This project aims to simulate and analyze population dynamics in evolutionary systems, using stochastic differential equations and probabilistic rules for crossbreeding and benefits. The study employs advanced computational techniques to model the evolution of populations over an extended period. Specifically, we explore a scenario with ten distinct groups, each starting with an equal population and evolving under defined genetic and cooperative behaviors. The simulation spans 1000 years, incorporating individual lifespans, stochastic updates, and probabilistic interactions. To ensure robustness and reliability, the study includes detailed statistical analysis, encompassing descriptive statistics, confidence intervals, and ANOVA tests. We further visualize the temporal behavior of populations and subpopulations, providing insights into the evolutionary dynamics and stability of the system. The results demonstrate the effectiveness of balanced cooperation and genetic diversity in maintaining stable population distributions. The project showcases the integration of mathematical modeling, statistical analysis, and computational simulations, contributing valuable insights into evolutionary biology and complex systems. It highlights the importance of interdisciplinary approaches in understanding and predicting population behaviors, with implications for both theoretical research and practical applications in fields such as ecology, genetics, probability and social sciences.

In this work, the analytical treatment of Fourth order pd equations has been discussed with the variational iteration algorithm with an auxiliary parameter. The technique has the capability of reducing the size of computational work and easily overcomes the difficulty of the perturbation method or Adomian polynomials. Comparison with the classic variational iteration algorithm- is carried out, showing that the modification is more efficient and reliable.

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.

Biohydrogen is a versatile energy carrier for the generation of electric energy from renewable sources. Hydrogenases can be used in enzymatic fuel cells to oxidize dihydrogen. The rate of electron transfer (ET) at the anodic side between the [NiFe]-hydrogenase enzyme distal iron-sulfur cluster and the electrode surface can be described by the Marcus equation. All parameters for the Marcus equation are accessible from DFT calculations. The distal cubane FeS-cluster has a three cysteine and one histidine coordination [Fe₄S₄](His)(Cys)₃ first ligation sphere. The reorganization energy (inner- and outer-sphere) is almost unchanged upon a histidine-to-cysteine substitution. Differences in rates of electron transfer between the wild-type enzyme and the all-cysteine mutant can be rationalized by a diminished electronic coupling between the donor and acceptor molecules in the [Fe₄S₄](Cys)₄ case. The fast and efficient electron transfer from the distal iron-sulfur cluster is realized by a fine-tuned protein environment which facilitates the flow of electrons. This study enables the design and control of electron transfer rates and pathways by protein engineering.

Here we are concerning with two problems of a coupled system of random and stochastic nonlinear differential equations with two coupled systems of nonlinear nonlocal random and stochastic integral conditions. The existence of solutions will be studied. The sufficient condition for the uniqueness of the solution will be given. The continuous dependence of the unique solution on the nonlocal conditions will be proved.

The development of virtual models has recently been generalized in the field of complex mechatronic product design. Virtual models have various advantages such as: the systemic design approach, most often parametric, the implementation of extreme, expensive, and perhaps risky scenarios for the operation of the designed product, the testing of a large number of variants, etc. The main contribution of the paper consists of the development of an interface family called DeSeRoI (Dedicated Serial Robot Interface). Each member of the interface family integrates Simulink libraries and is created by the programmer in accordance with user requests. It follows that the interfaces composing the DeSeRoI family can have different levels of complexity depending on user needs and constraints. We are implementing a MATLAB-based application with user-provided configuration for serial robots in order to automatically visualize the kinematics data and simulation. Within MATLAB, two scripts are created responsible for generating Simulink models that compute the kinematics problem. One of the scripts (Main) saves information about the configuration of the robot and the other one (Generates_Simulink_Models) computes the kinematics problem. Different types of functions (software module) have been developed. Using these functions, the Simulink models result as modular entities. The automated approach eases user’s interaction and understanding of serial robots’ kinematics by performing the simulation procedure in a shorter amount of time and with higher efficiency, assuring a precise outcome despite the chosen parameters.

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.

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.

This study aimed at exploring what role artificial intelligence techniques could play in the futural numerical analysis. In this paper, a convolutional neural network techniques based on modified loss function is proposed as a surrogate of finite element method(FEM). Several surrogate-based physics-informed neural networks(PINNs) are developed to solve representative boundary value problems based on elliptic partial differential equations (PDEs). Results from the proposed surrogate-based approach are in good agreement with ones from conventional FEM. It is found that modification of the loss function could improve the prediction accuracy of the neural network. It is indicated that to some extent the artificial intelligence technique could replace conventional numerical analysis as a great surrogate model.

The purpose of this paper is to find the time optimal control to a target set for semilinear stochastic functional differential equations involving time delays or memories under general conditions on a target set and nonlinear terms even though the equations contain unbounded principal operators. Our research approach is construct a fundamental solution for corresponding linear systems and establish variations of constant formula of solutions for given stochastic equations. The existence result of time optimal controls for one point target set governed by the given semilinear stochastic equation is also established.

In this study, we first present a time-fractional L$\hat{e}$vy diffusion equation of the exponential option pricing models of European option pricing and the risk-neutral parameter. Then, we modify a particular L$\hat{e}$vy-time fractional diffusion equation of European-style options. Introduce a more general model from the models based on the L$\hat{e}$vy-time fractional diffusion equation and review some recent findings regarding of the Europe option pricing of risk-neutral free.

Intratumoral heterogeneity can exist along multiple axes: Cancer Stem Cells (CSCs)/non-CSCs, drug-sensitive/drug-tolerant states and a spectrum of epithelial-hybrid-mesenchymal phenotypes. Further, these diverse cell-states can switch reversibly among one another, thereby posing a major challenge to therapeutic efficacy. Therefore, understanding the origins of phenotypic plasticity and heterogeneity remains an active area of investigation. While genomic components (mutations, chromosomal instability) driving heterogeneity have been well-studied, recent reports highlight the role of non-genetic mechanisms in enabling both phenotypic plasticity and heterogeneity. Here, we discuss various processes underlying phenotypic plasticity such as stochastic gene expression, chromatin reprogramming, asymmetric cell division and the presence of multiple “attractors”. These processes can facilitate a dynamically evolving cell population such that a subpopulation of (drug-tolerant) cells can survive lethal drug exposure and recapitulate population heterogeneity on drug withdrawal, leading to relapse. These drug-tolerant cells can be both pre-existing and also induced by the drug itself through cell-state reprogramming. The dynamics of cell-state transitions both in absence and presence of the drug can be quantified through mathematical models. Such a dynamical systems approach to elucidating patterns of intratumoral heterogeneity by integrating longitudinal experimental data with mathematical models can help design effective combinatorial and/or sequential therapies for better clinical outcomes.

In this study, we present a numerical method for solving two--dimensional space--time fractional partial differential equations (FPDEs), where the solutions of the FPDEs are expanded in terms of the shifted Chebyshev polynomials. The numerical approximations are evaluated at the Chebyshev-Gauss-Lobatto points. In the case when the FPDE is nonlinear, we employ a Newton-Raphson approach to linearize the equation. Both the linear and nonlinear cases lead to a consistent system of linear algebraic equations. The scheme is tested on selected FPDEs and the numerical results show that the proposed numerical scheme is accurate and computationally efficient in terms of CPU times. To establish the accuracy of the method, we also present an error analysis which shows the convergence of the numerical method. These positive attributes make the proposed method a good approach for solving two--dimensional fractional partial differential equations with both space and time fractional orders.

In this paper, mean-field type games between two players with backward stochastic dynamics are defined and studied. They make up a class of non-zero-sum differential games where the players' state dynamics solve backward stochastic differential equations (BSDEs) that depend on the marginal distributions of player states. Players try to minimize their individual cost functionals, also depending on the marginal state distributions. Under some regularity conditions, we derive necessary and sufficient conditions for existence of Nash equilibria. Player behavior is illustrated by numerical examples, and is compared to a centrally planned solution where the social cost, the sum of player costs, is minimized. The inefficiency of a Nash equilibrium, compared to socially optimal behavior, is quantified by the so-called price of anarchy. Numerical simulations of the price of anarchy indicate how the improvement in social cost achievable by a central planner depends on problem parameters.

The information data accuracy affects the working reliability of production management system directly. Mobile equipment is an important part of integrated manufacturing system, in the course of its works, due to the complex working environment and the dynamic change of its position, it lead to the important problem of information detection distortion. Because the application of fractional differential operator has the dual functions of enhancing signal strength and reducing data error, we puts forward a data processing method of obtaining production information data of various accuracy by changing the parameters of fractional differential operator. Establish a mobile equipment detection data fusion processing model based on fractional order partial differential equations and apply it in the processing experiment of mobile equipment testing information detection data in an integrated manufacturing system, the feasibility and effectiveness of the method are verified. We conclude that the fractional order partial differential equations used in the processing of mobile equipment monitoring information data of an integrated manufacturing system has the function of obtaining production information data of various accuracy, which are of great significance to improve the working reliability in integrated manufacturing system. which is of great significance to improve the working reliability and scientific decision of integrated manufacturing system.

At present paper, we aim to study the long-time behavior of a stochastic semi-linear degenerate parabolic equation on bounded or unbounded domain and driven by a nonlinear noise and defined. Since the theory of pathwise random dynamical systems can not be applied directly to the equation with nonlinear noise, first, we establish the existence of weak pullback mean random attractors for the equation by applying the theory of mean-square random dynamical systems; then, we prove the existence of (pathwise) pullback random attractors for the Wong-Zakai approximate system of the equation. In addition, we establish the upper semicontinuity of pullback random attractors for the Wong-Zakai approximate system of the equation under consideration driven by a linear multiplicative noise.

The paper is concerned with a class of stochastic differential equations in infinite dimensional Hilbert space with random coefficients driven by Teugel's martingales which are more general processes. and its optimal control problem. Here Teugels martingales are a family of pairwise strongly orthonormal martingales associated with L\'{e}vy processes (see Nualart and Schoutens). There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous dependence theorem of solutions combining with the parameter extension method. The second is to establish the stochastic maximum principle and verification theorem for our optimal control problem by the classicconvex variation method and dual technique.The third is to represent an example of a Cauchy problem for a controlled stochastic partial differential equation driven by Teugels martingales which our theoretical results can solve.

Epilepsy is known to cause alterations in neural networks. However, many details of these changes remain poorly understood. The objective of this study was to investigate changes in the properties of hippocampal CA1 pyramidal neurons and their synaptic inputs in a rat lithium-pilocarpine model of epilepsy. In the chronic phase of the model, we found a marked loss of pyramidal neurons in the CA1 area. However, the membrane properties of the neurons remained essentially unal-tered. The results of the electrophysiological and morphological studies indicate that the direct pathway from the entorhinal cortex to CA1 neurons is reinforced in epileptic animals, whereas the inputs to them from CA3 are either unaltered or even diminished. In particular, the dendritic spine density in the str. lacunosum moleculare, where the direct pathway from the entorhinal cortex ter-minates, was found to be 2.5 times higher in epileptic rats than in control rats. Furthermore, the summation of responses upon stimulation of the temporoammonic pathway was enhanced by approximately twofold in epileptic rats. This enhancement is believed to be a significant con-tributing factor to the heightened epileptic activity observed in the entorhinal cortex of epileptic rats using an ex vivo 4-aminopyridine model.

System-of-systems (SoS) evolution is a complex and unpredictable process. Although various principles to facilitate collaborative SoS evolution have been proposed, there is a lack of experimental data validating their effectiveness. To address these issues, we present an Agent-Based Model (ABM) for SoS evolution in the Internet of Vehicles (IoV) , serving as a quantitative analysis tool for SoS research. By integrating multiple complex and rational behaviors of individuals, we aim to simulate real-world scenarios as accurately as possible. To simulate the SoS evolution process, our model employs multiple agents with autonomous interactions and incorporates external environmental variables. Furthermore, we propose three evaluation metrics: evolutionary time, degree of variation, and evolutionary cost, to assess the performance of SoS evolution. Our study demonstrates that enhanced information transparency significantly improves the evolutionary performance of distributed SoS. Conversely, the adoption of uniform standards only brings limited performance enhancement to distributed SoSs. Although our proposed model has limitations, it stands out from other approaches that utilize Agent-Based Modeling to analyze SoS theories. Our model focuses on realistic problem contexts and simulates realistic interaction behaviors. This study enhances the comprehension of SoS evolution processes and provides valuable insights for the formulation of effective evolutionary strategies.

Paratemporal methods based on tree expansion have proven to be effective in efficiently generating trajectories of stochastic systems. However, combinatorial explosion of branching arising from multiple choice points presents a major hurdle that must be overcome to implement such techniques. In this paper we tackle this scalability problem by developing a systems theory-based framework covering both conventional and proposed tree expansion algorithms for speeding up discrete event system stochastic simulations while preserving desired accuracy. An example is discussed to illustrate the tree expansion framework in which a discrete event system specification (DEVS) Markov stochastic model takes the form of a tree isomorphic to a free monoid over the branching alphabet. We derive the computation times for baseline, non-merging, and merging tree expansion algorithms to compute the distribution of output values at any given depth. The results show the remarkable reduction from exponential to polynomial dependence on depth effectuated by node merging. We relate these results to the similarly reduced computation time of binomial coefficients underlying Pascal’s triangle. Finally, we discuss application of tree expansion to estimating temporal distributions in stochastic simulations involving serial and parallel compositions with potential real world use cases.

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.

This paper presents an optimized energy management strategy for Li-ion power batteries used on electric vehicles (EVs) at low temperatures. Under low-temperature environments, EVs suffer a sharp driving range loss resulted from the energy and power capability reduction of the battery. Simultaneously, because of Li plating, battery degradation becomes an increasing concern as temperature drops. All these factors could greatly increase the total vehicle operation cost. Prior to battery charging and vehicle operating, preheating battery to a battery-friendly temperature is an approach to promote energy utilization and reduce total cost. Based on the proposed LiFePO4 battery model, the total vehicle operation cost under certain driving cycles is quantified in the present paper. Then given a certain ambient temperature, a target temperature of preheating is optimized under the principle of minimizing total cost. As for the preheating method, a liquid heating system is also implemented on an electric bus. Simulation results show that the preheating process becomes increasingly necessary with a decreasing ambient temperature; however, the preheating demand declines as driving range grows. Vehicle tests verify that the preheating management strategy proposed in this paper is able to save total vehicle operation cost.

This research work deals with the formulation of numerical scheme with algorithm to compute singularly perturbed partial differential equations(SP-PDEs) involving a significant negative shift. The problem involves small parameter which causes a rapidly changing boundary layers in the vicinity of a body, and the negative shift term causes interior layer. Such appearance of an abruptly varying layers causes difficulties to find the exact solution and it is not adequate to employ classical numerical methods. The technique presented in this research work simplifies these challenges and yields accurate numerical solution.The stability and convergence analyses of the methods are examined and proven. To test the developed technique, numerical experiments are carried out and confirmed with theoretical analysis.

The (numerical) solution of Ordinary Differential Equations (ODEs) problems is of paramount relevance, ODEs system being an ubiquitous mathematical formulation of many physical phenomena (such as those involved in fluid dynamics, chemistry, biology, evolutionary-anthropology, ...): almost every dynamici phenomenon can be modeled by means of an ODEs system. The present paper is the first manifesto of FOODIE, a library aimed to numerically solve ODEs problems by means of a clear, concise and efficient abstract interface. FOODIE, meaning Fortran Object oriented Ordinary Differential Equations integration library, has manifolds aims: to provide a set to built-in numerical schemes that are accurate, robust, validated and efficient and to allow easy application of these schemes to (almost) all ODEs problems by means of an effective Abstract Calculus Pattern. The key idea is to allow the same solver-implementation to be applied to all ODEs problems thus avoiding the re-implementation of the ODEs solver for each different ODEs problem: code re-usability is consequently maximized, FOODIE being a general robust framework. Besides, the same framework also allows rapid development of new ODEs solvers due to the high abstraction level of the library itself. The present paper is the first announcement of FOODIE project: the current implementation is extensively discussed and its capabilities are proved by means of tests and examples.

In this paper we introduce a computational model for the simulation of hypervelocity impact (HVI) phenomena which is based on the Discrete Element Method (DEM). Our paper constitutes the first application of DEM to the modeling and simulating of impact events for velocities beyond 5 kms⁻¹. We present here the results of a systematic numerical study on HVI of solids. For modeling the solids, we use discrete spherical particles that interact with each other via potentials. In our numerical investigations we are particularly interested in the dynamics of material fragmentation upon impact. We model a typical HVI experiment configuration where a sphere strikes a thin plate and investigate the properties of the resulting debris cloud. We provide a quantitative computational analysis of the resulting debris cloud caused by impact and a comprehensive parameter study by varying key parameters of our model. We compare our findings from the simulations with recent HVI experiments performed at our institute. Our findings are that the DEM method leads to very stable, energy–conserving simulations of HVI scenarios that map the experimental setup where a sphere strikes a thin plate at hypervelocity speed. Our chosen interaction model works particularly well in the velocity range where the local stresses caused by impact shock waves markedly exceed the ultimate material strength.

Bats are natural hosts for a wide variety of viruses and could therefore be the reservoir, source and spillover for several mammalian viruses, including adenoviruses. We examined faecal samples from 12 bats (five species of the family Vespertilionidae) from central Russia (Moscow Region) and found that two of them (16%) were positive for mastadenoviruses. One of the identified viruses was isolated from faeces of Nyctalis noctule and named BatAdV/MOW15-Nn19. The genome of the BatAdV/MOW15-Nn19 was 37,915 bp in length. Comparative studies have shown significant divergence of the nucleotide sequence of the BatAdV/MOW15-Nn19 genome from European mastadenoviruses, the highest genome sequence similarity was to isolate WA3301 from an Australian bat. Phylogenetic analysis, as well as a comparative analysis of the protein coding genes to homologous available from public database, showed evidence of novel species within Mastadenovirus genus (preliminary named «K»). Analysis of the short part of the DNA polymerase gene of BatAdV/MOW15-Nn19 reveals few NCBI records from Europe with high identity to the new virus, i.e. mastadenoviruses related to the new species are circulating in European bats. The partial genome of another mastadenovirus from Pipistrellus nathusii was identified, it represented bat adenovirus species B, which is widely distributed in European Vespertilionidae bats. New data on the genetic diversity of bat adenoviruses may help to better understand how they evolved in mammals and spread across Europe.

The existence of multiple copies of genes is a well-known phenomenon. A gene family is a set of sufficiently similar genes, formed by gene duplication. In earlier works conducted on limited number of completely sequenced and annotated genomes it was found that size of gene family and size of genome are positively correlated. Additionally, it was found that several atypical microbes deviated from the observed general trend. In this study, we reexamined these associations on a larger dataset consisting of 1484 prokaryotic genomes and using several ranking approaches. We applied ranking methods in such a way that genomes with lower number of paralogs would have lower rank. Until now only simple ranking methods were used; we applied the Kemeny optimal aggregation approach as well. Regression and correlation analysis were utilized in order to accurately quantify and characterize the relationships between measures of paralog indices and genome size. In addition, boxplot analysis was employed as a method for outlier detection. We found that, in general, all paralog indexes positively correlate with an increase of genome size. As expected, different groups of atypical prokaryotic genomes were found for different types of paralog quantities.

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.

In engineering practice, various types of information data are affected by many factors during the collection process. For example, information data measurement errors are caused by equipment performance and the working environment. During the transmission of detection information, the signal distortion caused by energy loss and signal interference causes unpredictable detection errors in the collected information data. Through the study of fractional calculus theory, it was found that it is suitable for studying nonlinear, non-causal, and non-stationary signals, and has the dual functions of improving detection information and enhancing signal strength. Therefore, under the influence of many factors, we applied the fractional difference algorithm to the field of information data processing. Multi-sensor detection data fusion algorithm based on the fractional partial differential equation was adopted to establish its online detection data. A multi-sensor detection data fusion algorithm based on a fractional partial differential equation is established, which effectively fuses the information data detection errors caused by various influencing factors and greatly improves the detection accuracy of information data. The effectiveness of this method is proved through its application in an experiment.

Conditions under which compositions of component systems form a well-defined system-of-systems here are formulated at a fundamental level. Statement of what defines a well-defined composition and sufficient conditions guaranteeing such a result offers insight into exemplars that can be found in special cases such as differential equation and discrete event systems. For any given global state of a composition, two requirements can be stated informally as: 1) the system can leave this state, i.e., there is at least one trajectory defined that starts from the state, and 2) the trajectory evolves over time without getting stuck at a point in time. Considered for every global state, these conditions determine whether the resultant is a well-defined system and if so, whether it is non-deterministic or deterministic. We formulate these questions within the framework of iterative specifications for mathematical system models that are shown to be behaviorally equivalent to the Discrete Event System Specification (DEVS) formalism. This formalization supports definitions and proofs of the afore-mentioned conditions. Implications are drawn at the fundamental level of existence where the emergence of a system from an assemblage of components can be characterized. We focus on systems with feedback coupling where existence and uniqueness of solutions is problematic.

Food systems will need to undergo considerable transformation. To be better prepared for and resilient to uncertainty and disturbances in the future, resource users and managers need to further develop knowledge about the food and farming system, with its dominating feedback structures and complexities, and to test robust and integrated system-based solutions. This paper investigates how participatory system dynamics modeling can be adapted to groups at the community level with low or no formal educational background. The paper also analyzes the refinement of workshop participants’ mental models as a consequence of a participatory system dynamics intervention. For this purpose, we ran two workshops with small-scale farmers in Zambia. Analysis of workshop data and post-workshop interviews shows that participatory system dynamics is well adaptable to support an audience-specific learning-by-doing approach. The use of pictures, objects and water glasses in combination with the basic aspects of causal loop diagramming makes for a well-balanced toolbox. Participants acquire understanding that is also relevant beyond systems thinking in that is offers a range of practical insights such as a critical evaluation of common food security strategies.

Dynamic virtual testing by Hardware in the Loop (HIL) real time simulation systems is common to minimize physical tests to validate and verify control algorithms, logics and software, under normal and emergency conditions. The accurate but costly HIL models setup activities could have an extended use to simulate faulty conditions that are seldom observable in the real system, yet they must be detected in advance and recognized. Data driven diagnostic methods have reached a mature development, in various sectors, proving effective in early detecting slowly varying deviations from nominal patterns of signals, even without a priori knowledge of their nature and behavior. These methods rely on vast amount of data logged from real systems that are ever and ever richer of monitoring telemetries that are worth being exploited. However, due to the usually reliable and safe systems being managed, it is often difficult to collect enough data on anomalous situations to validate fault detection and isolation and limit false positives. HIL model-based simulations allow generating and observing operational domains or transients rarely observed in real operations. This allows identifying the signals that are most correlated to faults and that could be selected to setup data-based diagnostic models of parts or subsystems, which are more suitable than the whole HIL model for online diagnostics, as well as to identify the features and trends that are most symptomatic of anomalous conditions.

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.

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.

Prior studies have focused on the overall behavior of randomly moving particle swarms. However, the characteristics of the stochastic-constrained particles that form ubiquitously within these swarms remain oblivious. This study demonstrates a generalized diffusion equation for stochastic-constrained particles that considers the velocity and location aggregation effects observed from their parent particle swarm (i.e., a completely random particle swarm). This equation can be approximated as the form of Schr\"odinger equation in the microcosmic case (low relative density) and describe the dynamics of the total mass distribution in the macrocosmic case (high relative density). The predicted density distribution of the particle swarm in the stable aggregation state is consistent with the total mass distribution of massive, relaxed galaxy clusters (at least in the range of r < r_s), preventing cuspy problems in the empirical Navarro-Frenk-White (NFW) profile. This study opens a window to observe the dynamics of stochastic-constrained particles from a third perspective, from which the aggregation effect of particles without gravitation can be saw.

The work proposes a backtesting analysis in comparison between the Lee-Carter and the Cairns-Blake-Dowd mortality models, employing Italian data. The mortality data come from the Italian National Statistics Institute (ISTAT) database and span the period 1975-2014, over which we computed back-projections evaluating the performances of the models in comparisons with real data. We propose three different backtest approaches, evaluating the goodness of short-run forecast versus medium-length ones. We find that both models were not able to capture the improving shock on the mortality observed for the male population on the analyzed period. Moreover, the results suggest that CBD forecast are reliable prevalently for ages above 75, and that LC forecast are basically more accurate for this data.

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.

: In this paper we present an optimization of the planar manufacturing scheme for stretch-free, shape induced metal interconnects to simplify the fabrication with the aim of maximizing the flexibility in the structure regarding to stress and strain. The Formation of trenches between silicon islands are actively used in the lithographic process to create arc shape structures by spin coating resist into the trenches. The resulting resist form is used as a template for the metal lines, which are structured on top. Because this arc shape is beneficial for the flexibility of these bridges. The trench depth as a key parameter for the stress distribution is investigated by applying numerical simulations. The simulated results show that the increase in penetration depth of the metal bridge into the trench increases the tensile load which is converted into a shear Force Q(x), that usually leads to increased strains the structure can generate. For the fabrication the filling of the trenches with resist is optimized by varying the spin speed. Compared to the theoretical resistance, the current-voltage measurements of the metal bridges show a similar behavior and almost every structural variation is capable of functioning as a flexible electrical interconnect in a complete island-bridge array.

We present a class of efficient parametric closure models for 1D stochastic Burgers equations. Casting it as statistical learning of the flow map, we derive the parametric form by representing the unresolved high wavenumber Fourier modes as functionals of the resolved variables’ trajectory. The reduced models are nonlinear autoregression (NAR) time series models, with coefficients estimated from data by least squares. The NAR models can accurately reproduce the energy spectrum, the invariant densities, and the autocorrelations. Taking advantage of the simplicity of the NAR models, we investigate maximal and optimal space-time reduction. Reduction in space dimension is unlimited, and NAR models with two Fourier modes can perform well. The NAR model’s stability limits time reduction, with a maximal time step smaller than that of the K-mode Galerkin system. We report a potential criterion for optimal space-time reduction: the NAR models achieve minimal relative error in the energy spectrum at the time step where the K-mode Galerkin system’s mean CFL number agrees with the full model’s.

Non-standard Lagrangians do not display any discernible energy-like terms, yet they give the same equations of motion as standard Lagrangians, which have easily identifiable energy-like terms. A new method to derive non-standard Lagrangians for second-order nonlinear differential equations with damping is developed and the limitations of this method are explored. It is shown that the limitations do not exist only for those nonlinear dynamical systems that can be converted into linear ones. The obtained results are applied to selected population dynamics models for which non-standard Lagrangians and their corresponding null Lagrangians and gauge functions are derived, and their roles in the population dynamics are discussed.

: Tunnel instability and lining integrity are intimately tied to the creep properties of the surrounding rock. The acquisition of rock mass creep parameters is critical in ascertaining the appropriate timing for lining construction. Nevertheless, creep tests on rock specimens conducted in a controlled setting cannot be straightforwardly extrapolated to rock mass creep analysis. This study performs laboratory-based creep tests on mudstone samples and establishes the corresponding creep constitutive model. Integration of a Mohr-Coulomb element with the Burgers model in series serves to characterise the yield creep behaviour of the rock mass. Additionally, the research outlines a series of 100 orthogonal experiments utilising randomised creep parameters, and formulates a GA-BP neural network inversion model. Employing long-term deformation measurements from the crown and sidewalls of the project site, this study deduces the creep parameters of the mudstone in the investigated tunnel section and examines the prolonged deformation traits of the surrounding rock. Drawing on the deformation traits of the surrounding rock and the forces impacting the primary support and lining structures, this paper evaluates the earliest and latest viable lining casting periods and pinpoints an optimal timing interval for lining implementation. The methodologies employed herein can serve as a benchmark for analogous endeavors internationally.

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.

Existing methods for simulating missile dynamics and training often rely on three degrees of freedom (3DOF) motions, limiting their ability to represent the complex maneuvers and targeting strategies of modern missiles. This paper proposes integrating virtual reality (VR) technology with six degrees of freedom (6DOF) dynamics to enhance the accuracy and efficiency of missile simulation and training. By incorporating 6DOF dynamics, simulations can capture the full range of missile motion, providing a comprehensive understanding of their capabilities and limitations. Through VR, users can immerse themselves in realistic missile scenarios, interact with dynamic behaviors in real-time, and refine their targeting and interception skills. The integration of VR with 6DOF dynamics also facilitates real-time feedback and evaluation, enhancing training efficiency and proficiency in missile operations. This approach aims to revolutionize missile training by bridging the gap between traditional simulation methods and real-world dynamics.

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.

Being forced to live in an area following a catastrophic landslide may adversely impact people's mental well-being. Unprivileged communities such as Adivasis, Dalits, plantation workers, and people with low incomes in Kerala's hilly districts are forced to live in landslide-affected areas despite their fear. This paper examines the fears and concerns of landslide survivors from the marginalized sections of society from a broader framework of the political economy of mental health. This approach aligns with the assertion made by the World Health Organisation that individual factors do not solely determine mental health but are intricately linked to broader social, political, and economic circumstances. Data were collected through in-depth interviews with fatal landslide survivors and key informants [ ]. The study employed thematic data analysis from in-depth interviews of various fatal landslide survivors since 2018. The three major themes unveiled in the analysis are: 1. post-disaster fears, 2. The factors that triggered fear and concern and 3. Socio-economic marginality and mental health. The study asserts that individuals who are poor and unprivileged are highly susceptible to mental health issues associated with landslides.

A population dynamics epidemic model is developed that incorporates age of infection and age of vaccination. The model analyzes pre-symptomatic and symptomatic periods of an infected individual in terms of infection age. The model analyzes the efficacy of vaccination in terms of vaccination age. The model is applied to the 2003 SARS epidemic in Taiwan and the current COVID-19 epidemic in New York State.

We have shown that the use of evolutionary gravitational constants G, the speed of light c, and cosmological constant Λ in the Einstein’s field equations leads to a very simple model that fits the supernovae Ia data with a single parameter as well as the standard ΛCDM model with two parameters, and has the predictive capability superior to the latter. We have shown that at the current time G and c both increase as dG/dt = 5.4GH₀ and dc/dt = 1.8cH₀ with H₀ as the Hubble constant, and Λ decreases as dΛ/dt = −1.2ΛH₀. Negative finding on the variation of G with time derived from the analysis of lunar laser ranging data in several studies has been attributed to the fact that these studies did not consider the variation of c simultaneously with G.

We outline and test a new methodology for genuine simulation of stochastic processes with any dependence and any marginal distribution. We reproduce time dependence with a generalized, time symmetric or asymmetric, moving-average scheme. This implements linear filtering of non-Gaussian white noise, with the weights of the filter determined by analytical equations in terms of the autocovariance of the process. We approximate the marginal distribution of the process, irrespective of its type, using a number of its cumulants, which in turn determine the cumulants of white noise in a manner that can readily support the generation of random numbers from that approximation, so that it be applicable for stochastic simulation. The simulation method is genuine as it uses the process of interest directly without any transformation (e.g. normalization). We illustrate the method in a number of synthetic and real-world applications with either persistence or antipersistence, and with non-Gaussian marginal distributions that are bounded, thus making the problem more demanding. These include distributions bounded from both sides, such as uniform, and bounded form below, such as exponential and Pareto, possibly having a discontinuity at the origin (intermittence). All examples studied show the satisfactory performance of the method.

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.

Heating systems such as heat pump and combined heat and power cycle systems (CHP) are representing a key component in the future smart grid. Their capability to couple the electricity and heat sector promises a massive potential to the energy transition. Hence, these systems are continuously studied numerical and experimental to quantify their potential and develop optimal control methods. Although numerical simulations provide time and cost-effective solution for system development and optimization, they are exposed to several uncertainties. Hardware in the loop (HiL) system enables system validation and evaluation under different real-life dynamic constraints and boundary conditions. In this paper, a HiL system of heat pump testbed is presented. This system is used to present two case studies. In the first case, the conventional heat pump testbed operation method is compared to the HiL operation method. Energetic and dynamic analyses are performed to quantify the added value of the HiL and its necessity for dynamics analysis. The second case, the HiL testbed is used to validate the heat pump operation in a single family house participating in a local energy market. It enables not only the dynamics of the heat pump and the space heating circuit to be validated but also the building room temperature. The energetic analysis indicated a deviation of 2% and 5% for heat generation and electricity consumption of the heat pump, respectively. The model dynamics emphasized the model capability to present the dynamics of a real system with a temporal distortion of 3%.

Attention-Deficit/Hyperactivity Disorder (ADHD) exhibits a notable prevalence across diverse populations, with estimates ranging from 4% to 6%. This wide range prompts an investigation into the evolutionary and genetic underpinnings of ADHD, especially considering the markedly different environments faced by ancestral human populations compared to today's structured societies. This study examines the potential adaptive advantages of ADHD-associated traits in hunter-gatherer contexts, where hyperactivity, impulsivity, and novelty-seeking behaviors may have conferred survival benefits. We employ the principles of population genetics, including Hardy-Weinberg equilibrium, selection coefficients, and genetic drift, to model the dynamics of ADHD allele frequencies over time. Additionally, we discuss balancing selection as a mechanism for maintaining genetic diversity and how gene-environment interactions (GxE) contribute to the expression of ADHD in contemporary settings. Our analysis suggests that traits associated with ADHD, while potentially maladaptive in modern structured environments, could have been preserved through evolutionary processes due to their adaptive value in ancestral contexts. Understanding these dynamics provides a comprehensive view of ADHD's prevalence and highlights the significance of genetic and environmental interplay in shaping human behavior.

In the present study, a mathematical model of non-steady partial differential equation from the process of oxygen mass transport in the human pulmonary circulation is proposed. Mathematical modelling of this kind of problems lead to a non-steady partial differential equation and for its numerical simulation, we have used finite differences. The aim of the process is the exact numerical analysis of the study, wherein consistency, stability and convergence is proposed. The necessity of doing the process is that, we would like to increase the order of numerical solution to a higher order scheme. An increment in the order of numerical solution makes the numerical simulation more accurate, also makes the numerical simulation being more complicated. In addition, the process of numerical analysis of the study in this order of solution needs more research work.

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.

This study investigates the stochastic dynamics of hepatitis B virus (HBV) infection using a newly proposed stochastic model. Contrary to deterministic models that fail to encapsulate the inherent randomness and fluctuations in biological processes, our stochastic model provides a more realistic representation of HBV infection dynamics. It incorporates random variability, thereby acknowledging the changes in viral and cellular populations and uncertainties in parameters such as infection rates and immune responses. We examine the solution's existence, uniqueness, and positivity for the proposed model, followed by a comprehensive stability analysis. We provide the necessary and sufficient conditions for local and global stability, offering deep insight into the infection dynamics. Furthermore, we utilize numerical simulations to corroborate our theoretical results. This research provides a robust tool for understanding the complex behavior of HBV dynamics, contributing significantly to the ongoing quest for more effective HBV control and prevention strategies.

Bio-inspired gyroid triply periodic minimum surface (TPMS) lattice structures have been the focus of research in automotive engineering because they can absorb a lot of energy and have wider plateau ranges. The main challenge is determining the optimal energy absorption capacity and accurately capturing plastic plateau areas using finite element analysis (FEA). Using nTop's Boolean subtraction method, this study combined walled TPMS gyroid structures with normal TPMS gyroid lattice. This made a composite TPMS-gyroid lattice with relative densities ranging from 14% to 54%. Using the ideaMaker software and the fused deposition modeling (FDM) Raise3D Pro 2 3D printer to print polylactic acid (PLA) bioplastics in 1.75 mm filament made it possible to slice computer aided design (CAD) models and fabricate 36 lattices samples precisely layer by layer technique. Shimadzu 100kN testing equipment was utilized for the mechanical compression experiments. And the validation using finite element analysis (FEA). Further, CTG was examined using a field emission scanning electron microscope (FE-SEM) before and after compression testing. The composite TPMS gyroid lattice showed potential as shock absorbers for vehicles with relative densities of 33%, 38%, and 54%. The Gibson-Ashby model showed that the composite TPMS gyroid lattice deformed mainly by bending, and the size effect was seen when the relative densities were less than 15%. The lattice's relative density had a significant impact on its ability to absorb energy. The research also explored the use of these innovative foam-like composite TPMS-gyroid lattices in high-speed crash box scenarios, potentially enhancing vehicle safety and performance.

An exploding demand for processing capabilities related to the emergence of the IoT, AI and big data, has led to the quest for increasingly efficient ways to expeditiously process the rapidly increasing amount of data. These ways include different approaches like improved devices capable of going further in the more Moore path, but also new devices and architectures capable of going beyond Moore and getting more than Moore. Among the solutions being proposed, Stochastic Computing has positioned itself as a very reasonable alternative for low-power, low-area, low-speed, and adjustable precision calculations; four key-points beneficial to edge computing. On the other hand, chaotic circuits and systems appear to be an attractive solution for (low-power, green) secure data transmission in the frame of edge computing and IoT in general. Classical implementations of this class of circuits require intensive and precise calculations. This paper discusses the use of the SC framework for the implementation of nonlinear systems, showing that it can provide results comparable to those of classical integration, with much simpler hardware, paving the way for relevant applications.

To assess the community health workers’ (CHWs) knowledge, attitude, and practices (KAP) in type-2 diabetes (T2D) and hypertension (HTN) management. We thus also sought to assess the potential health system barriers for incorporating CHWs in T2D and HTN management. Mixed-method study comprised (1) a survey among 153 active CHWs to assess their KAP of T2D and HTN, and (2) semi-structured interviews with key informants to understand challenges of the health system and proposed solutions in incorporating CHWs in T2D and HTN management. The majority of CHWs correctly answered general knowledge questions on NCDs, risk factors, and prevention; however, only one-quarter correctly answered questions on smoking, family history, or tobacco use as risk factors. Most respondents appeared to have positive attitudes and have been practicing some activities related to T2D and HTN. Both financial and non-financial resource constraints were cited as challenges of the health system; therefore, re-structuring the role definition of CHWs and task of responsibilities, and assessment the need and workload have been proposed as ways forwards to effectively incorporate CHWs in T2D and HTN care. CHWs in Cambodia have shown their potential in T2D and HTN management; however, a well-designed strategy including technical training, clearly defined roles and responsibilities, and strong supporting structure are important to maximize their potential in the health system.

In this paper, we report orthogonal fuzzy versions of some celebrated iterative mappings. We provide various concrete conditions on the real valued functions J,S:(0,1]→(−∞,∞) for the existence of fixed-points of (J,S)-fuzzy iterative mappings. We obtain many fixed point theorems in orthogonal fuzzy metric spaces. We apply (J,S)-fuzzy version of Banach fixed point theorem to show the existence and uniqueness of the solution. We support these results with several non-trivial examples and applications to Volterra-type integral equations and fractional differential equations.

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.

As the most active plateau on the Earth, the Qinghai-Tibet Plateau has a complex crust-mantle structure. Knowledge of the distribution of such a structure provides information for understanding the underlying geodynamic processes. We obtains a three-dimensional density model of crustal and upper mantle beneath Qinghai-Tibet plateau and its surrounding areas from the residual geoid anomalies using the Earth Gravitational Model (EGM) 2008. We estimate a refined density model by iterations, using an initial density contrast model. We confirm that the EGM2008 mission products can be used to constrain the crust-mantle density structures. Our major findings are: (1). At 300-400 km depth, high-D anomalies terminate around Jinsha River Suture (JRS) in the central TP, suggesting that the Indian plate has been reached over the Bangong Nujiang Suture (BNS) and almost reach to the JRS. (2). On the eastern TP, low-D anomalies at the depth of 0-300 km together with high-D anomalies at 400-670 km further verified the current eastward subduction of Indian plate. The ongoing subduction provides forces to the occurrences of frequent earthquakes and volcano. (3). At 600 km depth, low-D anomalies inside the TP illustrate the existence of hot weak material beneath there, contributing to the external material inward-thrusting.

In the recent years, tubular nanostructures have been related with immense advances in various fields of science and technology. Considerable research efforts have been centered on the theoretical prediction and manufacturing of non-carbon nanotubes (NTs), which meet modern requirements for the developing of novel devices and systems. In this context, diatomic inorganic nanotubes formed by atoms of elements from the 13th group of the periodic table (B, Al, Ga, In, Tl) and nitrogen (N), have received much research attention. In the present work, the elastic properties of single-walled boron nitride, aluminium nitride, gallium nitride, indium nitride and thallium nitride nanotubes were numerically evaluated using the nanoscale continuum modelling approach (also called molecular structural mechanics). The elastic properties (rigidities, surface Young´s and shear moduli, and Poisson´s ratio) of nitride nanotubes are discussed with respect to the bond length of the corresponding diatomic hexagonal lattice. The results obtained contribute to a better understanding of the mechanical response of nitride compound-based nanotubes, covering a broad range from the well-studied boron nitride NTs to the hypothetical thallium nitride NTs.

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.

We propose the traditional goal of cancer therapists to develop a single drug or drug combination that can, by itself, eliminate all cancer cells within a host has neglected potential treatments that may achieve curative outcomes by strategically combining agents that are individually effective but non-curative. We derive basic principles for such an approach from the eco-evolutionary dynamics of background extinctions in which a “first strike” reduces the size and heterogeneity of the initial population and is followed immediately by demographic and ecological “second strikes” that push the population below an extinction threshold. This proposed strategy appears identical to the empirically-derived curative therapy in childhood Acute Lymphocytic Leukemia.

The paper explores the features of numerical simulation to analyze the dynamic behavior of drives controlled by pulse-width modulators. Modern motor control systems widely use pulse width modulation. Effective numerical modeling of such systems has specific features because the models employed are continuous-event and have hybrid behavior due to the presence of nonlinear links with discontinuities of the first kind. Therefore, it is essential to have special integration methods with variable steps, which should be factored in when developing the model. The paper shows how these problems are solved when modeling an electric drive with a DC motor in the SimInTech software.

The optimization of photovoltaic (PV) systems is vital for enhancing efficiency and economic viability, especially under Partial Shading Conditions (PSCs). This study focuses on the development and comparison of traditional and advanced algorithms, including Perturb and Observe (P&O), Incremental Conductance (IC), Fuzzy Logic Control (FLC), Grey Wolf Optimization (GWO), Particle Swarm Optimization (PSO), and Artificial Neural Networks (ANN), for efficient Maximum Power Point Tracking (MPPT). Simulations conducted in MATLAB/SIMULINK evaluated these algorithms’ performance under various shading scenarios. The results indicate that while traditional methods like P&O and IC are effective under uniform conditions, advanced techniques, particularly ANN-based MPPT, exhibit superior efficiency and faster convergence under PSCs. The study concludes that integrating AI and ML into MPPT algorithms significantly enhances the reliability and efficiency of PV systems, paving the way for broader adoption of solar energy technologies in diverse environmental conditions. These findings contribute to advancing renewable energy technology and support the green energy transition.

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.

Metaheuristic algorithms are widely used as optimization methods, due to their global exploration and exploitation characteristics, which obtain better results than a simple heuristic. The Stochastic Fractal Search (SFS) is a novel method inspired by the process of stochastic growth in nature and the use of the fractal mathematical concept. Considering the chaotic-stochastic diffusion property, an improved Dynamic Stochastic Fractal Search (DSFS) optimization algorithm is presented. The DSFS algorithm was tested with benchmark functions, such as the multimodal, hybrid and composite functions, to evaluate the performance of the algorithm with dynamic parameter adaptation with type-1 and type-2 fuzzy inference models. The main contribution of the article is the utilization of fuzzy logic in the adaptation of the diffusion parameter in a dynamic fashion. This parameter is in charge of creating new fractal particles, and the diversity and iteration are the input information used in the fuzzy system to control the values of diffusion.

Virus taxonomy uses a Linnaean-like subsumption hierarchy to classify viruses into taxonomic units at species and higher rank levels. Virus species are considered monophyletic groups of mobile genetic elements (MGEs) often delimited by phylogenetic analysis of aligned genomic or metagenomic sequences. Taxonomic units are assumed independent organizational, functional and evolutionary units that follow a ‘natural’ historical rationale. Here, I use phylogenomic and other arguments to show that viruses are not self-standing genetically-driven biological systems. Instead, they are crucial components of holobionts, units of biological organization that dynamically integrate the genetics, epigenetic, physiological and functional properties of their co-evolving members. Remarkably, phylogenomic analyses show viruses share protein domain and loop structures with cells throughout history via massive processes of reticulate evolution, helping spread evolutionary innovations across a wider taxonomic spectrum. Thus, viruses are not merely MGEs or microbes. Instead, their genomes and proteomes conduct cellularly integrated processes akin to those cataloged by the GO Consortium. This prompts the generation of compositional hierarchies that replace the ‘is-a-kind-of’ by a ‘is-a-part-of’ logic to better describe the mereology of integrated cellular and viral makeup. My analysis demands a new paradigm that integrates virus taxonomy into a modern evolutionarily centered taxonomy of organisms.

Relationships of the three bryophyte lineages (liverworts, mosses, and hornworts) to vascular plants is a pivotal question in the study of origin and evolution of land plants. In recent decades, this question has been subject to intense phylogenetic analyses using morphological characters, multigene DNA sequences, and genome structural characters. A tentative consensus reached ten years ago suggested that bryophytes are a paraphyletic group, with liverworts being sister to all other land plants and hornworts being sister to vascular plants. However, several more recent nuclear phylogenomic studies have concluded that bryophytes represent a monophyletic group that is sister to vascular plants. A discussion is presented here on strengths and weaknesses of different types of characters (morphological traits, nucleotide sequences, and genome structural arrangements), and their suitability for resolving deep phylogenetic relationships. Moreover, several criteria for credible phylogenetic reconstruction are proposed. Strong statistical support for reconstructed relationships should be derived from high quality, independent characters selected for suitability to the particular question being addressed. The relationships inferred in a study should be congruent with those from as many other lines of phylogenetic evidence as possible. Any incongruities should be explicable by well-understood biological mechanisms. It is concluded that the relationships of the three bryophyte lineages to vascular plants should currently be viewed as unresolved. This is a difficult phylogenetic problem; the land plants underwent a rapid radiation a long time ago. Yet, further exploration of analytical methods and careful choice of characters should lead to eventual elucidation of diversification patterns among early land plants.

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.

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.

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.

In this essay, I revisit Neural Networks (NNs) through the lens of evolutionary dynamics. From the two most important features of NNs, I recover the two most general equations of evolutionary dynamics. These two equations may thus serve as a connection between NNs and a body of knowledge that has been built over multiple centuries and has found application across a vast range of disciplines. This connection may therefore also help explain why NNs with the two features in question are applicable across a much broader range of domains than initially envisioned.

As a model for economic and ecological systems, replicator dynamics represents a basic form of agent competition for finite resources. Here, we investigate the effects of stochastic resetting in this kind of processes. Random reset events abruptly lead individual resources to a small value from which dynamics must start anew. Numerical results show that resource distribution over the population of competing agents develops highly nonuniform profiles, exhibiting clustering and fluctuations with anomalous dependence on the population size. This non-standard statistical behavior jeopardizes an analytical treatment based on mean-field assumptions. We propose alternative simplified analytical approaches which provide a stylized description of entropy evolution for the clustered distribution of resources and explain the unusually slow decrease of fluctuations.

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.

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".

A Partial discharge (PD) occurrence in high-voltage (HV) and medium-voltage (MV) power assets is a warning sign of insulation system degradation or defective manufacturing/assembly, that may cause catastrophic damage and eventually lead to the breakdown of the power equipment. Ultra-high frequency (UHF) PD measurement technology has extensively been used to monitor the insulation health of the HV or MV equipment due to its high immunity against ambient noise and conducted disturbances. This paper presents experimental validation of a new design of a UHF planar rectangular microstrip antenna that can be used for PD monitoring of HV and/or MV power equipment, such as power transformers. The designed planar rectangular microstrip antenna has a compact size of 80mmx70mmx1.6mm. Laboratory experiments were performed to validate the antenna sensitivity to PD activity caused by insulation defects created inside an oil-filled transformer tank model. PD measurement results confirm that the proposed rectangular microstrip antenna has high sensitivity and high signal-to-noise ratio (SNR), thanks to its capability to suppress external noise disturbances, especially during online PD monitoring. Thus, the proposed UHF antenna seems to be a promising and alternative PD sensor that can be employed in UHF PD monitoring systems of HV or MV power equipment.

The main sources of intrinsic noise in excitable cells at the microcircuit and network levels are the stochastic characteristics of ion channel gating and activation of the synaptic conductance. Studies using in vivo, in vitro, and in silico methods to examine the effects of synaptic background activity were not adequately investigated in non-neuronal excitatory cells, where neurotransmitter-based innervation also occurs. We created a mathematical model to replicate the background synaptic noise dynamics in a non-neuronal cell. We utilized the stochastic Ornstein-Uhlenbeck process to represent excitatory synaptic conductance, which was incorporated into a whole-cell model to produce spontaneous and evoked cellular electrical activities. The single-cell model includes many biophysically detailed ion channels represented by a set of ordinary differential equations in Hodgkin-Huxley and Markov formalisms. This paradigm effectively induced irregular spontaneous depolarizations (SDs) and spontaneous action potential (sAP) resembling in vitro-like electrical activity in the cells. The input resistance decreased by multiple factors, and the spontaneous action potential firing rate elevated. The potential to reach the action potential threshold is altered. Background synaptic activity can alter the input/output characteristics of non-neuronal excitatory cells. Suppressing these baseline activities would facilitate the discovery of new pharmaceutical targets for different clinical diseases.

The objective of this study is to evaluate the effect of constitutive equations on the prediction accuracy for springback in cold stamping with various deformation modes. In this study, two types of yield functions—Hill’48 and Yld2000-2d—were considered to describe yield behavior. Isotropic and kinematic hardening models based on the Yoshida–Uemori model were also adopted to describe hardening behavior. Various material tests (such as uniaxial tension, tension- compression, loading-unloading, and hydraulic bulging tests) were carried out to determine the material parameters of the models. The obtained parameters were implemented in the finite element (FE) simulation to predict springback, and the results were compared with experimental data. U-bending and T-shape drawing were employed to evaluate the springback prediction accuracy. Obviously, the springback prediction accuracy was greatly influenced by constitutive equations. Therefore, it is important to choose appropriate constitutive equations for accurate description of material behaviors in FE simulation.

In this paper, the boiling flow inside a nanochannel with 700000 argon particle has been simulated by molecular dynamics (MD) simulation. This approach has been employed to analysis the superheated flow and its heat transfer pattern as well. For all simulations an external thrust force varying from 1 PN to 12 PN is exerted on inlet nanoparticles along the channel to have the forced annular boiling flow. Computations reveal that saturation condition and superheat degree have significant impacts on the liquid-vapor interface. Furthermore, because of the major influence of surface tension throughout a nanochannel, the x-velocity of liquid film and vapor core has not considerable fluctuations and stay smooth. All provided results show the behaviors completely similar to the available outcomes in the literature.

Obesity poses significant challenges in rural communities worldwide due to limited resources and healthcare access. Practical, innovative, and culturally sensitive approaches are essential. Time-Restricted Eating (TRE), aligning food intake with circadian rhythms, emerges as a promising strategy. By restricting eating to specific time windows, TRE synchronizes with the body's internal clock, offering potential metabolic health benefits. This review examines TRE's potential in rural obesity management, highlighting its simplicity and scalability. While TRE may address rural health disparities, cultural considerations and challenges such as undernutrition must be acknowledged for effective implementation. Overall, TRE shows promise in improving metabolic health and well-being in rural populations.

Background/Purpose: Multimorbidity of malaria, anaemia, and malnutrition (MAMM) is a condition in which an individual cohabits with two or more of these health outcomes and is becoming an emergent public health concern in sub-Saharan African countries. The independent associations of a child’s demographic variables and socioeconomic disparities with a child’s health outcomes have been established in literature. However, the effects of the intersection of these factors on MAMM, while accounting for other covariates have not been studied. Therefore, this study aimed to determine how children’s sex, age and socioeconomic status interact to explain the variations in MAMM among children aged 6-59 months in Nigeria. Methods: Data from the 2018 Nigeria Demographic and Health Survey and the 2018 National Human Development Report (NHDR) were used. The study includes weighted samples of 10,184 children aged 6-59 months in Nigeria. A three-level multilevel mixed effect ordinal logistic regression model such that individual characteristics at level 1 are nested in communities at level 2 and nested in states at level 3 was used. Subsequently, predictive probability charts and average adjusted probability tables were used to interpret the intersectional effects. Five models were created in this scenario. Model 1 is the interaction between the child's sex and wealth status; model 2, child's sex and age; model 3 is between child's age and wealth status; model 4 has the three 2-way interactions of child's sex, age, and household wealth status, and model 5 includes model 4 and the 3-way interactions between a child's sex, age, and wealth quintiles. Results: The prevalence of children with ‘none of the three diseases’ outcomes was 17.3% (1767/10,184), while, 34.4% (3499/10,184) had ‘only one of the diseases’, and 48.3% (4,918/10,184) cohabit with ‘two or more’ of MAMM. However, in the multivariate analyses, model 3 was the best fit compared with other models, so, that the two-way interaction effects of a child's age and wealth status are significant predictors in the model. Children aged 36-47 months living in the poorest households have the probability of 0.11, 0.18, and 0.32 of contracting MAMM above the probability of children of the same age and live in the middle, more prosperous and richest households, respectively, while all other covariates are held constant. Thus, the variation in MAMM over a child's age differs depending on the household wealth quintile. In other words, as the children grow older, variations in MAMM become more evident between the rich and the poor household. Conclusion: Therefore, it is recommended that policies that are geared toward economic redistribution will help bridged the disparities observed in multiple diseases among children aged 6-59 months in Nigeria

In this paper, we first establish upper stochastic bounds on the lifetime of a used cold standby system with arbitrary age, using the likelihood ratio order and the usual stochastic order. Then, stochastic comparisons are made between the lifetime of a used cold standby system with age t and the lifetime of a cold standby system consisting of used components with age t using the likelihood ratio order and the usual stochastic order. We use illustrative examples to explore the results presented.

Rotational jumps are crucial techniques in sports competitions. Estimating ground reaction forces (GRFs), one of the components constituting jumps, through a biomechanical model-based approach enables analysis even in environments where force plates or machine learning training data cannot be utilized. In this study, rotational jump movements involving twists on land were measured using inertial measurement units (IMUs) and estimated GRFs and body loads using a 3D forward dynamics model. Our estimation method, based on forward dynamics and optimization calculations, generated and optimized body movements using cost functions defined by motion measurements and internal body loads. To reduce the influence of the dynamic acceleration in the optimization calculation, the 3D orientation using sensor fusion composed of acceleration and angular velocity data obtained from IMUs and an extended Kalman filter was estimated. As a result, by generating movements based on the cost function, it was possible to calculate biomechanically valid GRFs while following the measured movements even if not all joints are covered by IMUs. This estimation method allows for 3D motion analysis independent of measurement conditions or training data.

The advanced industrial systems are characterized by complex event-driven processes. The specification and computer analysis are illustrated by the common problem of a servo drive with the PWM controller. A mathematical model from the class of Cauchy problems with non-liner control logic is presented to resolve the task discussed. The designed model is performed in two stages: the mathematical model specification (modeling) and implementation (simulation). Two approaches to make a model specification are considered, the first one is the traditional structural technique, and the advanced method is based on the finite state machine paradigm. Structural and finite state software models are built in progressive simulation tools. Computer implementation of the software models of hybrid systems is performed using platform built-in libraries with numerical methods and algorithms for correct event detection. The results of computational experiments for transient processes of phase variables are qualitatively identical, that proves the adequacy of the developed models. The algorithm for asymptotic event detection is considered in detail. This technique demonstrated the best results by the one-sidedness criterion, which is explained by using the author’s algorithm for the integration step determining and the event function dynamics monitoring in the vicinity of the event limits.

Predicting ground reaction forces (GRFs) and ground reaction moments (GRMs) through a biomechanical model-based approach offers advantages for biomechanical analysis, particularly in situations where the application of a statistical model is limited by insufficient training data. However, the current prediction method is unsuitable for clinical applications due to its long computational time. The present study developed a new optical motion capture (OMC)-based method to predict GRFs, GRMs, and joint torques. The proposed approach performed the estimation process by distributing external forces, as determined by the equation of motion, between the left and right feet based on foot deformations, thereby predicting the GRFs and GRMs without relying on machine learning or optimization techniques. We investigated the prediction accuracy during walking by comparing a conventional analysis using a force plate with the OMC results. The comparison revealed excellent or strong correlations between the prediction and measurement for all GRFs, GRMs, and lower limb joint torques. The proposed method, which provides practical estimation with low computational cost, facilitates efficient biomechanical analysis and rapid feedback of analysis results, thereby increasing its applicability for kinetics estimation in clinical settings.

This work considers the existence of heteroclinic solutions for second order differential equations with ϕ-Laplacians and generalized impulsive conditions on the real line. For the construction of the results, it was only imposed that ϕ is a homeomorphism and the Schauder’s fixed point theorem allied with the concepts of L1-Carathéodory functions and sequences together with the equiconvergence on infinity and on each impulsive moments. Finally, a practical part illustrates the main theorem.

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.

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.

In this paper, we introduce some basic idea of Variational iteration method for short (VIM) to solve the Volterra’s integro-differential equations. The VIM is used to solve effectively, easily, and accurately a large class of non-linear problems with approximations which converge rapidly to accurate solutions. For linear problems, it’s exact solution can be obtained by only one iteration step due to the fact that the Lagrange multiplier can be exactly identified. It is to be noted that the Lagrange multiplier reduces the iteration on integral operator and also minimizes the computational time. The method requires no transformation or linearization of any forms. Two numerical examples are presented to show the effectiveness and efficiency of the method. Also, we compare the result with the result from Homotopy perturbation method (HPM). Finally, we investigate the absolute difference between variational iteration method and homotopy perturbation method and draw the graph of difference function by using Mathematica.

In this paper, we study the entire or meromorphic solutions for differential-difference equations in f(z) , its shifts, its derivatives and derivatives of its shifts. and study some Hayman's results for differential-difference polynomials.

In this paper, we established the existence of PC-mild solutions for non local fractional impulsive functional integro-differential equations with finite delay. The proofs are obtained by using the techniques of fixed point theorems, semi-group theory and generalized Bellman inequality. In this paper, we have used the distributed characteristic operators to define the mild solution of the system. Results obtained here improve and extend some known results.

This article proposes a particular strategy to proceed with a progressive electrification of public transport systems in cities. Starting from a bus operation model, the possible electrification of two routes is analysed, one urban and another extra-urban in the city of Pisa. An estimate is made of the energy uses associated with certain operating modes. The maximum level of consumption is estimated at approximately 280 kWh per day per bus for the urban route and excluding some special days, less than 215 kWh per day for the extra-urban route, for which a hybrid bus is proposed. Starting from an estimate of the daily consumption for the management of the two routes, the sizing of a photovoltaic system distributed on some modular shelters which serves to power the same routes is carried out. The resulting system has a power of the order of 190-200 kW. The modular solution is also outlined, and an installation is proposed. The analyzed case lends itself to being easily replicated.

The coseismic surface three-dimensional deformation fields were significant for quantified the geometric and kinematic characteristics of earthquake rupture faults. Traditional geodetic techniques were constrained by their intrinsic limitations, such as InSAR, which could only extract far-field deformation fields due to its incoherence, and GNSS, which could only acquire deformations at discrete points. The recently developing optical pixel correlation technique based on high resolution remote sensing images could acquire the near-field coseismic horizontal deformation. In this study, the vertical displacement field of the 2022 Mw 6.6 Menyuan earthquake was obtained by differencing the pre- and post-earthquake DEMs from GaoFen-7 stereo satellite images. Further, the line-of-sight (LOS) and azimuthal (AZI) directions far-field deformations by InSAR, the horizontal near-field deformation by optical pixel correlation based on pre- and post-earthquake GF-2/7 images, and the vertical deformation by differencing the pre- and post-earthquake DEMs, were incorporated to comprehensively solve the complete three-dimensional deformation fields of the 2022 Mw 6.6 Menyuan earthquake. Firstly, the vertical displacement field by differencing DEMs indicated there were significant vertical displacements about 1 m at the bend region, which was induced by the local compressive stress. In addition, at the epicenter on the middle segment of ruptured Lenglongling fault (LLLF), the maximum lifting occurred on the southern sides of the main and secondary faults exceeded 2 m. Secondly, the three-dimensional deformation fields solved by multiple deformation data demonstrated that the near-field deformation field calculated by optical pixel correlation method could quantify the displacements distributed over the rupture fault zone, which were not available on the InSAR deformation maps. Finally, the surface 2D strain derived from the displacement maps calculated by optical pixel correlation revealed high strain concentration on the rupture fault zone. Our study focused on the complete surface three-dimensional deformation estimation from multiple far- and near-field deformation data, and provided a new perspective for a deeper understanding of the characteristics of coseismic surface deformation and the rupture pattern of the fault.

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.