetric 2-algebras are equivalent to crossed modules of modified $\lambda$-differential left-symmetric algebras.

Multiple sclerosis (MS) is an immune-mediated disease characterized by inflammation, demyelination, and neurodegeneration within the central nervous system. Brain plasticity, the brain's ability to adapt its structure and function, plays a crucial role in mitigating MS's impact. This paper explores the potential benefits of lifestyle changes and nutraceuticals on brain plasticity in MS population. Lifestyle modifications, including physical activity and dietary adjustments, can enhance brain plasticity by upregulating neurotrophic factors, promoting synaptogenesis, and reducing oxidative stress. Nutraceuticals, such as vitamin D, omega-3 fatty acids, and antioxidants like alpha-lipoic acid, have shown promise in supporting brain health through anti-inflammatory and neuroprotective mechanisms. Regular physical activity has been linked to increased levels of brain-derived neurotrophic factor and improved cognitive function. Dietary interventions, including caloric restriction and the intake of polyphenols, can also positively influence brain plasticity. Integrating these lifestyle changes and nutraceuticals into the management of MS could provide a complementary approach to traditional therapies, potentially improving neurological outcomes and enhancing the quality of life for MS population.

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.

This study developed a three-dimensional kinematic and dynamic model of a center-driven linkage system (CDLS). Force analysis was conducted to determine the required driving torque to ensure that the input link of the CDLS rotates at a constant speed with a certain angular velocity, even in the presence of frictional resistance torque. The primary objective was to optimize the maximum angular acceleration of the output links to reduce wiper noise. This optimization can enhance the stability of the linkage system while maintaining its operational functionality. In the adopted methodology, the frames of the fixed links are assumed to remain unchanged, and the input link is considered to operate at a constant angular speed and have a constant length. To meet standard vehicle windshield wiper requirements, 10 constraints were imposed on the optimization problem, which was solved using the differential evolution method. The lengths of both output links were reduced by over 10% after optimization.

In this paper, we compile the fractional power series method and the Laplace transform to design a new algorithm for solving the fractional Volterra integro-differential equation. For that, we assume the Laplace power series (LPS) solution in terms of power q=1m,m∈Z+, where the fractional derivative of order α=qγ for which γ∈Z+. This assumption will help us to write the integral, the kernel, and the nonhomogeneous terms as a LPS with the same power. The recurrence relations for finding the series coefficients can be constructed using this form. To demonstrate the algorithm's accuracy, the residual error is defined and calculated for several values of the fractional derivative. Two strongly nonlinear examples are discussed to provide the efficiency of the algorithm. The algorithm gains powerful results for this kind of problem. Under Caputo meaning the obtained results are illustrated numerically, and graphically. Geometrically, the behavior of the solution declares that the changing of the fractional derivative parameter values' in their domain alters the style of the attained solution in a symmetrical meaning and fully coinciding to the ordinary derivative value'. From these simulations, the results report that the recommended novel algorithm is a straightforward, accurate, and superb tool to generate analytic-approximate solutions for Integral, and integro-differental equations of fractional order.

The application of evolutionary optimization algorithms in problem solving is currently gaining wide popularity. Use of Differential Evolution (DE) algorithm in obtaining analytically approximate solution of unstable second order initial value Ordinary Differential Equation (ODE) is presented in this work. The methodology involves solving an associated problem of optimization with con-strains to get an analytically approximate solution for the ODE under consider-ation. Three test cases were used to demonstrate the efficiency of our method. In comparison with other methods discussed in the literature, our method gave significant improvement on the accuracy of the obtained results.

The theory of fractional calculus extends the order of classical integer calculus from integer to non-integer. As a new engineering application tool, it has made many important research achievements in many fields, including image processing. This paper mainly studies the application of fractional calculus theory in image enhancement and denoising, including the basic theory of fractional calculus and its amplitude frequency characteristics, the application of fractional differential operator in image enhancement, and the application of fractional integral operator in image denoising. The experimental results show that the fractional calculus theory has more special advantages in image enhancement and denoising. Compared with the existing integer order image enhancement operators, the fractional differential operator can more effectively enhance the "weak edge" and "strong texture" details of the image. The fractional order integral image denoising operator can not only improve the signal-to-noise ratio of the image compared to traditional denoising methods, but also better preserve detailed information such as edges and textures of the image.

This paper investigates a range of popular differential evolution (DE) configurations to identify components responsible for emergence of structural bias – a recently identified tendency of algorithms to prefer some regions of search space over others, for reasons unrelated to objective function values. Previous work has explored this tendency for genetic algorithms (GA) and particle swarm optimisation (PSO), finding a relationship between population size and extent of structural bias, hence highlighting potential weaknesses of those algorithms. In current article, we focus on DE, extend the investigation to include consideration of an algorithmic component that is often overlooked – constraint handling mechanism. Towards this end, a wide range of DE configurations was tested here. Results suggest that DE is generally robust to structural bias. Unlike the case with GA and PSO, population size seems to have no influence on DE structural bias. Only one of variants studied – DE/current-to-best/1/bin – shows clear signs of bias, however, we show that this effect is mitigated by a judicious choice of constraint handling technique. These findings contribute towards explaining widespread success of DE variants in algorithm comparison studies; its robustness to structural bias represents the absence of a factor that may confound other algorithms.

This study examines the differential impact of proactive and reactive job crafting behaviors on job well-being, drawing from the perspective of boundary theory. The increasing popularity of work connectivity behavior after-hours (WCBA) after work has attracted widespread attention from scholars on the relationship between WCBA and employee well-being. One view suggests that the impact of WCBA is negative, while another view suggests it is positive. Obviously, the impact of (WCBA) on well-being at work is still contradictory. To clarify the complexity of the impact of WCBA on well-being at work, based on boundary theory, we divided WCBA into proactive WCBA (PC) and reactive WCBA (RC), and examined the double-edged sword effect of WCBA on well-being at work, as well as the mediating mechanisms of job control and work-to-home conflict, and the moderated effects of boundary segmentation preferences. This study uses empirical sampling method to collect data from 125 employees for a period of five days for quantitative research. The results show that, first, PC has an inverted U-shaped effect on job control, and job control is negatively related to well-being at work. Thus the mediating effect of job control is significant. Second, RC has a negative impact on job control, and there is also a negative relationship between job control and well-being at work. Therefore, the mediating effect of job control is significant. Third, PC and RC are positively correlated with work-to-home conflict, and work-to-home conflict has a significant positive impact on well-being at work. Therefore, the mediating effect of work-family conflict is significant. Fourth, the study also found that integration preference moderates the relationship between work-to-home conflict and PC on well-being at work, that is, the mediating effect of work-to-home conflict is stronger for employees with low integration preference. This study enriches our understanding of WCBA, PC and RC from the perspective of proactive and passive employee behaviors. The study also provides a new interpretation of the impact of WCBA on well-being at work and offers valuable insights for the sustainable development in digital social transformation and the application of boundary theory and the theory of empowerment-subjugation in achieving the United Nations Sustainable Development Goals. In addition, the study deepens our understanding of the heterogeneous regulatory role played by work-family integration preferences in influencing well-being at work under different types of WCBA.

Lirianthe delavayi has valuable ornamental and medicinal value, is an important economic tree, and has a long history of cultivation. As important regulatory molecules, miRNAs are involved in important physiological processes, such as the plant stress response, organ morphogenesis, hormone secretion, and signaling. In this study, based on miRNA sequencing analysis of wild and cultivated Lirianthe delavayi, we explored the differences in posttranscriptional regulation during the cultivation of Lirianthe delavayi from the aspect of miRNA molecular regulation. The results revealed the following: 1. A total of 365 miRNAs were sequenced and identified, and their first bases had obvious uracil (U) base preferences. Among them, 242 miRNAs were classified into 32 miRNA families; 2. Analysis of miRNA expression differences revealed that 39 miRNAs had significant expression differences between wild and cultivated populations; 3. Bioinformatics target gene prediction and target gene enrichment analysis of significantly differentially expressed miRNAs revealed that the target genes were significantly enriched in plant‒pathogen interactions, sphingolipid metabolism, defense responses, and ADP binding. 4. The plant‒pathogen interaction pathway involves seven differentially expressed miRNAs and 30 miRNA‒target gene regulatory pairs, which are involved mainly in pathogen signature molecule recognition and binding, signal transduction, and the regulation of disease resistance molecules or gene expression; Ath-MIR169g-p3_2ss7AG19GA, ath-MIR169g-p5_2ss7AG19GA, and ath-miR408-3p_L-3 are expressed only in wild population, and it is hypothesized that the domestication process from wild to cultivation species may be accompanied by the loss of disease resistance-related miRNAs. This study provides a reference for exploring the posttranscriptional-level regulatory mechanisms of adaptive changes in Lirianthe delavayi from wild to cultivated.

The core reasoning task for datalog engines is materialization, the evaluation of a datalog program over a database alongside its phys- ical incorporation into the database itself. The de-facto method of computing it, is through the recursive application of inference rules. Due to it being a costly operation, it is a must for datalog engines to provide incremental materialization, that is, to adjust the computation to new data, instead of restarting from scratch. One of the major caveats, is that deleting data is notoriously more involved than adding, since one has to take into account all possible data that has been entailed from what is being deleted. Differential Dataflow is a computational model that provides efficient incremen- tal maintenance, notoriously with equal performance between ad- ditions and deletions, and work distribution, of iterative dataflows. In this paper we investigate the performance of materialization with three reference datalog implementations, out of which one is built on top of a lightweight relational engine, and the two others are differential-dataflow and non-differential versions of the same rewrite algorithm, with the same optimizations.

Background: The purpuse was to investigate the influence induced by magnesium chloride (MgCl2) and zinc gluconate (ZnG) supplementation on liver and kidney injuries experimentally-induced with acetaminophen (AAPh) and potentiated by ciprofloxacin addition in rats. Material and methods: The experiment was performed on 5 animals groups: group 1 – control, treated for 6 weeks with normal saline, 1mL/kg; group 2 – AAPh, treated for 6 weeks with AAPh, 100 mg/ kg/day; group 3 – AAPh+C, treated AAPh 100 mg/kg/ day for 6 weeks and ciprofloxacin, 50mg /kg/day, only in the last 14 days of the experiment; group 4 – AAPh+C+Mg, with the same treatment as group 3, but, and in the last 14 days, MgCl2 10 mg/ kg/day was added; group 5 – AAPh+C+Zn, with the same treatment as group 3, but, and in the last 14 days, zinc gluconate (ZnG),10 mg/kg/day was added. All administrations were performed by oral gavage. At the end of the experiment, the animals were sacrificed and blood samples were collected for biochemistry examinations. Results: Treatment with AAPh for 6 weeks determined an alteration of the liver function (increases in alanine aminotransferase, aspartate aminotransferase, lactic dehydrogenase and, and gamma-glutamyl transferase) and of renal function (increases in serum urea and creatinine) (P < 0.001 group 2 vs. group 1 for all mentioned parameters). Also, the antioxidant defense capacity was impaired in group 2 vs. group 1 (superoxide dismutase and glutathione peroxidase activity decreased in group 2 vs. group 1, 0.001 < P < 0.01, respectively 0.01 < P < 0.05). The addition of ciprofloxacin, 50 mg/kg/day during the last 14 days resulted in further increases in alkaline phosphatase, alanine aminotransferase, aspartate aminotransferase, urea and creatinine (0.01 < P < 0.05, group 3 vs. group 2). MgCl2 provided a slight protection against liver enzymes increase and a more pronounced protection against the increase in serum urea and creatinine (0.001 < P < 0.01 group 4 vs. group 3). MgCl2 provided a slight protection against the decrease in superoxide dismutase (0.01 < P < 0.05 group 4 vs. group 3), but not against decrease of glutathione peroxidase. The improvement of mentioned parameters could also be seen in case of ZnG, to a higher extent especially in the case of alanine aminotransferase and lactic dehydrogenase (0.01 < P < 0.05 group 5 vs. group 4). Conclusions: This study represents a furthermore proof for beneficial effect of magnesium and zinc salts against toxicity induced by different agents, including antibacterials added to the analgesic and antipyretic acetaminophen; the protection is proven on the liver and kidney’s function; the antioxidant profile improvement has a key role, especially in case of zinc gluconate.

This paper presents Chebyshev Type inequalities for the Riemann-Liouville variable-order fractional integral operator using two synchronous functions on the set of real numbers. It is the first result of its kind in the current literature using variable-order Riemann-Liouville fractional integral operator. Some special cases for the result obtained in the paper are discussed.

We consider rotational hypersurface in the four dimensional Euclidean space. We calculate the mean curvature and the Gaussian curvature, and some relations of the rotational hypersurface. Moreover, we define the third Laplace-Beltrami operator and apply it to the rotational hypersurface.

Intuitionistic fuzzy set, which can be represented using the triangular intuitionistic fuzzy number (TIFN), is a more generalized platform for expressing imprecise, incomplete and inconsistent information when solving multi-criteria decision-making problems, as well as for reflecting the evaluation information exactly in different dimensions. In this paper, the TIFN has been applied for solving some multi-criteria decision-making problems by developing a new triangular intuitionistic fuzzy geometric aggregation operator, that is the generalized triangular intuitionistic fuzzy ordered weighted geometric averaging (GTIFOWGA) operator, and defining some triangular intuitionistic fuzzy geometric aggregation operators including the triangular intuitionistic fuzzy weighted geometric averaging (TIFWGA) operator, the ordered weighted geometric averaging (TIFOWGA) operator and the hybrid geometric averaging (TIFHWGA) operator. Based on these operators, a new approach for solving multicriteria decision-making problems when the weight information is fixed has been proposed. Finally, the proposed method has been compared with some similar existing computational approaches by virtue of a numerical example to verify its feasibility and rationality.

Neuronal cells are believed to rely on autophagy to maintain cellular homeostasis. Nevertheless, autophagy may be a therapeutic target for neurodegenerative diseases because of the role it plays in neuronal cell death. Despite Beclin 1 association with autophagy and apoptosis, the molecular mechanisms that underlie Tau-induced vesicular pathology and Tau protein aggregates in humans remain poorly understood. Here, we set out to examine the role of three genes-ATG14L, Beclin 1 and VPS34- in autophagy nucleation failure-associated Tau disorders in fruit fly models. We found that either reduced ATG14L levels improve neuronal outcomes, or transgenic expression of ATG6/Beclin 1 greatly reduced age-dependent neurodegeneration and Tau pathology; whereas, the loss of Beclin 1 exacerbated these effects. Prior to p-Tau accumulation, the neuronal Beclin 1 network is critical for reducing p-Tau accumulation, indicating that the loss of Beclin 1 causes Tau pathology and neurodegeneration. As neurodegeneration progressed, glial cells showed an upregulation of vesicular Beclin 1 immunoreactivities. The reduced VPS34 also resulted in p-Tau accumulation, suggesting that neurons require both Beclin 1 and VPS34 to reduce p-Tau accumulation. Our results provide mechanistic insight into the molecular pathways that cause age-dependent Tau pathology and neurodegeneration due to an excess of autophagy nucleation processes and autophagy activity, and we derive novel inferences on the therapeutic possibilities of rebalanced Beclin 1 network by reducing autophagic specific nucleation component of ATG14L.

The differential transformation, an approach based on Taylor's theorem, is proposed as convenient for finding exact or approximate solution to the initial value problem with multiple Caputo fractional derivatives of generally non-commensurate orders. The multi-term differential equation is first transformed into a multi-order system and then into a system of recurrence relations for coefficients of formal fractional power series. The order of the fractional power series is discussed in relation to orders of derivatives appearing in the original equation. Application of the algorithm to an initial value problem results in a reliable and expected outcome.

The study is devoted to the issues of mathematical modeling and simulating the sport differential mechanism (DM) with controllable torque redistribution. The issue is caused by the elaboration of ADAS systems with the automated torque vectoring for transmissions of all-wheel-drive (AWD) vehicles and the inclusion of such devices in the combined autonomous vehicle trajectory control scheme. At the article's beginning, the use of devices for redistributing traction forces is reasoned by analyzing the curvilinear vehicle motion, where they could ensure the accuracy of vehicle steerability. The literature review highlights modern developments in the field of modeling and researching such DMs. Considering the vehicle turn with a minimum radius, the conditions corresponding to passing greater torque over the outrunning rear axle are determined. All the mechanism's components and loads acting between them are described in detail. To form an original method of mathematical description of the mechanism functioning, the system of differential equations, systems of kinematic and force connections are considered separately. The article details the mathematical approach to generalize the way for automating the equation compilation for rotational mechanical systems such as vehicle transmissions. In the simulation section, a Simulink model reflecting the functional components and calculation procedures is presented. A series of testing and simulations on the DM operation with forcible torque distribution is carried out. Modeling data are presented, and the analysis of simulation results is performed. In the completion, conclusions are made regarding the scope and use of this model and the prospects for further developing the method proposed to automate the formation of equation systems.

In this paper, we study the problem of controllability of impulsive neutral evolution integrodifferential equations with state dependent delay in Banach spaces. The main results are completely new and are obtained by using Sadovskii's fixed point theorem, theory of resolvent operators, and an abstract phase space. An example is given to illustrate the theory.

Fibrosis is a ubiquitous pathology, and prior studies have indicated that various artemisinin (ART) derivatives (including artesunate (AS), artemether (AM), and dihydroartemisinin (DHA)) can reduce fibrosis in vitro and in vivo. The medicinal plant, Artemisia annua L., is the natural source of ART and is widely used, especially in underdeveloped countries, to treat a variety of diseases including malaria, while A. afra contains no ART but is also antimalarial. Using human dermal fibroblasts (CRL-2097), we compared the effects of A. annua and A. afra tea infusions, ART, AS, AM, DHA, and a liver metabolite of ART, deoxyART (dART), on fibroblast viability and expression of key fibrotic marker genes after 1 and 4 days of treatment. AS, DHA, and Artemisia tea significantly reduced fibroblast viability at 1 and 4 d post-treatment. After 4 d post treatment, AS, DHA, and A. afra tea downregulated ACTA2, and upregulated MMP3, with other genes either being unaffected or differentially affected. ART and AM had no significant effect on either fibroblast viability or fibrotic gene expression. Although A. annua contains ART, it had a significantly greater anti-fibrotic effect than ART alone. Immunofluorescent staining for smooth muscle α-actin (α-SMA) correlated well with transcriptional responses of drug-treated fibroblasts. Together, proliferation, qPCR, and immunofluorescence results show that treatment with ART, AS, DHA, and the two Artemisia teas yield differing responses, including those related to fibrosis, in human dermal fibroblasts.

As screen sizes are becoming larger and larger, which are beyond human’s physical limitation for direct touching interaction, remote controls are inevitable. However, as techniques applied so far, inertial gyroscopes are susceptible to position inaccuracies, and gesture recognition is limited by cameras’ focus depth and viewing angle. Grating antenna light trapping technology will be an ideal candidate providing the ghost point problem for multipoint inputs can be solved. Therefore, we propose a differential amplitude modulation scheme for grating antenna based multi beam optical touch, which can recognize different incidence points. Where, the amplitude of the incident beams was coded with different pulse width at first. Then, after been trapped by the grating antenna and been transferred into currents by the lined detector arrays, the incident points of the individual beams were recognized and differentiated. The scheme was successfully verified on an 18-inch screen, where two-point optical touch with position accuracy error under 3mm and response time less than 7ms under modulation frequency of 10kHz on both incident beams are obtained. This work paves a practical way for remote multi-point touch, which can make digital mouse in consistent to the users pointing direction obeying natural three-point one ling aiming rule instantaneously.

We consider a Cauchy problem for differential equations in a Hilbert space $X$. The problem is stated in a time interval $I$, which can be finite or infinite. Weuse a fixed point argument for history-dependent operators to prove the unique solvability of the problem. Then, we state and prove convergence criteria for both a general fixed point problem and thecorresponding Cauchy problem. These criteria provide necessary and sufficient conditions on a sequence $\{u_n\}$ which guarantee its convergence to the solution of the corresponding problem, in the space of both continuous and continuously differentiable functions. We then specify our results in the study of a particular differential equation governed by two nonlinear operators. Finally, we provide an application in viscoelasticity and give a mechanical interpretation of the corresponding convergence result.

Estimation and planning play a vital role in the construction of an autonomous navigation framework. However, these problems are often considered separately, while planning gives robot a free-collision path towards the desired goal, estimation algorithm presents the executed trajectory in the sense that it has to be closed to the ground truth path as much as possible. Recently, a unified probabilistic framework, which supports solving these problems simultaneously, dubbed STEAP has been proposed. Nevertheless, its current version is only designated for an omni wheels robot, which allows robot to move and turn in vertical direction. Differential drive robot, on the other hand, though limited to move along only one direction, has been used in various situations due to its flexibility and lower cost in hardware designing. Thus, in this extension, our aim is to control a differential drive robot via STEAP. Moreover, in a more complicated environment such as labyrinth or maze, the original STEAP sometimes fails to find a path. Indeed, this problem is mainly caused by the poor initialization and the non-linearity in optimizer constraints. In our implementation, instead of dealing with these constraints, we employ a global planner algorithm such as Dijkstra or RRT to treat STEAP as an effective local planner module that focus on following the global path. Consequently, the experimental results show that the extended STEAP not only able to navigate a differential drive robot but also in a more complicated and unstructured environment.

Evaluation of biliary strictures remains a challenge due to the low sensitivity of standard diagnostic work up, but the introduction of direct single-operator cholangioscopy (DSOC) changed this paradigm. Aim of our study was to evaluate diagnostic performance of DSOC and DSOC-targeted biopsies, intraductal ultrasound (IDUS) and brush cytology in patients with indeterminate biliary stricture (IBS). We evaluated patients who underwent advanced diagnostic work up for IBS in our endoscopy unit from ‘01/2018 to ‘12/2022; all patients had at least one previous attempt to characterize the biliary stricture. Final diagnosis was based on surgical pathology and/or clinical and radiological follow-up of at least 12 months. A total of 57 patients with a mean age of 67.2 ± 10.0 years were included, with a mean follow up of 18.2 ± 18.1 months. IBS were mostly located in the distal common bile duct (45.6%) and final diagnosis was consistent with malignancy in 35 patients (61.4%). DSOC and IDUS showed a significantly higher accuracy (89.5% and 82.7% respectively) compared to standard cytology (61.5%, p <0.05). In our experience, DSOC visualization and IDUS both demonstrated an optimal diagnostic yield in the differentiation of IBS, with an acceptable safety profile both quantitatively and qualitatively.

The multivariate Gaussian random fields with matrix-based scaling laws are widely used for inference in statistics and many applied areas. In such contexts interests are often in symmetry and in the rates of change of spatial surfaces in any given direction. This article analyzes the almost sure sample function behavior for operator fractional Brownian motion, including multivariate fractional Brownian motion. We obtain the estimations of small ball probability and the strongly locally nondeterministic for operator fractional Brownian motion in any given direction. Applying these estimates we obtain Chung's laws of the iterated logarithm for spatial surfaces of operator fractional Brownian motion. Our results show that the precise rates of change of spatial surfaces are completely determined by the self-similarity exponent.

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η-convex function. Moreover, our results include several new and known results as special cases.

Climate change and the increasing frequency and severity of drought events pose significant challenges for sustainable agriculture worldwide. Soil microorganisms, both beneficial and pathogenic, play a crucial role in mediating plant-environment interactions and shaping the overall functioning of agroecosystems. This review synthesizes the current knowledge on the contrasting adaptive mechanisms utilized by different groups of plant-soil microorganisms focusing on beneficial and pathogenic bacterial and fungal communities in response to drought and desiccation stresses. The review examines the common survival strategies employed by microbes specifically rhizobacteria and arbuscular mycorrhizal fungi, such as the production of osmoprotectants, altered gene expression, and biofilm formation. It also highlights the distinct adaptive mechanisms of pathogenic versus mutualistic microbes, with pathogens tending to prioritize virulence factors and suppress plant growth, while beneficial microbes enhance plant growth and stress tolerance. Genetic exchange such as horizontal gene transfer (HGT) is identified as a key adaptive mechanism, allowing both pathogenic and non-pathogenic microbes to acquire beneficial traits like stress tolerance and virulence factors. Environmental stressors like drought can promote increased genetic exchange and the spread of pathogenic traits within the soil microbiome. The complex interplay between drought-adapted microbes and their interactions with plants is discussed, emphasizing the need for a deeper understanding of soil microbiome dynamics under climate change. This knowledge can be utilized in sustainable agricultural practices to mitigate the impacts of drought on plant health and productivity. This review provides insights into the divergent survival strategies of soil microorganisms in response to drought and desiccation, for managing the resilience of agroecosystems to climate change.

In the paper, the authors present an explicit form for a family of inhomogeneous linear ordinary differential equations, find a more significant expression for all derivatives of a function related to the solution to the family of inhomogeneous linear ordinary differential equations in terms of the Lerch transcendent, establish an explicit formula for computing all derivatives of the solution to the family of inhomogeneous linear ordinary differential equations, acquire the absolute monotonicity, complete monotonicity, the Bernstein function property of several functions related to the solution to the family of inhomogeneous linear ordinary differential equations, discover a diagonal recurrence relation of the Stirling numbers of the first kind, and derive an inequality for bounding the logarithmic function.

Fermented foods and ingredients, including fermentates derived from lactic acid bacteria (LAB) in dairy products, can modulate the immune system. Here we describe the use of reconstituted skimmed milk powder to generate novel fermentates from Lactobacillus helveticus strains SC232, SC234, SC212, and SC210, and from Lacticaseibacillus casei strains SC209 and SC229, and demonstrate using in vitro assays that these fermentates can differentially modulate cytokine secretion by bone marrow derived dendritic cells (BMDCs) when activated with either the viral ligand, loxoribine, or an inflammatory stimulus, lipopolysaccharide. Specifically, we demonstrate that SC232 and SC234 increase cytokines IL-6, TNF-α, IL-12p40, IL-23, IL-27 and IL-10, and decreased IL-1β in primary bone marrow derived dendritic cell (BMDCs) stimulated with a viral ligand. In contrast exposure of these cells to SC212 and SC210 resulted in increased IL-10, IL-1β, IL-23, and decreased IL-12p40 following activation of the cells with the inflammatory stimulus LPS. Interestingly SC209 and SC229 had little or no effect on cytokine secretion by BMDCs. Overall, our data demonstrates that these novel fermentates have specific effects and can differentially enhance key immune mechanisms that are critical to viral immune responses, or can suppress responses involved in chronic inflammatory conditions, such as Ulcerative Colitis (UC), and Crohn’s disease (CD).

The purpose of this paper is to summarize and share the field experiment results of KEPCO's project consortium to create a TSO-DSO-DERA interaction scheme. The field experiment was conducted based on the prequalification algorithm proposed in the previous research from the same consortium and was designed to verify the validity of the algorithm under realistic grid conditions. In addition, during the course of the field experiment, it was found that points that were missed or not given much importance in the existing prequalification algorithm could affect the completeness of the overall system, and then practical improvements were made to improve it. The demonstration results confirm that the proposed algorithm is effective in real-world grid environments and can help DSOs ensure the reliability of the distribution system while supporting DERA's participation in the wholesale market using the proposed prequalification scheme.

The ability to handle spatiotemporal information makes contribution for improving the prediction performance of machine RUL. However, most existing models for spatiotemporal information processing are not only complex in structure but also lack adaptive feature extraction capabilities. Therefore, a lightweight operator with adaptive spatiotemporal information extraction ability named Involution GRU (Inv-GRU) is proposed for aero-engine RUL prediction. Involution, the adaptive feature extraction operator, is replaced by the information connection in the gated recurrent unit for obtaining the adaptively spatiotemporal information extraction ability and reducing the parameters. Thus, Inv-GRU can well extract the degradation information the of aero-engine. Then for RUL prediction task, the Inv-GRU based deep learning (DL) framework is firstly constructed, where features extracted by Inv-GRU and several human-made features are separately processed to generate the health indicators (HIs) from multi-raw data of aero-engines. Finally, fully connection layers are adopted are adopted to reduce dimension and regress RUL based on the generated HIs. By applying the Inv-GRU based DL framework to the Commercial Modular Aero Propulsion System Simulation (C-MAPSS) datasets, successful predictions of aero-engines RUL have been achieved. Comparative analysis reveals that the proposed model exhibits superior overall prediction performance compared to recent public methods.

Skeletal muscles are crucial for voluntary movements, and impairments in their function significantly impact our activity. Dysferlin, a protein predominantly present in skeletal muscle, is a focal point of extensive research due to its vital role in muscle repair and maintenance. This study investigates Dysferlin's levels and function in skeletal muscles, emphasizing its significance and the potential effects of its dysregulation on fast and slow muscle fibers. We employed Western blotting on two different rat muscles. The results revealed distinct expressions of Dysferlin in fast and slow fibers, as demonstrated by Western blotting. We propose that Dysferlin may have a metabolic role in addition to its involvement in the repair mechanism.

We propose a notion of $(q,\sigma,\tau)$-differential graded algebra, which generalizes the notions of $(\sigma,\tau)$-differential graded algebra and $q$-differential graded algebra. We construct two examples of $(q,\sigma,\tau)$-differential graded algebra, where the first one is constructed by means of generalized Clifford algebra with two generators (reduced quantum plane), where we use a $(\sigma,\tau)$-twisted graded $q$-commutator. In order to construct the second example, we introduce a notion of $(\sigma,\tau)$-pre-cosimplicial algebra.

Previous studies had shown that mRNA, miRNA and lncRNA were associated with cardiovascular diseases. The study was aimed to explore the differential expressions of mRNA, lncRNA and miRNA between coronary artery disease (CAD) and healthy control, and their interaction in CAD. We investigated the differential expression of ceRNA between CAD and healthy control through data collected from Gene Expression Omnibus (GEO) microarrays. Furthermore, we investigated the biological function of these differential expressions of ceRNAs by Gene Ontology (GO), Kyoto Encyclopedia of Genes and Genomes (KEGG) analyses. Protein-protein interaction (PPI) network was created to identify the hub genes. Biosystems and literature search were performed for signaling pathways and their function of the included differential expression ceRNAs. A total of 456 miRNA expression profiles, 16,325 mRNA expression profiles, and 2,869 lncRNA expression profiles were obtained. Eleven Go and KEGG pathways (count ≥9), top 15 of PPI network node connectivity rank, and top 15 of ceRNA network node degree centrality rank were achieved at the statistical significance level (P<0.05). We further identified that several differential expressions of ceRNAs and their signaling pathways were associated with CAD through biosystems and literature search. Based on eleven Go and KEGG pathways, top 15 of PPI network node connectivity rank, and top 15 of ceRNA network node degree centrality rank in CAD population, our findings would contribute to further exploration for the molecular mechanism of CAD.

Modeling and assessing the sustainability of machining systems has been considered to be a crucial approach to improving the environmental performance of the machining processes. As the most common machining system, the computer numerical control (CNC) milling system is a typical man-machine cooperative system where the activities of the machine tool and operator generate material and energy consumption. However, the energy consumption of the operator in the CNC milling system has often been ignored in most existing research. Therefore, existing methods fail to provide a comprehensive understanding of the sustainability of the CNC milling system. To fill this gap, an exergy loss assessment method is proposed to investigate the sustainability of the CNC milling system, where the energy consumption of the operator, the energy consumption of the machine tool, and material consumption are taken into consideration. The key performance indexes of the energy consumption of the operator, the energy consumption of the machine tool, the exergy loss, and the specific exergy loss (SEL) are analyzed and modeled. To demonstrate the feasibility of the proposed method, a case study was carried out on a three-axis machining center (XH714D), in which SEL was found to be 88.04J/mm3. The proposed method is effective to assess the sustainability of the CNC milling system, and the established exergy loss models build a good basis for exergy efficiency optimization.

Often, when solving forward, inverse or data assimilation problems, only a part of the solution is needed. As a model, we consider the stationary diffusion problem. We demonstrate an algorithm that can compute only a part or a functional of the solution, without calculating the full inversion operator and the complete solution. It is a well-known fact about partial differential equations that the solution at each discretisation point depends on the solutions at all other discretisation points. Therefore, it is impossible to compute the solution only at one point, without calculating the solution at all other points. The standard numerical methods like a conjugate gradient or Gauss elimination compute the whole solution and/or the complete inverse operator. We suggest a method which can compute the solution of the given partial differential equation 1) at a point; 2) at few points; 3) on an interface; or a functional of the solution, without computing the solution at all points. The required storage cost and computational resources will be lower as in the standard approach. With this new method, we can speed up, for instance, computation of the innovation in filtering or the likelihood distribution, which measures the data misfit (mismatch). Further, we can speed up the solution of the regression, Bayesian inversion, data assimilation, and Kalman filter update problems. Applying additionally the hierarchical matrix approximation, we reduce the cubic computational cost to almost linear $\mathcal{O}(k^2n \log^2 n)$, where $k\ll n$ and $n$ is the number of degrees of freedom. Up to the hierarchical matrix approximation error, the computed solution is exact. One of the disadvantages of this method is the need to modify the existing deterministic solver.

Myasthenia gravis (MG) is a disease characterized by typical clinical and immunopathogenic pe-culiarities, which correlate with age and sex/gender. Accordingly, MG patients show thymic al-terations and auto-antibodies productions, that can be the expression of a different pathogenetic mechanism related to age and gender. This determines, in relation to age at and sex/gender, a dif-ferent MG onset, prognosis, and outcome. Therefore, diverse MG forms can be identified, classi-fied, and characterized in relation to their different features, and precisely there are early onset and late-onset forms of MG. It has been hypothesized that the cause of appearance the two diverse forms of MG can be ascribed mainly to the diverse genetic and epigenetic factors. In this narrative review, we will analyze and discuss about the interplay of age- and sex-related factors (i.e. genet-ic and epigenetic factors) related to two different MG forms and how they contribute to their di-verse pathogenesis.

Planar differential systems whose angular velocity is constant are called rigid differential systems. We characterize the existence and non-existence of limit cycles, and the finite and infinite singularities of the rigid polynomial differential systems with homogeneous nonlinearities of arbitrary degree in the Poincaré disc. Moreover, we classify the phase portraits in the Poincaré disc of the rigid polynomial differential systems of degree two, and of one class of rigid polynomial differential systems with cubic homogeneous nonlinearitie that can exhibit one limit cycle.

Observation of parity-violating effects in chiral molecules is a long-standing challenge of the molecular spectroscopy community. In the microwave regime, the difference in transition frequencies between enantiomers is predicted to be below the mHz level, which is considerably beyond current experimental capabilities. The most promising future efforts combine vibrational spectroscopy, buffer gas cooling, and carefully chosen molecular candidates with large predicted parity-violating shifts. Here, we demonstrate for the first time high-precision differential microwave spectroscopy, achieving sub-Hz precision by coupling a cryogenic buffer gas cell with a tunable microwave Fabry-Perot cavity. We report statistically limited sub-Hz precision of (0.08±0.72) Hz, observed between enantiopure samples of (R)-1,2-propanediol and (S)-1,2-propanediol at frequencies near 15 GHz. We confirm highly repeatable spectroscopic measurements compared to traditional pulsed-jet methods, opening up new capabilities in probing subtle molecular structural effects at the 10−10 level and providing a platform for exploring sources of systematic error in parity-violation searches. We discuss dominant systematic effects at this level and propose possible extensions of the technique for higher precision.

Autonomous differential equations of fractional order and non-singular kernel are solved. While solutions can be obtained through numerical, graphical, or analytical solutions, we seek an implicit analytical solution.

In this paper we use the conformable fractional derivative to discuss some fractional linear differential equations with constant coefficients. By applying some similar arguments to the theory of ordinary differential equations, we establish a sufficient condition to guarantee the reliability of solving constant coefficient fractional differential equations by the conformable Laplace transform method. Finally, we analyze the analytical solution for a class of fractional models associated with Logistic model, Von Foerster model and Bertalanffy model is presented graphically for various fractional orders and solution of corresponding classical model is recovered as a particular case.

In this paper, we consider the zero distributions of q-shift monomi-als and difference polynomials of meromorphic functions with zero order, that extends the classical Hayman results on the zeros of differential poly-nomials to q-shift difference polynomials. We also investigate problem of q-shift difference polynomials that share a common value.

Using the World Bank Global Findex Database for 91 countries in 2014, 2017, and 2021, we examine whether fintech levels influence bank performance and whether fintech’s interaction with GDP per capita causes differential effects on bank performance globally. Since fintech levels were already very high for rich countries when the World Bank started providing fintech development statistics in 2014, we estimate AbFintech by regressing fintech levels on GDP per capita by year. AbFintech is the difference between the fintech level and its fitted values. Then, using multiple regression analyses, we investigate the impact of AbFintech on bank performance worldwide, focusing on the differential effects of AbFintech and GDP levels on bank performance. We find AbFintech significantly increases bank performance, primarily in less developed countries. Specifically, AbFintech increases banks’ ROA in the least developed countries and net interest margin in the 75th percentile countries. Also, AbFintech decreases the cost-to-income ratio in the 75th percentile countries, while it increases the ratio in the most developed countries. AbFintech does not affect the ratio of noninterest income to total income, regardless of the level of economic development.

A linear Cauchy problem with polynomial coefficients wich combines q-difference operators for q>1 and differential operators of irregular type is examined. A finite set of sectorial holomorphic solutions w.r.t the complex time is constructed by means of classical Laplace transforms. These functions share a common asymptotic expansion in the time variable which turns out to carry a double layers structure which couples q-Gevrey and Gevrey bounds. In the last part of the work, the problem of confluence of these solutions as q tends to 1 is investigated.

The prevalence of differential equations as a mathematical technique has refined the fields of control theory and constrained optimization due to the newfound ability to accurately model chaotic, unbalanced systems. However, in recent research, systems are increasingly more nonlinear and difficult to model using Differential Equations only. Thus, a newer technique is to use policy iteration and Reinforcement Learning, techniques that center around an action and reward sequence for a controller. Reinforcement Learning (RL) can be applied to control theory problems since a system can robustly apply RL in a dynamic environment such as the cartpole system (an inverted pendulum). This solution successfully avoids use of PID or other dynamics optimization systems, in favor of a more robust, reward-based control mechanism. This paper applies RL and Q-Learning to the classic cartpole problem, while also discussing the mathematical background and differential equations which are used to model the aforementioned system.

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

Environmental estrogen pollution and estrogen effects on the female reproduction system are well-recognized scientifically. Among the estrogens, 17 β-estradiol is a priority in environmental estrogen pollution, and it is also a major contributor to estrogen which regulates the female reproduction system. 17 β-estradiol is carcinogen and has a tumor promotion effect relating to breast cancer, lung cancer and others. It also affects the psychological well-being such as depression, fatigue and others. Thus, a simple method of detection of 17 β-estradiol will be important for both environmental estrogen pollution and women’s health care. This study demonstrates a simple-use, cost effective 17 β-estradiol biosensor system which can be used for both environment and women’s health care applications. The bio-recognition mechanism is based on the influence of the redox couple, K₃Fe (CN) ₆/K₄Fe (CN) ₆ by the interaction between 17 β-estradiol antigen and its α-receptor (ER- α; α-estrogen antibody). The transduction mechanism is an electrochemical analytical technique, differential pulse voltammetry (DPV). The levels of 17 β-estradiol antigen studied was between 2.25 pg/mL to 2,250 pg/mL, Phosphate buffered saline (PBS), tap water from the Cleveland regional water district, and simulate urine were used as the test media covering the potential application areas for 17 β-estradiol detection. An interference study by testosterone which has a similar chemical structure and molecular weight as those of 17 β-estradiol was carried out, and this 17 β-estradiol biosensor showed excellent specificity without any interference by similar chemicals.

This study develops a predictor-corrector algorithm for the numerical simulation of IVPs involving singular generalized fractional derivatives with Mittag-Leffler kernels. The proposed algorithm converts the considered IVP into a Volterra-type integral equation and then uses Trapezoidal rule to obtain approximate solutions. Numerical approximate solutions of some singular generalized fractional derivative with Mittag-Leffler kernels models have been presented to demonstrate the efficiency and accuracy of the proposed algorithm. The algorithm describes the influence of the fractional derivative parameters on the dynamics of the studied models. The suggested method is expected to be effectively employed in the field of simulating generalized fractional derivative models

Objectives: Few studies in literature evaluate the "mean measure" of root divergence. Most of them are linear measurements, they hardly describe the dental furcation conformation. It is left to the subjectivity of the operator deciding whether a furcation is convergent or divergent. The goal of this study is to create a visual evaluation method to overcome these problems giving a conformation of the entire interradicular space. Material and methods: A user-friendly software (Paint®, Windows10®) was used to measure endo-oral radiographs of upper and lower molars. Three kinds of measurements were taken. Three operators used the software to measure 20 radiographs, then the technique was repeated on 250 radiographic images to identify an average measurement. The ratio of these three measurements allowed to develop a new visual evaluation method of the interradicular space. Results: Intra and inter-operator reproducibility was statistically assessed on a sample of 20 anonymous endo-oral radiographs measured by 3 blind operators. Then, a sample of 250 anonymous endo-oral radiographs were measured by a blind operator and were statistically evaluated to identify an average value to define a main conformation of the interradicular space. Measurements made by the 3 operators on the 20 radiographic images showed that the technique is reproducible, and a mean value of the interradicular space was obtained. Conclusions: A new anatomical evaluation of the interradicular space in its entirety, which could help the clinicians in the therapy of furcated molars, can be obtained.

This article describes the choice of an optimization algorithm for solving problems and the optimal design of an unmanned aerial vehicle propeller. To solve the problem using evolutionary algorithms, it was transformed into an unconstrained optimization problem using a penalty function. The airfoil contours were constructed using a Bezier curve. Design variables were divided into two types: those that describe in general terms the propeller geometry or operation, such as propeller diameter, number of blades, and rev/min; and those that vary with propeller radius, such as chord length, effective airfoil angle, and airfoil geometry. The objective function is the calculation of the propeller power required to achieve a given thrust. The differential evolution algorithm was used to solve this problem.

Perforating dermatoses are dermatologic disorders with transepidermal elimination (TE) of dermal substances. While TE is typically associated with collagen and elastin, it can also occur as a secondary event in other processes, and it is important to keep a broad differential. We present a case of perforating tophaceous gout, which underscores the need for a thoughtful approach to perforating disorders. An updated review of recent literature is also presented.

In this paper, we consider with a class of system of differential equations whose argument transforms are involution. In this an initial value problem for a differential equation with involution is reduced to an initial value problem for a higher order ordinary differential equation. Than either two initial conditions are necessary for a solution, the equation is then reduced to a boundary value problem for a higher order ODE.

A new type of ordinary differential equation is introduced and discussed, namely, the time-dependent order ordinary differential equations. These equations can be solved via fractional calculus and are mapped into Volterra integral equations of second kind with singular integrable kernel. The solutions of the time-dependent order differential equations smoothly deforms solutions of the classical integer order ordinary differential equations into one-another, and can generate or remove singularities. An interesting symmetry of the solution in relation to the Riemann zeta function and Harmonic numbers was also proved.

In the paper, by virtue of techniques in combinatorial analysis, the authors simplify two families of nonlinear ordinary differential equations in terms of the Stirling numbers of the first kind.