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.

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.

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.

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.

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.

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 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.

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.

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.

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.

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).

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.

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 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.

Concatemeric viral DNA is packaged into Bacteriophage P22 procapsids via a headful packaging mechanism mediated by a molecular machine consisting of small (gp3) and large (gp2) terminase subunits. Although a negative stain reconstruction exists for the terminase holoenzyme, it is not clear how this complex binds dodecameric portal protein located at a 5-fold mismatch vertex. Herein, we describe new assemblies for the holoenzyme. Both native mass spectrometry and transmission electron microscopy reveal that the P22 terminase complex adopts three main assemblies, which include a nonameric S-terminase bound to two L-terminase 1(gp3)9:2(gp2), two nonameric S-terminase bound to five L-terminase 2(gp3)9:5(gp2), and three nonameric S-terminase bound to seven L-terminase 3(gp3)9:7(gp2). Native agarose gel electrophoresis shows that the terminase complex interacts with procapsid with mild crosslinking. These results herein illustrate the P22 terminase complex can adopt a variety of confirmations and assembly states.

The fractional derivatives are a generalization the derivatives of integer order and find applications in studying memory processes in various scientific fields. Numerical methods are used to solve and analyze fractional models of real world problems. In this paper, we consider an approximation of the Caputo fractional derivative and its asymptotic formula, whose generating function is the polylogarithmic function. In the paper, we prove the convergence of the approximation and derive an estimate for the error and order. We consider an application of the approximation for the construction of finite difference schemes for numerical solution of the two-term ordinary fractional differential equation and the time-fractional Black-Scholes equation for option pricing. The properties of the approximation are used to prove the convergence of the methods used for numerical solution of the fractional differential equations. The theoretical results for the error and order of the methods are illustrated by the results of numerical experiments.

Fractional differential systems have received much attention in recent decades likely due to its powerful ability in modeling memory processes, which are mostly observed in real world. Fractional models have been widely investigated and applied in many fields such as physics, biochemistry, electrical engineering, continuum and statistical mechanics. It is shown by many researchers that fractional derivatives can provide more accurate models than integer order derivatives do. Obviously, bang-bang property is of a significant importance in optimal control theory. In this paper a Bang-Bang property and time-optimal control problem for time-Fractional Differential System (FDS) is under consideration. First we formulate our problem and we prove the existence theorem. We state and prove the bang-bang theorem. Finally we give the optimality conditions that characterized the optimal control. Some illustrate applications are given to clarify our results.

The current study explores the problem of illiquidity in the corporate bond market and examines a broad set of liquidity proxies through empirical investigation. Purpose: The purpose of this paper is to give solution to the global issue of illiquidity in the corporate bond market. The problem is identified by many researchers and this paper attempts to find out the viable solution of the "fungibility route" as an alternative to the "liquidity route". Design/ Methodology: An Analysis of a sample size of 2,34,772 trade data of corporate bonds and a sample size of 2,00,607 trade data of G-securities is done to identify the problem. Findings / Solution proposed: A mathematical model based on credit risk differential and sensitivity differential is proposed to find out the fair value at which an illiquid bond can be swapped by a liquid bond. To arrive at the fair value of the illiquid bond, we have calculated risk adjusted discount rate using modified duration and credit risk differential. With our solution, it is possible to enhance the liquidity of the bond not directly but through fungibility route. Originality: the research is first of its kind in which solution is given to the global problem of corporate bond illiquidity. To execute the trade in the fungibility route, proposed parties involved are the Fungibility platform, the initiator, and the bidder. The derived fair value would facilitate trade and serve as an exit strategy for illiquid bond holders worldwide.

We derive some Quantum Central Limit Theorems for expectation values of macroscopically coarse-grained observables, which are functions of coarse-grained hermitean operators consisting of non-commuting variables. Thanks to the hermicity constraints, we obtain positive-definite dis- tribution for the expectation values of observables. These probability distributions open some pathway for an emergence of classical behaviours in the limit of innitely large number of identical and non-interacting quantum constituents. This is in contradistinction to other mechanisms of classicality emergence due to environmental decoherence and consistent histories. The probabil- ity distributions so derived also enable us to evaluate the nontrivial time-dependence of certain differential entropies.

We examine a family of nonlinear q-difference-differential Cauchy problems obtained as a coupling of linear Cauchy problems containing dilation q-difference operators, recently investigated by the author, and quasi-linear Kowalevski type problems that involve contraction q-difference operators. We build up local holomorphic solutions to these problems. Two aspects of these solutions are explored. One facet deals with asymptotic expansions in the complex time variable for which a mixed type Gevrey and q-Gevrey structure is exhibited. The other feature concerns the problem of confluence of these solutions as q tends to 1.

This paper reports applying Minimax principle and impulsive differential inequality to derive the existence of multiple stationary solutions and the global stability of a positive stationary solution for a delayed feedback Gilpin-Ayala competition model with impulsive disturbance. The conclusion obtained in this paper reduces the conservatism of the algorithm compared with the known literature, for the impulsive disturbance is not limited to impulsive control.

In order to overcome this problem our group designed a novel machine learning technique, multivariate linear method (MLM) which can capture convergent data from voxel-based morphometry, functional resting state and task-related neuroimaging and the relevant clinical measures. In this paper we report results from convergent cross-validation of biological signatures of disease in a sample of patients with schizophrenia as compared to depression. Our model provides evidence that the combination of the neuroimaging and clinical data in MLM analysis can inform the differential diagnosis in terms of incremental validity to reach 90 % accuracy of the prediction.

Enzymatic degradation of organic pollutants is a new and promising remediation approach. Peroxidases are one of the most commonly used classes of enzymes to degrade organic pollutants. However, it is generally assumed that all peroxidases behave similarly and produce similar degradation products. In this study, we conducted detailed studies of the degradation of a model aromatic pollutant, Sulforhodamine B dye (SRB dye), using two peroxidases—soybean peroxidase (SBP) and chloroperoxidase (CPO). Our results show that these two related enzymes had different optimum conditions (pH, temperature, H₂O₂ concentration...etc.) for efficiently degrading SRB dye. High-performance liquid chromatography and LC-mass spectrometry analyses confirmed that both SBP and CPO transformed the SRB dye into low molecular weight intermediates. While most of the intermediates produced by the two enzymes were the same, the CPO treatment produced at least one different intermediate. Furthermore, toxicological evaluation using lettuce (Lactuca sativa) seeds demonstrated that the SBP-based treatment was able to eliminate the phytotoxicity of SRB dye, but the CPO-based treatment did not. Our results show, for the first time, that while both of these related enzymes can be used to efficiently degrade organic pollutants, they have different optimum reaction conditions and may not be equally efficient in detoxification of organic pollutants.

The fixed and random effects models are popular methods for identifying the causal effects of treatment. First, I introduce the two-way fixed effects model and show a class of the estimators for the random effects models. Misidentification may occur in these models due to the treatment effect heterogeneity. Then, I propose the differential error component models to address such problems while the models exclude the fixed effects of units and time periods and consider the random effects of units and time periods. Meanwhile, I present a simulation of a staggered design and revisit the application in (De Chaisemartin and D'Haultfoeuille, 2020). The results demonstrate that one additional newspaper increases the 0.31% average effect of the presidential turnout and the 1.05% average effect when the newspapers’ changes are non-negative, where the proposed estimators are robust and efficient.

Coronavirus disease 2019 (COVID-19), the emissary behind the worst global pandemic of the 21st century, is primarily a respiratory disease-causing virus called SARS-CoV-2 which is responsible for millions of new cases (incidence) and deaths (mortalities), worldwide. Many factors have played a role in the differential morbidity and mortality experienced by nations and ethnicities against SARS-CoV-2, such as the quality of primary medical health facilities or enabling economies. Nevertheless, the most important variable, i.e., the subsequent ability of individuals to be immunologically sensitive or resistant to the infection, was not properly discussed before. Therefore, an astounding issue arose when some developed countries experienced higher morbidity and mortality, compared with their relatively underdeveloped counterparts, despite having excellent medical health facilities. Hence this investigative review attempts to analyze the issue from an angle of previously undiscussed genetic, epigenetic, and molecular immune resistance mechanisms in correlation with the pathophysiology of SARS-CoV-2 and varied ethnicity-based immunological responses against it. The biological factors discussed here include the overall landscape of human microbiota, endogenous retroviral genes spliced into the human genome, copy number variation, and how they could modulate the innate and adaptive immune systems, which put a particular ethnic genetic architecture at a higher risk of SARS-CoV-2 infection than others. Considering an array of these factors in their entirety may help explain the geographic disparity of disease incidence, severity, and subsequent mortality associated with the disease while at the same time encouraging scientists to design new experimental approaches to investigation.

Fluid flow and chemokine gradients play a large part in not only regulating homeostatic processes in the brain, but also in pathologic conditions by directing cell migration. Tumor cells in particular are superior at invading into the brain resulting in tumor recurrence. One mechanism that governs cellular invasion is autologous chemotaxis, whereby pericellular chemokine gradients form due to interstitial fluid flow (IFF) leading cells to migrate up the gradient. Glioma cells have been shown to specifically use CXCL12 to increase their invasion under heightened interstitial flow. Computational modeling of this gradient offers better insight into the extent of its development around single cells, yet very few conditions have been modelled. In this paper, a computational model is developed to investigate how a CXCL12 gradient may form around a tumor cell and what conditions are necessary to affect its formation. Through finite element analysis using COMSOL and coupled convection-diffusion/mass transport equations, we show that velocity (IFF magnitude) has the largest parametric effect on gradient formation, multidirectional fluid flow causes gradient formation in the direction of the resultant which is governed by IFF magnitude, common treatments and flow patterns have a spatiotemporal effect on pericellular gradients, exogenous background concentrations can abrogate the autologous effect depending on how close the cell is to the source, that there is a minimal distance away from the tumor border required for a single cell to establish an autologous gradient, and finally that the development of a gradient formation is highly dependent on specific cell morphology.

We give an operator solution to an advanced-retarded differential equation. The application of the operators involved produces a solution in terms of Bessel functions.

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 ).

: Shear-wave elastography (SWE) has become popular in clinical practice for many diseases.However, there are not adequate research for spleen-related diseases.This study aimed to investigate the potential of quantitative values obtained through SWE in evaluating spleen pathologies in the pediatric population and to demonstrate its perfomance to differentiate splenomegaly-related diseases.Research group retrospectively included children with pathological diagnoses related to spleen from November 2016 to April 2021 and they were categorized three groups as portal hypertension (PH), benign lymphoid hyperplasia (BLH), malignant infiltration (MI).Spleen sizes and parenchymal stiffness were also calculated for each group.Subsequently, mean spleen stiffness in each compared with normal values within the same age group.In total 2781 children (1379 children for study group, 1402 children for control group) were enrolled to the study.The highest stiffness were observed in the PH group, which is statistically higher than others (p&lt;0.05). Although the mean spleen stiffness in the group with BLH was higher than the control and MI group, the difference was not statistically significant (p=0.08).The mean stiffness in the group with MI was significantly lower than both the control group (p=0.005) and PH (p=0.01).In conclusion, using SWE in the differential diagnosis of etiologies causing splenomegaly, could make important contribution.

In this study, we deal with a nonlinear system of neutral Volterra integro-differential equations (NVIDEs) with infinite delay. We study stability, uniform stability and instability of zero solution of the system of NVIDEs with infinite delay. We obtain three new results with regard to these concepts via two new Lyapunov– Krasovskii functionals (LKFs), respectively. As the main contributions of this work, we improve and generalize some earlier results in the relevant database from the linear case to more general nonlinear cases.

(1) Background: Angiotensin II, a major culprit in cardiovascular disease, activates mediators that are also involved in pathological cardiac remodelling. We aimed at investigating the effects of two of them: aldosterone (Ald) and transforming growth factor-beta-1 (TGF-β1 ), on cardiac remodelling in an in vivo model. (2) Methods: Six-week-old male wild-type (WT) and TGF-β1 -overexpressing transgenic (TGF-β1 -TG) mice were infused with subhypertensive doses of Ald for 2 weeks, and/or treated orally with eplerenone from postnatal day 21. Heart’s ventricles were examined: by morphometry, immunoblotting to assess intracellular signalling pathways, RT qPCR to determine hypertrophy and fibrosis marker genes. (3) Results: TGF-β1 -TG mice spontaneously developed cardiac hypertrophy and interstitial fibrosis, exhibited higher baseline phosphorylation of p44/42 and p38 kinases, fibronectin and ANP mRNA expression. Ald induced a comparable increase in ventricular heart weight-to-body-weight ratio and cardiomyocyte diameter in both strains, but less pronounced increase in interstitial fibrosis in transgenic compared to WT mice (23.6% vs 80.9%, p&lt;0.005). Ald increased phosphorylation of p44/42 and p38 in WT but not TGF-β1 -TG mice. While eplerenone-enriched chow partially prevented Ald-induced cardiac hypertrophy in both genotypes and interstitial fibrosis in WT controls, it completely protected from additional fibrosis in transgenic mice. (4) Conclusions: Ald appears to induce cardiac hypertrophy independently of TGF-β1 , while in case of fibrosis downstream signalling pathways of these two factors probably converge

In this work, we offer a novel and accurate method in order to find the solution of the linear differential equations over the intervals [0, 1) based on the generalization of Legendre wavelets. The mechanism is still upon workable implementation of the operational matrix of integration and its derivatives. This method reduces the problems into algebraic equations via the properties of generalized Legendre wavelet (GLW) together with the operational matrix of integration. The function approximation has been picked out in such a way so as to enumerate the connection coefficients in an facile manner. The proposed numerical technique, based on the GLW, has been examined on three linear problems as a consequence of this investigation. The outcomes have shown that this method, as opposed to some other existing numerical and analytical methods, is a very useful and advantageous for tackling such problems.

ExuR and UxuR are paralogous proteins belonging to the GntR family of transcriptional regulators. Both are known to control hexuronic acid metabolism in a variety of Gammaproteobacteria but the relative impact of each of them is still unclear. Here, we apply 2D difference electrophoresis followed by mass-spectrometry to characterise the changes in the Escherichia coli proteome in response to the uxuR or exuR deletion. Our data clearly show that the effects are different: deletion of uxuR resulted in significantly enhanced expression of D-mannonate dehydratase UxuA and flagellar protein FliC, and inhibition of outer membrane porin OmpF, while the absence of ExuR did not significantly alter the spectrum of detected proteins.This suggests that the roles of proteins predicted as homologs are far from identical. Effects of uxuR deletion were largely dependent on the cultivation conditions: during growth with glucose, UxuA and FliC were dramatically altered, while during growth with glucuronate activation of both was not so prominent. During growth on glucose, the maximal activation was detected for FliC. This was further confirmed by expression analysis and physiological tests thus suggesting involvement of UxuR in the regulation of bacterial motility and biofilm formation.

Background: Left ventricular hypertrophy (LVH) may be due to different causes, ranging from benign secondary forms to severe cardiomyopathies. Transthoracic Echocardiography (TTE) and ECG are the first level examination for LVH diagnosis. Cardiac magnetic resonance (CMR) defines accurately LVH type, extent and severity. Objectives: to evaluate the diagnostic and prognostic role of CMR in patients with TTE and/or ECG evidence of LVH. Methods: We performed CMR in 300 consecutive patients with echocardiographic and/or ECG signs of LVH. Results: Overall, 275 patients had TTE evidence of LVH with initial suspicion of hypertrophic cardiomyopathy (HCM) in 132 (44%), cardiac amyloidosis in 41 (14%), hypertensive LVH in 48 (16%), aortic stenosis in 4 (1%), undetermined LVH in 50(16%). The initial echocardiographic diagnostic suspicion of LVH was confirmed in 172 patients (57.3%) and changed in 128 patients (42.7%, p<0.0001): the diagnosis of HCM increased from 44% to 71% of patients; hypertensive and undetermined LVH decreased significantly (respectively to 4% and 5%). CMR allowed a diagnosis in 41 out of 50 (82%) with undetermined LVH at TTE. CMR also identified HCM in 17 out of 25 patients with apparently normal echo but with ECG criteria for LVH. Finally, the reclassification of the diagnosis by CMR was associated with a change of survival risk of patients: after CMR reclassification no events occurred in patients with undetermined or hypertensive LVH. Conclusions: CMR changed echocardiographic suspicion in almost half of patients with LVH. In the subgroup of patient with abnormal ECG, CMR identified LVH (particularly HCM) in 80% of patients. This study highlights the indication of CMR to better characterize the type, extent and severity of LVH detected at echocardiography and suspected with ECG.

The research field of two dimensional (2D) materials strongly relies on optical microscopy characterization tools to identify atomically thin materials and to determine their number of layers. Moreover, optical microscopy-based techniques also opened the door to study the optical properties of these nanomaterials. We present a comprehensive study of the differential reflectance spectra of 2D semiconducting transition metal dichalcogenides (TMDCs), MoS₂, MoSe₂, WS₂ and WSe₂, with thickness ranging from one layer up to six layers. We analyze the thickness-dependent energy of the different excitonic features, indicating the change in the band structure of the different TMDC materials with the number of layers. Our work provides a route to employ differential reflectance spectroscopy for determining the number of layers of MoS₂, MoSe₂, WS₂ and WSe₂.

Uncertain fractional differential equation (UFDE) is an excellent tool for describing complicated dynamic systems. This paper analyzes the valuation problems of currency option based on UFDE under optimistic value criterion. Firstly, an uncertain fractional currency model is formulated to describe the dynamics of foreign exchange rate. Then, the pricing formulae of European, American and Asian currency option are obtained under optimistic value criterion, respectively. Finally, numerical simulations are provided to illustrate the validity of our theoretical results.

In this work we present some driving strategies for a type of omnidirectional mobile robot, the offset-differential robot. This system presents omnidirectionality while using any type of standard wheels, allowing for applications in all terrain. The work is based on the full kinematic and dynamic analysis of the robot, including the passive elements, to explain some unexpected behaviors that appear during its motion. The stable and unstable behaviors are characterized and some driving strategies are stated in order to achieve the desired performance regarding precise positioning and speed.

Partial differential equations (PDEs) are used to describe a wide range of phenomena, such as heat transfer, fluid dynamics, and quantum mechanics. By solving PDEs, we can ob- tain insights into the behavior of the system and make predictions about its future evolution. Conventional numerical methods for obtaining the approximate solutions of PDEs may re- quire extensive computational resources and time, especially for complex PDEs and large- scale problems. The recently developed physics-informed neural network (PINN) has shown promise in a variety of scientific and engineering fields by incorporating physical laws into the loss functions of the neural network (NN). In addition, the training of PINN does not require ground truth data, but it has poor generalization ability to unseen domains. On the other hand, a convolutional neural network (CNN) has fast inference and better generalization ability, but it requires a large amount of training data. Taking the advantages of PINN and CNN by using Legendre multiwavelets (LMWs) as basis functions, we introduce a new method to approach the PDEs in this paper, namely Physics-Informed Legendre Multiwavelets CNN (PiLMWs-CNN), in order to continuously approximate a grid-based state representation that can be handled by a CNN. PiLMWs-CNN enable us to train our models using only physics-informed loss functions without any pre- computed training data, simultaneously providing fast and continuous solutions that gener- alize to previously unknown domains. In particular, the LMWs can simultaneously possess compact support, orthogonality, symmetry, high smoothness, and high approximation order. Compared to orthonormal polynomial (OP) bases, the approximation accuracy can be greatly increased and computation costs can be significantly reduced by using LMWs. We applied PiLMWs-CNN to approximate the damped wave equation, incompressible Navier-Stokes (N- S) equation, and two-dimensional heat conduction equation. The experimental results show that this method provides more accurate, efficient, and fast convergence with better stability when approximating the solution of PDEs.

Background Polycystic ovary syndrome (PCOS) is a common hormonal disorder worldwide among women of reproductive age. It is characterized by endocrine, reproductive, and metabolic abnormalities. Insulin resistance (IR) is one of its most important clinical features, associated with metabolic disorders and increased risk of type 2 diabetes (T2D). This study aimed to explore the whole blood gene expression profiling related to IR in PCOS patients compared to controls. Methods Blood RNA was extracted from 5 PCOS and 5 non-PCOS women with matched age and BMI. Homeostasis model assessment (HOMA-IR) was used to estimate the IR. The expression of IR genes was analyzed by Profiler PCR array. Results Both groups have similar levels of HOMA-IR (p>0.05). However, differential expression levels were observed between them. Fourteen genes were upregulated and 26 genes were downregulated in PCOS samples. Among the upregulated genes (>2 fold-change, p-value<0.05) are ADIPOQ, ADIPOR1, OLR, IGF-1, and APOE. Downregulated genes (>-2 fold-change, p-value<0.05) include HK-2, IRS1, and SERPINE1. These genes are involved in insulin and adipokines signaling, commonly dysregulated in T2D. They are also involved in innate immunity and inflammatory processes and are essential for lipid and carbohydrate metabolism. Conclusion Our finding suggests that despite both groups having no difference in IR level, there are differentially expressed genes involved in the IR pathway.

Physicists have employed various approaches to solve the “paradox” and offered a consistent conclusion that the traveller twin is younger than the homebody twin. However, some authors attribute the cause of differential aging to acceleration, while others believe that acceleration should not be regarded as the source of differential aging, but frame switch is. So far there is no agreement on this issue. Actually, acceleration and frame switch should not be regarded as the source of differential aging. The author will introduce a thought experiment in which two very long spacecraft are moving in opposite directions at a speed close to the speed of light to discuss the real cause of differential aging. The author found that the real cause of differential aging in the twin “paradox” is because of the asymmetry of destination choice. People always choose their destinations in the universe rather than in spacecraft. The destinations are always stationary relative to the homebody twin and moving relative to the traveller twin. Once we choose a destination in a reference frame, the distance is the proper length in this reference frame, but the distance will contract in another moving reference frame, thus the recording time will be shorter.

Conventionally, partial differential equations (PDE) problems are solved numerically through discretization process by using finite difference approximations. The algebraic systems generated by this process are then finalized by using an iterative method. Recently, scientists invented a short cut approach, without discretization process, to solve the PDE problems, namely by using machine learning (ML). This is potential to make scientific machine learning as a new sub-field of research. Thus, given the interest in developing ML for solving PDEs, it makes an abundance of an easy-to-use methods that allows researchers to quickly set up and solve problems. In this review paper, we discussed at least three methods for solving high dimensional of PDEs, namely PyDEns, NeuroDiffEq, and Nangs, which are all based on artificial neural networks (ANNs). ANN is one of the methods under ML which proven to be a universal estimator function. Comparison of numerical results presented in solving the classical PDEs such as heat, wave, and Poisson equations, to look at the accuracy and efficiency of the methods. The results showed that the NeuroDiffEq and Nangs algorithms performed better to solve higher dimensional of PDEs than the PyDEns.

The main bottleneck when performing computational fluid dynamics (CFD) simulations of combustion systems is the computation and integration of the highly non-linear and stiff chemical source terms. In recent times, machine learning has emerged as a promising tool to accelerate combustion chemistry, involving the use of regression models to predict the chemical source terms as functions of the thermochemical state of the system. However, combustion is a highly nonlinear phenomenon, and this often leads to divergence from the true solution when the neural network representation of chemical kinetics is integrated in time. This is because these approaches minimize the error during training without guaranteeing successful integration with ordinary differential equation (ODE) solvers. In this work, a novel neural ODE approach to combustion modeling, ChemNODE, is developed to address this issue. The source terms predicted by the neural network are integrated during training, and by backpropagating errors through the ODE solver, the neural network weights are adjusted accordingly to minimize the difference between the predicted and actual ODE solutions. It is shown that even when the dimensionality of the thermochemical manifold is trimmed to remove redundant species, the proposed approach accurately captures the correct physical behavior and reproduces the results obtained using the full chemical kinetic mechanism.

This document focuses attention on the fundamental solution of an autonomous linear retarded functional differential equation (RFDE) along with its supporting cast of actors: kernel matrix, characteristic matrix, resolvent matrix, and the Laplace transform. The fundamental solution is presented in a form of the convolutional powers of the kernel matrix in the manner of a convolutional exponential matrix function. The fundamental solution combined with a solution representation gives an exact expression in explicit form for the solution of a RFDE. Algebraic graph theory is applied to the RFDE in the form of a weighted loop-digraph to illuminate the system structure and system dynamics and to identify the strong and weak components. Examples are provided in the document to elucidate the behavior of the fundamental solution. The paper introduces fundamental solutions of other functional differential equations.

An easier method for the calibration of differential drive robots is presented. Most of the calibration is done on-board and it is not necessary to expend too much time taking note of the robot's position. The calibration method does not need a big free space to perform the tests. The bigger space is just in a straight line, which is easy to find. Results with the proposed method are compared with those from UMB as a reference, and they show very little deviation while the proposed calibration is much simpler.

In this article, we consider the three dimensional $\alpha$-fractional nonlinear delay differential system of the form \begin{align*} D^{\alpha}\left(u(t)\right)&=p(t)g\left(v(\sigma(t))\right),\\D^{\alpha}\left(v(t)\right)&=-q(t)h\left(w(t))\right),\\D^{\alpha}\left(w(t)\right)&=r(t)f\left(u(\tau(t))\right),~ t \geq t_0, \end{align*} where $0 < \alpha \leq 1$, $D^{\alpha}$ denotes the Katugampola fractional derivative of order $\alpha$. We have established some new oscillation criteria of solutions of differential system by using generalized Riccati transformation and inequality technique. The obtained results are illustrated with suitable examples.

This paper showed that turbulence closure problem is not an issue at all. All mistakes in the literature regarding the numbers of unknown quantities in the Reynolds turbulence equations stem from the misunderstandings of physics of the Reynolds stress tensor, i.e., all literature has stated that the symmetric Reynolds stress tensor has six unknowns; however, it actually has only three unknowns, i.e., the three components of fluctuation velocity. We showed the integral-differential equations of the Reynolds mean and fluctuation equations have exactly eight equations, which equal to the numbers of quantities in total, namely, three components of mean velocity, three components of fluctuation velocity, one mean pressure and one fluctuation pressure. With this understanding, the closed Reynolds Navier-Stokes turbulence equations of incompressible flows were formulated. This study may help to solve the puzzle that has eluded scientists and mathematicians for centuries.

In the note, the authors find several simple and explicit forms for a family of inhomogeneous linear ordinary differential equations studied in "D. Lim, Differential equations for Daehee polynomials and their applications, J. Nonlinear Sci. Appl. 10 (2017), no. 4, 1303-1315; Available online at http://dx.doi.org/10.22436/jnsa.010.04.02".

The fractional reduced differential transform method is a finite iterative method based on infinite fractional expansions. The result obtained is the approximation of the real value. There are few reports on the approximate error and the applicable condition. In this paper, according to the fractional expansions, we study the factors related to the approximate errors. Our research shows that the approximate errors relate not only to fractional order but also to time $t$ and increase rapidly with time $t$. This method can only be applied within a certain time range and the time range is relevant to fractional order and fractional expansions. Then, many obtained achievements may be incorrect if the applicable conditions are not satisfied. Some examples presented in this paper verify our analysis.

In this paper, a class of nonlinear ordinary differential equations with impulses at variable times is considered. The existence and uniqueness of solution are given. At the same time, modifying the classical definitions of continuous dependence and Ga^teaux differentiability, some results on continuous dependence and Ga^teaux differentiable of solution relative to the initial value also are presented in new topology sense. For the autonomous impulsive system, the periodicity of solution is given. As an application, properties of solution for a type of controlled nonlinear ordinary differential equation with impulses at variable times is obtained. These results are foundation to study optimal control problems of systems governed by the differential equations with impulses at variable times.

In this paper, we propose a partial differential equation model based on phase-field for sentiment analysis in the field of hotel comment texts. The comment texts are converted into word vectors using the Word2Vec tool, and then we utilize the multifractal detrended fluctuation analysis (MF-DFA) model to extract the generalized Hurst exponent of the word vector time series to achieve dimensionality reduction of the word vector data. The dimensionality reduced data is represented in a two-dimensional computational domain, and the modified Allen-Cahn (AC) function is used to evolve the phase values of the data to obtain a stable nonlinear boundary, thereby achieving automatic classification of hotel comment texts. The experimental results show that the proposed method can effectively classify positive and negative samples and achieve excellent results in classification indicators. We compared our proposed classifier with traditional machine learning models and the results indicate that our method possesses a better performance.

In this article, we present a comparative study between the Adomian Decomposition Method (ADM) and Variational Iteration Method (VIM). The study outlines the significant features of the two methods, for solving nonlinear Volterra-Fredholm integro-differential equations. From the computational viewpoint, the VIM is more efficient, convenient and easy to use. Moreover, we proved the existence and uniqueness results and convergence of the solution. Finally, an example is included to demonstrate the validity and applicability of the proposed techniques.

Background: Gut-Brain-Axis provides bidirectional communicational route; imbalance of which can have pathophysiological consequences. It is a frontier in autism research, affects 85% of autistic children (NIH report). Their microbiome has few overall microbes and smaller number of health promising microbes than their neurotypical peers. We hypothesize autism gut might play a role in manifestation of autism behaviours and on treatment, can revert back to normal behaviour considerably. The aim is to better understand to what degree gut microbiota of autism subjects differs from controls and identify bacterial species present exclusively in autism. Materials and Methods: 16s-rRNA-sequence of autism-subjects were retrieved from the American Gut Project Archive. Taxonomic assignment was inferred by similarity based methods using Quantitative Insights Into Microbial Ecology (QIIME). Species abundance was characterized and co-occurrence network was built to infer species interaction using measures of diversity. Statistical parameters were considered to validate the findings. Result: A total of 206 (1.8%) of American Gut Project datasets onstituted of autistic samples. Various bacteria such as Akkermansia sp., and Prevotella sp., were harboured in higher abundance in autistic children with statistical significance than in controls. Conclusion: These findings indicate connecting-link between gut-microbiome-brain-axis and autistic behaviour which can result in improved management

Flavonoids, compounds present in many dietary supplements, affect growth of different bacterial species when tested as purified or synthetic substances. Here, we asked if soy isoflavone extracts, commonly used in many products sold as anti-menopausal dietary supplements, influence bacterial growth similarly to synthetic isoflavone, genistein. Four commercially available products were tested in amounts corresponding to genistein concentrations causing inhibition of growth of Vibrio harveyi (a model bacterium sensitive to this isoflavone) and Escherichia coli (a model bacterium resistant to genistein). Differential effects of various extracts on V. harveyi and E. coli growth, from stimulation, through no changes, to inhibition, were observed. Moreover, contrary to genistein, tested extracts caused a decrease (to different extends) in viability of human dermal fibroblasts. These results indicate that effects of various soy isoflavone extracts on bacterial growth and viability of human cells are different, despite similar declared composition of the commercially available products.

Traditional potential transformers have problems of large volume, difficulty in insulation, iron core saturation, ferroresonance overvoltage and poor transient response characteristics. The voltage sensor based on the principle of electric field coupling and differential input structure does not need to contact the measured object or ground, and can avoid the above problems. However, it requires a sufficiently high capacitance between the differential electrodes to obtain sufficient accuracy and a high voltage division ratio. The existing method of using mutual capacitance between the differential electrodes will cause many problems and fail to meet the practical needs. To solve the above problems, this paper innovatively uses multi-layer ceramic capacitor to replace the mutual capacitance and designs a new type of voltage sensor. In addition, by using single bypass small resistance grounding method to increase the input impedance of the differential signal processing circuit, error of the sensor is further reduced. The experimental results show that the sensor has excellent accuracy and great transient response characteristics. The ratio error under power frequency is within ±0.5% and the phase error is within 1. The ratio error in the range of 500 Hz∼30 kHz is within ±5% and the phase error is within 5. Moreover, it has the advantages of low cost, miniaturization, flexible shape and easy to adjust the voltage division ratio. These characteristics indicate that the sensor has good voltage measurement and sensor network potential.

Differential Evolution (DE) is an evolutionary algorithm that has become increasingly popular due to its effectiveness and efficiency. However, its adaptation for multi-objective optimization requires further investigation. To address this issue, a novel algorithm called ILSDEMO has been proposed, which incorporates indicator-based selection and local search into a self-adaptive DE. ILSDEMO employs an archive population to store non-dominated solutions, generating an initial population uniformly distributed over the feasible solution space using orthogonal design. Additionally, two variants of DE are used to expedite convergence, while q-Gaussian mutation is utilized to exploit better trial individuals. The k-nearest neighbor rule is used to eliminate crowded solutions, and indicator-based selection is employed to generate a new parent population without diversity preservation. The performance of ILSDEMO was investigated on the test instances from the ZDT series and DTLZ series in terms of the selected indicators. The results suggest that ILSDEMO accurately and evenly approximates the true Pareto front compared to NSGAII, IBEA, and DEMO.

A methodology for selecting rational parameters of atmospheric aircrafts at the initial stages of design using an optimization algorithm of differential evolution and numerical mathematical modeling of aerodynamics problems is proposed. The technique involves the implementation of weight and aerodynamic balance in the main flight modes, has the ability to consider atmospheric aircrafts with one or two lifting surfaces, apply parallel calculations and automatically generate a three-dimensional geometric model of aircraft appearance based on the optimization results. A method for accelerating the process of optimizing the parameters of an aircraft in terms of take-off weight by more than three times by introducing a objective function into a set of design variables is proposed and demonstrated. The results of assessing the reliability of the used mathematical models of aerodynamics and the correctness of the calculation the objective function, taking into account various constraints, are presented. A comprehensive test of the performance and efficiency of the methodology is considered by solving demonstration problems to optimize more than ten main design parameters the appearance of two existing heavy-class unmanned aerial vehicles with known characteristics from open sources.

In this paper, we obtain the existence and uniqueness theorem for solutions of Caputo type fractional stochastic delay differential systems (FSDDSs) with Poisson jumps by utilizing delayed perturbation of Mittag-Leffler function. Moreover, by using Burkholder-Davis-Gundy's inequality, Doob's martingale inequality and Holder inequality, we prove that the solution of the averaged FSDDSs converges to that of the standard FSDDSs in the sense of Lp. Some known results in the literature are extended.

We classify all the topologically non-equivalent phase portraits of the quadratic polynomial differential system dx/dt = (1-2x)(y-x), dy/dt =y (2-g y-(5g-4)x/(g-1)), in the Poincaré disc for all the values of the parameter g in R\{1}. The differential system dx/dt = y-x, dy/dt =y (2-g y-(5g-4)x/(g-1))/(1-2x), when the parameter g in (1,2] models the structure equations of a static star in general relativity in the case of the existence of a homologous family of solutions, being x = m(r)/r where m(r)>= 0 is the mass inside the sphere of radius r of the star, y = 4pi r^2 rho where rho is the density of the star, and t = ln (r/R) where R is the radius of the star. We classify the possible values of m(r)/r and 4pi r^2 rho when r-->0.

Ageing is associated with a decline in both Nrf2 activity and DNA repair efficiency, leading to the accumulation of DNA damage and an increased risk of cancer. Understanding the mechanisms behind the increased level of damaged DNA during ageing is crucial for developing interventions to mitigate age-related cancer risk and improve overall health in older individuals. (Poly)phenols are plant-derived bioactive compounds that undergo metabolism into simpler phenolic catabolites following ingestion. While these compounds have been associated with various health benefits, further analysis of their bioavailable catabolites is necessary. To this end, four phenolic catabolites derived from colonic microbiota were investigated for their ability to reduce DNA damage in response to oxidative challenge and modulate the Nrf2-Antixoidant Response Element pathway. Normal and adenocarcinoma colonocyte cell lines (CCD 841 CoN, & HT29 respectively) were exposed to sub cytotoxic concentrations (>10 µM,) of hydroxylated (4-hydroxybenzoic acid, 3-(3’-hydroxyphenyl) propionic acid) and non-hydroxylated (benzoic acid or 3-phenylpropionic acid) phenolic acids. Using the COMET assay, each catabolite demonstrated significant (p<0.001) geno-protective activity, albeit with varying potency. They also significantly modulated expression of key genes in the Nrf2-ARE pathway, including Nrf2, Heme oxygenase-1 (HO-1), and NAD(P)H dehydrogenase quinone 1 (NQO1). Hydroxylation of the phenolic acids appeared to have a limited effect with respect to bioactivity. Overall, the colon derived phenolic metabolites, when assessed at physiologically relevant concentrations, reduced DNA damage in both normal and adenocarcinoma colonic cells in response to oxidative challenge, mediated – at least in part via upregulation of the Nrf2-ARE pathway.