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.

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

In this paper, we investigate the equilibrium points of following a system of difference equations x_n+1 = x_n 2y_n−1, y _n+1 = y_n 2x_n−1. We also study the asymptotic stability of related system of difference equations. Further we examine the periodic solutions of related system with period two. Additionally, we find out the invariant interval and periodic cycles of related system of difference equations.

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.

In this paper, we investigate the equilibrium points, stability of two equilibrium points, convergences of negative equilibrium point, periodic solutions, and existence of bounded or unbounded solutions of a system of nonlinear difference equations x_n+1 =x_n-1y_n - 1, y_n+1 = y_n-1x_n - 1 n = 0,1,..., where the initial values are real numbers. Additionally we present some numerical examples to verify our theoretical results.

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

In this paper, we employ fuzzy Sumudu transform for solving system of linear fuzzy differential equations with fuzzy constant coefficients. The system with fuzzy constant coefficients is interpreted under strongly generalized differentiability. For this purpose, new procedures for solving the system are proposed. A numerical example is carried out for solving system adapted from fuzzy radioactive decay model. Conclusion is drawn in the last section and some potential research directions are given.

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.

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.

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.

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 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 paper aims to investigate the global asymptotic stability of following system of higher order difference equations with quadratic terms: x_{n+1}=A+B((y_{n})/(y_{n-m}²)),y_{n+1}=A+B((x_{n})/(x_{n-m}²)) where A and B are positive numbers and the initial values are positive numbers. We also study the rate of convergence and oscillation behaviour of the solutions of related system.

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.

In this paper we investigate the global asymptotic stability of following system ofhigher order difference equations with quadratic terms:xn+1=A+Byn/yn−m^2, yn+1=A+Bxn/xn−m^2, where A and B are positive numbers and the initial values are positive numbers.We also study the boundedness, rate of convergence and oscillation behaviour of thesolutions of related system.

In this study, we investigate the form of solutions, stability character and asymptotic behavior of the following four rational difference equations x_{n+1} = (1/(x_{n}(x_{n-1}±1)±1)), x_{n+1} = ((-1)/(x_{n}(x_{n-1}±1)∓1)), such that their solutions are associated with Tribonacci numbers.

This paper deals with the form, the stability character, the periodicity and the global behavior of solutions of the following four rational difference equations x_{n+1} = ((±1)/(x_{n}(x_{n-1}±1)-1)) x_{n+1} = ((±1)/(x_{n}(x_{n-1}∓1)+1)).

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".

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.

Hessenberg differential algebraic equations (Hessenberg-DAEs) with high index play a critical role in the modeling of mechanical systems and multibody dynamics. Motivated by the widely used Lie Group Differential Algebraic Equation (LGDAE) method which only handles index 2 systems, we propose a Modified Extended Lie Group Differential Algebraic Equation (MELGDAE) method for solving index 3 Hessenberg-DAEs, and provide theoretical analysis to deepen the foundation of the MELGDAE method.The performance of the MELGDAE method is compared with the standard methods RADAU and MEBDF on index 2 and 3 DAE systems, and it is demonstrated that the MELGDAE integrator exhibits competitive performance in terms of high accuracy and the preservation of algebraic constraints. In particular, all differential variables in index 3 Hessenberg DAEs achieve second-order convergence using the MELGDAE method, which suggests potential for extension to Hessenberg-DAEs with an index of 4 or higher.

A new generation of universal tools and languages for modeling and simulation multi-physical domain applications emerged and became widely accepted, which generate large-scale systems of differential algebraic equations (DAEs) automatically. Motivated by the characteristics of DAEs systems with large dimension, high index or block structures, we first propose a modified Pantelides’ algorithm (MPA) for any high order DAEs based on its Σ matrix, which is similar to Pryce’s Σ method. By introducing a vital parameter vector, a modified Pantelides’ algorithm with parameter has been presented.It leads to a block Pantelides’ algorithm (BPA) naturally which can immediately compute the crucial canonical offsets for whole (coupled) systems with block-triangular form. We illustrate these algorithms by some examples. And numerical experiments show that the time complexity of BPA can be reduced by at least O(ℓ) compared to the MPA, which is mainly consistent with the results of our analysis.

A theoretical model to translate the evolution over time, in early stages, of growth and accumulation of biofilm bacterial mass is introduced. The model implies the solution of a system of differential-difference master equations. The application of an algorithm like Miller´s tree term recurrence, already known for Bessel functions of first kind, allows an exact calculation of the solutions of such equations, for a wide range of parameters values and time. For biofilm model a five term recurrence is deduced and applied in a backwards computation. A suitable normalisation condition completes the reach of the solution.

In this paper, we consider the fourth-order parabolic equations with integer and fractional order time derivatives with Neumann boundary conditions. The integer order time derivatives are approximated by backward Euler difference quotients, and the fractional order time derivatives are approximated by L1 interpolation. We propose the block-centered finite difference scheme for fourth-order parabolic equations of integer and fractional order time derivatives. We prove the stability of the block-centered finite difference scheme and the second-order convergence of the discrete L2 norms of the approximate solution and its derivatives of every order. Numerical examples are given to verify the effectiveness of the block-centered finite difference scheme.

In this article, author performs computational analysis for the generalized zeta functions by using computational software Mathematica. To achieve the purpose recently obtained difference equations are used. These difference equations have a computational power to compute these functions accurately while they can not be computed by using their known integral represenations. Several authors investigated such functions and their analytic properties, but no work has been reported to study the graphical representations and zeors of these functions. Author performs numerical computations to evaluate these functions for different values of the involved parameters. Taylor series expansions are also presented in this research.

The asymptotic dynamics of the classes of rational difference equations (RDEs) of third order defined over the positive real-line as $$\displaystyle{x_{n+1}=\frac{x_{n}}{ax_n+bx_{n-1}+cx_{n-2}}}, \displaystyle{x_{n+1}=\frac{x_{n-1}}{ax_n+bx_{n-1}+cx_{n-2}}}, \displaystyle{x_{n+1}=\frac{x_{n-2}}{ax_n+bx_{n-1}+cx_{n-2}}}$$ and $$\displaystyle{x_{n+1}=\frac{ax_n+bx_{n-1}+cx_{n-2}}{x_{n}}}, \displaystyle{x_{n+1}=\frac{ax_n+bx_{n-1}+cx_{n-2}}{x_{n-1}}}, \displaystyle{x_{n+1}=\frac{ax_n+bx_{n-1}+cx_{n-2}}{x_{n-2}}}$$ is investigated computationally with theoretical discussions and examples. It is noted that all the parameters $a, b, c$ and the initial values $x_{-2}, x_{-1}$ and $x_0$ are all positive real numbers such that the denominator is always positive. Several periodic solutions with high periods of the RDEs as well as their inter-intra dynamical behaviours are studied.

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.

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.

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.

This paper aims to investigate the criteria of behaviour of certain type of third order neutral generalized difference equations with distributed delay. With the technique of generalized Riccati transformation and Philos-type method, some oscillation criteria are obtained to ensure convergence and oscillatory solution of suitable example is listed to illustrate the main result.

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.

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.

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.

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 work is devoted to the development of methods for constructing asymptotic formulas as x→∞ of a fundamental system of solutions of linear differential equations generated by a symmetric two-term differential expression of odd order. The coefficients of the differential expression belong to classes of functions that allow oscillation (for example, those that do not satisfy the classical Titchmarsh-Levitan regularity conditions). As a model equation, the 5th order equation i2p(x)y′′′′′+p(x)y′′′′′+q(x)y=λy, for which various cases of behavior of the coefficients p(x),q(x), is investigated. New asymptotic formulas are obtained for the case when the function h(x)=−1+p−1/2(x)∉L1[1,∞) significantly influences the asymptotics of solutions to the equation. The case when the equation contains a nontrivial bifurcation parameter is studied.

In this paper, we study the global asymptotically stability of following system of difference equations with quadratic terms: x_{n+1}=A+B((y_{n})/(y_{n-1}²)),y_{n+1}=A+B((x_{n})/(x_{n-1}²)) where A and B are positive numbers and the initial values are positive numbers. We also investigate the rate of convergence and oscillation behaviour of the solutions of related system.

In this paper, we study the dynamics of following system of nonlinear difference equations x_n+1 = x_n-1y_n - 1, y_n+1 = y_n-1z_n - 1, z_n+1 = z_n-1x_n - 1. Especially we investigate the periodicity, boundedness and stability of related system of difference equations.

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.

We study the existence of positive solutions for a system of Hadamard fractional differential equations on an infinite interval with nonnegative nonlinearities, subject to coupled nonlocal boundary conditions which contain Hadamard fractional derivatives and Riemann-Stieltjes integrals. In the proof of the main results, we use the Guo-Krasnosel'skii fixed point theorem and the Leggett-Williams fixed point theorem.

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

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

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 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.

We investigate a singularly perturbed q-difference differential Cauchy problem with polynomial coefficients in complex time and space with quadratic nonlinearity. We construct local holomorphic solutions on sectors in the complex plane with respect to the perturbation parameter with values in some Banach space of formal power series in space with analytic coefficients on shrinking domains in time. Two aspects of these solutions are addressed. One feature concerns asymptotic expansions in the parameter for which a Gevrey type structure is unveiled. The other fact deals with confluence properties as q tends to 1. In particular the built up Banach valued solutions are shown to merge in norm to a fully bounded holomorphic map in all its arguments that solves a nonlinear partial differential Cauchy problem.

This paper presents a new low-voltage versatile mixed-mode filter which uses a multi-ple-input/output differential difference transconductance amplifier (MIMO-DDTA). The multi-ple-input of the DDTA is realized using a multiple-input bulk-driven MOS transistor (MI-BD-MOST) technique to maintain a single differential pair, thereby achieving simple structure with minimal power consumption. In a single topology, the proposed filter can provide five standard filtering functions (low-pass, high-pass, band-pass, band-stop, and all-pass) in four modes: voltage (VM), current (CM), transadmittance (TAM), and transimpedance (TIM). This provides the full capability of a mixed mode filter (i.e., twenty filter functions). Moreover, the VM filter offers high-input and low-output impedances and the CM filter offers high-output impedance; therefore, no buffer circuit is needed. The natural frequency of all filtering functions can be electronically controlled by a setting current. The voltage supply is 0.5 V and for a 4 nA setting current, the power consumption of the filter was 281 nW. The filter is suitable for low-frequency biomedical and sensor applications that require extremely low supply voltages and nano-watt power consumption. For the VM low-pass filter, the dynamic range was 58.23 dB @ 1 % total harmonic distortion. The proposed filter was designed and simulated in the Cadence Virtuoso System Design Platform using the 0.18 µm TSMC CMOS technology.

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

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

The 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.

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.

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 this paper, we analyze the convergence of a finite difference method with the implicit forward time central space (FTCS) scheme for solving the three-dimensional advection-diffusion-reaction equation (ADRE). It is proved that the method is unconditionally convergent. We apply the scheme to obtain numerical solutions for the transport of pollutants in street tunnel problems with various reaction coefficients and various rates of change of concentrations of sources or sinks of pollution.

The fractional diffusion equations with integrals play a significant role in describing anomalous diffusion phenomena. We first construct an appropriate resolvent family, and use the convolution theorem of Laplace transform, the probability density function, Cauchy integral formula and Fubini theorem to study its related equicontinuity, strongly continuity, compactness, etc. Then, a reasonable mild solution is defined. Finally, by combining some fixed point theorems, we obtain some conclusions on the existence and uniqueness of mild solutions.

This study focuses on the formulation and analysis of a numerical method to compute singularly perturbed functional differential equations (SP-FDEs) involving large mixed shifts. SP-FDEs are a class of differential equations with both shifts and small perturbation parameter. Such equations arise in various scientific fields to model phenomena with memory effects and perturbed dynamics. In this particular study, the considered SP-FDEs involve large negative shift (delay) and large positive shift (advance). Dealing with large mixed shifts in SP-FDEs gives rise to challenges in terms of stability analysis, numerical methods, and convergence of a solution. In this paper, the influence of the large mixed shifts is treated by choosing a uniform mesh discretized in such a way that the term with the shifts lie on the nodal points. Then, using the Numerov’s finite difference method, the continuous problem is transformed into a finite difference scheme and the influence of the perturbation parameter is handled by introducing a fitting factor in the difference scheme. Stability estimate and convergence analysis of the developed scheme are investigated and proved. Numerical experiments are carried out to demonstrate the validity and applicability of the developed scheme. It is shown that the numerical scheme obtained in this work is parameter-robust of second order convergence rate.

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

In this work, a mixture of Elzaki transform and projected differential transform method is applied to solve a nonlinear wave-like equations with variable coefficients. Nonlinear terms can be easily manipulated by using the projected differential transformation method. The method gives the results show that the proposed method is very efficient, simple and can be applied to other applications.

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

This article focuses on obtaining the analytical solutions for parabolic Volterra integro- differential equations in d-dimensional with different types frictional memory kernel. Based on theories of Laplace transform, Fourier transform, the properties of Fox-H function and convolution theorem, analytical solutions of the equations in the infinite domain are derived under three frictional memory kernel functions respectively. The analytical solutions are expressed by infinite series, the generalized multi-parameter Mittag-Leffler function, Fox-H function and convolution form of Fourier transform. In addition, the graphical representations of the analytical solution under different parameters are given for one-dimensional parabolic Volterra integro-differential equation with power-law memory kernel. It can be seen that the solution curves subject to Gaussian decay at any given moment.

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 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.

Shown is the derivation of Lorentz-Einstein k-factor in SRT as an amplitude-term of oscillation-differential equations of second order.This case is shown for classical Lorentz-factor as solution of an equation for undamped oscillation as well as the developed theorem as a second solution for advanced SRT of fourth order with an equation for damped oscillation-states.This advanced term allows a calculation for any velocities by real rest mass.Also accelerated coordinate -frames are discussed.

In this paper, by means of the Banach fixed point theorem and the Krasnoselskii's fixed point theorem, we investigate the existence of solutions for some fractional neutral functional integro-differential equations involving infinite delay. This paper deals with the fractional equations in the sense of Caputo fractional derivative and in the Banach spaces. Our results generalize the previous works on this issue. Also, an analytical example is presented to illustrate our results.

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.

This paper studies an effective finite difference scheme for solving two-dimensional Heston stochastic volatility option pricing model problems. A dynamically balanced up-downwind strategy for approximating the cross-derivative is implemented and analyzed. Semi-discretized and spatially nonuniform platforms are utilized. The numerical method comprised is simple, straightforward with reliable first order overall approximations. The spectral norm is used throughout the investigation and numerical stability is proven. Simulation experiments are given to illustrate our results.

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.

We point out an inconsistency in Newton's equations of celestial mechanics. A set of differential equations implied by Newton's equations are shown to be free of this inconsistency. We then investigate the integrals of motion associated with this relative difference system.

Differences are introduced as outputs of linear systems called differencers, being considered two classes: shift and scale-invariant. Several types are presented, namely: nabla and delta, bilateral, tempered, bilinear, stretching, and shrinking. Both continuous and discrete-time are described. ARMA type systems based on differencers are introduced and exemplified. In passing, the incorrectness of the usual delta difference is shown.

In the paper, by virtue of the Fa`a di Bruno formula, some properties of the Bell polynomials of the second kind, and the inversion formulas of binomial numbers and the Stirling numbers of the first and second kinds, the authors simplify meaningfully and significantly coefficients in two families of ordinary differential equations associated with higher order Frobenius–Euler numbers.

This paper applied the space-time generalized finite difference scheme for solving the nonlinear dispersive shallow water waves as the modified Camassa−Holm equation, modified Degasperis-Procesi equation, Fornberg-Whitham equation, and its modified form. The proposed meshless numerical scheme was composed of the space-time generalized finite difference method, the two-step Newton-Raphson method, and the time-marching method. The space-time approach can treat the temporal derivative as one of the spatial derivatives. This numerical technique enables all the partial derivatives in the governing equation can be discretized by a spatial discretization method, and the mixed derivative can efficiently deal with using the proposed meshless numerical scheme. The space-time generalized finite difference method is advanced from the Taylor series expansion and the moving-least square method. The numerical discretization process is only related to functional data and weighting coefficients on the central node and its nearby nodes. Thus, the matrix system composed of nonlinear algebraic equations will be a sparse matrix and can be efficiently solved by the two-step Newton-Raphson method. Furthermore, the time-marching method was utilized to proceed with the space-time domain along the time axis. In this paper, several numerical examples were tested to verify the capability of the proposed space-time generalized finite difference scheme.

For a linear ordinary differential equation (ODE in short) of the third order, results are presented that supplement the theory of conjugate points and extremal solutions by W. Leighton, Z. Nehari, M. Hanan. It is especially noted the sensitivity of solutions to the initial data, which makes their numerical study difficult. Similar results were obtained for the third-order nonlinear equations of the Emden-Fowler type.

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.

This article is a big picture of how electrical noise or conducted Electromagnetic Interference (EMI) is generated and mitigated in power converters. It gives an overview of what EMI in power converters is – from generation through to conduction and mitigation. It is meant to cover the complete subject as a summary so that the reader will have an outline of how to control conducted EMI by design (where possible) and how to mitigate by filtering. A clear distinction is made between Differential Mode (DM) and Common Mode (CM) EMI generation and mitigation. By using a boost converter as an example the trade-offs for DM noise control are discussed. It is shown how CM EMI is generated in a boost converter using the concept of the “Imbalance Difference Model” (IDM). Practical measurements for an in-line power filter is given showing the effect of the filter on the total EMI of a boost converter. Measurements for the CM current produced due to the imbalance difference for different values of the boost conductor are also shown. The main contribution of this study is linking CM noise generation to DM EMI. It is shown that CM noise is a direct consequence of DM noise (although circuit imbalance and coupling to a common ground also play a role). This paper will be useful to designers seeking the “bigger picture” of how EMI is generated in power converters and what can be done to mitigate the noise.

Among colours, the green has the most sensitivity in human vision so that green defects on displays can be effortlessly perceived by a photopic eye with the most intensity in the wavelength 555 nm of the spectrum. With the market moving forward to high resolution, displays can have resolutions of 10 million pixels. Therefore, the task detects the appearance the panel using ultra-high resolutions in TFT-LCD. The machine vision associated with reflective chromaticity spectrometer quantises the defects are explored, such as blackening and whitening. The result shows the significant phenomena to recognize the non-uniformity film-related chromatic tendency. In contrast, the quantitative assessment illuminates that the chromaticity CIE xyY at 0.001 is a just noticeable difference (JND) and detects even more sensitivity. Moreover, an optical device associated with a 198 Hg discharge lamp calibrates the spectrometer accuracy.

The aim of this document is to provide practical guidance on the choice of target difference used in the sample size calculation of a randomised controlled trial (RCT). Guidance is provided with a definitive trial, one that seeks to provide a useful answer, in mind and not those of a more exploratory nature. The term “target difference” is taken throughout to refer to the difference that is used in the sample size calculation (the one that the study formally “targets”). Please see the glossary for definitions and clarification with regards other relevant concepts. In order to address the specification of the target difference, it is appropriate, and to some degree necessary, to touch on related statistical aspects of conducting a sample size calculation. Generally the discussion of other aspects and more technical details is kept to a minimum, with more technical aspects covered in the appendices and referencing of relevant sources provided for further reading.The main body of this guidance assumes a standard RCT design is used; formally, this can be described as a two-arm parallel-group superiority trial. Most RCTs test for superiority of the interventions, that is, whether or not one of the interventions is superior to the other (See Box 1 for a formal definition of superiority, and of the two most common alternative approaches). Some common alternative trial designs are considered in Appendix 3. Additionally, it is assumed in the main body of the text that the conventional (Neyman-Pearson) approach to the sample size calculation of an RCT is being used. Other approaches (Bayesian, precision and value of information) are briefly considered in Appendix 2 with reference to the specification of the target difference.

The paper presents an adaptation of numerical solution of first order linear differential equation in fuzzy environment. The numerical method is re-established and studied with fuzzy concept to estimate its uncertain parameters whose values are not precisely known. Demonstrations of fuzzy solutions of the governing methods are carried out by the approaches, namely Modified Runge Kutta method and Runge Kutta Merson method. The results are compared with the exact solution which is found using generalized Hukuhara derivative (gH-derivative) concepts. Additionally, different illustrative examples and an application in industry of the methods are also undertaken with the useful table and graph to show the usefulness for attained to the proposed approaches.

Taste signaling is a complex process that is linked to obesity and its associated metabolic syndromes. The sweet taste is mediated through a heterodimeric G protein coupled receptor (GPRC) in a species-specific manner and at multi-tissue specific levels. The sweet receptor recognizes a large number of ligands with structural and functional diversities to modulate different amplitudes of downstream signaling pathway(s). The human sweet-taste receptor has been extremely difficult to study by biophysical methods due to inadequate methods for producing large homogeneous quantities of the taste-receptor protein and a lack of reliable in vitro assays to precisely measure productive ligand binding modes leading to activity upon their interactions with the receptor protein. We report a multimodal high throughput assays to monitor ligand binding, receptor stability and conformational changes to model the molecular interactions between ligand-receptor. We applied saturation transfer difference nuclear magnetic resonance spectroscopy (STD-NMR) complemented by differential scanning calorimetry (DSC), circular dichroism (CD) spectroscopy, and intrinsic fluorescence spectroscopy (IF) to characterize binding interactions. Our method using complementary NMR and biophysical analysis is advantageous to study the mechanism of ligand binding and signaling processes in other GPCRs.

In the paper, by virtue of the Faà di Bruno formula, some properties of the Bell polynomials of the second kind, and an inversion formula for the Stirling numbers of the first and second kinds, the authors establish meaningfully and significantly two identities which simplify coefficients in a family of ordinary differential equations associated with higher order Bernoulli numbers of the second kind.

The investigation on the issue of damage diagnosis based on strain modal parameters is conducted in this paper using simply supported wooden Beams as the study's object. First, ABAQUS is utilized to create finite element models of intact wooden beams as well as wooden beams with varying degrees of damage and perform modal analyses on them. Next, damage identification studies are conducted on the wooden beam structure using various strain modal parameters (strain mode strain modal difference, strain modal curvature difference), the timber beam damage identification test then yields the modal parameters of timber beams under various damage situations, and the test findings are contrasted with those of the numerical simulation. The outcomes demonstrate that the damage identification of the test data using the three types of damage identification indexes is consistent with the results of the numerical simulation; the three types of damage identification indexes can locate the damage to timber beams, but the identification effect of the indexes is different, the best-recognized metric is the strain mode curvature difference; the next best is the strain mode difference, and the worst is the strain modes. The study's findings can serve as a guide for future damage detection on wood beams.

The opioid crisis in the United States has had devastating effects on communities across the country, leading many states to pass legislation that limits the prescription of opioid medications in an effort to reduce the number of overdose deaths. This study evaluates the impact of two categories of PDMP and Pill Mill regulations on the supply of opioid prescriptions at the level of dispensers and distributors (excluding manufacturers) using ARCOS data. The study uses a difference-in-difference method with a two-way fixed design to analyze the data. The study finds that both of the regulations are associated with reductions in the volume of opioid distribution. However, the study reveals that these regulations may have unintended consequences, such as shifting the distribution of controlled substances to neighboring states. For example, in Tennessee, the implementation of Operational PDMP regulations reduces in-state distribution of opioid drugs by 3.36% (95% CI, 2.37 to 4.3), while the out-of-state distribution to Georgia, which did not have effective PDMP regulations in place, increases by 16.93% (95% CI, 16.42 to 17.44). Our studies emphasize that policymakers should consider the potential for unintended distribution shifts of opioid drugs to neighboring states with laxer regulations as well as varying impacts on different dispenser types.

Recent advances in differential topology single out four-dimensions as being special, allowing for vast varieties of exotic smoothness (differential) structures, distinguished by their handlebody decompositions, even as the coarser algebraic topology is fixed. Should the spacetime we reside in takes up one of the more exotic choices, and there is no obvious reason why it shouldn't, apparent pathologies would inevitably plague calculus-based physical theories assuming the standard vanilla structure, due to the non-existence of a diffeomorphism and the consequent lack of a suitable portal through which to transfer the complete information regarding the exotic physical dynamics into the vanilla theories. An obvious plausible consequence of this deficiency would be the uncertainty permeating our attempted description of the microscopic world. We tentatively argue here, that a re-inspection of the key ingredients of the phenomenological particle models, from the perspective of exotica, could possibly yield interesting insights. Our short and rudimentary discussion is qualitative and speculative, because the necessary mathematical tools have only just began to be developed.

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

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

As a behavior of bilingual individuals and an indispensable part of bilingual speech, code-switching has been investigated by many researchers. However, there are many variables influencing code-switching, and each variable has the potential to be a confounding variable. Among these variables is the gender; however, whether there are significant gender differences and what are the gender differences in code-switching remains unknown for Mandarin Mandarin-English child bilinguals, as previous literature diverse on the existence of gender differences. Therefore, this paper seeks potential code-switching and distribution of code-switching by quantitative analysis of speech data in Singapore Bilingual Corpus. The results indicate that gender differences are significant in the amount of intra code-switching. However, neither considerable gender difference is observed in the amount of inter nor the code-switching related environment.

The authors intend to establish new oscillation criteria for a class of generalized third order functional difference equation of the form \begin{equation}{\label{eq01}} \Delta_{\ell}\left(a_2(n)\left[\Delta_{\ell}\left(a_1(n)\left[\Delta_{\ell}z(n)\right]^{\beta_1}\right)\right]^{\beta_2}\right)+q(n)f(x(g(n)))=0, ~~n\geq n_0, \end{equation} where $z(n)=x(n)+p(n)x(\tau(n))$. We also present sufficient conditions for the solutions to converges to zero. Suitable examples are presented to validate our main results.

This paper compares the finite sample performance of three non-parametric threshold estimators via Monte Carlo method. Our results show that the finite sample performance of the three estimators is not robust to the relative position of the threshold level along the distribution of threshold variable, especially when a structural change occurs at the tail part of the distribution.

The pollution caused by nitrogen dioxide is a major environmental problem in China. This study introduces a new type of atmospheric trace gas remote-sensing instrument, an airborne fiber imaging spectrometer. This spectrometer has a spectral range of 300–410 nm and works in push-broom mode with a 30° field of view on a flight path. Flight experiments were conducted on December 30, 2022 and January 5, 2023, covering heavily polluted areas of east of Beijing and Tangshan. This equipment obtained the density distribution of NO2 over the flight area. The results showed that pollution was mainly concentrated in the Caofeidian area and at the power station in the north, and the main source of pollution was anthropogenic. Satellite and airborne data near the pollution points were compared, and the two datasets showed a positive correlation with a correlation coefficient of 0.78 and 0.7, on the two days, respectively. This study demonstrates the capability of an airborne fiber imaging spectrometer for NO2 regional emission remote sensing and identifying the pollution points.

This research presents a solution to the problem of planning the optimum area for economic crops by developed mathematical models and developed an algorithm to solve the problem of planning the optimum area by considered economic value for the maximize profit of farmers. The data were collected from farmers in 8 provinces in the northeastern region of Thailand. The 3 economic crops studied were rice, cassava and sugarcane. The solving problem methods were 1) Created mathematical models and solved the problems with Lingo V.11. 2) Improved Differential Evolution algorithms (I-DE) to solve the problems, which had 3 local search methods included (Swap, Cyclic Move and K-variable moves). The results of this study showed that in the small and medium problems instances, Lingo V.11 and DE provided equal profit outcome but DE was faster but in the large size of test instances DE generated better solution than that of Lingo v.11 when Lingo simulation time is set to 250 hours and DE simulation time has set to maximum 21.82 minutes. 2) Comparing DE and I-DE , I-DE outperforms DE in finding the better solution for all size of test instances (small, medium and large).

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

Developing new energy is critical to China's green and low-carbon development. And the New Energy Demonstration City Policy (NEDCP) is a vital innovation policy that inspires the development of new energy. Is the NEDCP facilitating green and low-carbon development, if so, how? Employing unbalanced panel data from 2003 to 2017, the impact of NEDCP on green and low-carbon development was studied by using the "difference in difference" (DID) model. We find that this policy can take significantly role. After various robustness tests, our results are still valid. According to the heterogeneity analysis, non-resource and non-old industrial base cities have a greater positive impact from this policy. The mechanism analysis denotes that the positive policy effect works through upgrading the industrial structure and stimulating urban innovation. The substantial empirical evidence presented in this article supports the continued promotion and implementation of new energy demonstration cities.

We discuss a remote sensing system that is used to simultaneously detect range-resolved differential absorption LIDAR (light detection and ranging; DIAL) signals and integrated path DIAL signals (IP-DIAL) from aerosol targets for ranges up to 22 km. The DIAL/IP-DIAL frequency converter consists of an OPO pumped at 1064 nm to produce light at 1.6 μm and operates at 100 Hz pulse repetition frequency. The probe light is free space coupled to a movable platform that contains one transmitter and two receiver telescopes. Hybrid photon counting/current systems increase the dynamic range for detection by two orders of magnitude. Range resolved and column integrated dry-air CO2 and CH4 mixing ratios are obtained from line shape fits of CO2 and CH4 centered at 1602.2 nm and 1645.5 nm, respectively and measured at 10 different frequencies over ≈ 1.5 cm-1 bandwidth. The signal-to-noise ratios (SNR) of the IP-DIAL returns from cloud aerosols approach 1000:1 and the uncertainties in the mixing ratios weighted according to the integrated counts over the cloud segments range from 0.1 % to 1 %. The range averaged DIAL mixing ratios are in good agreement with the IP-DIAL mixing ratios at the 1 % to 2 % level for both CO2 and CH4. These results can serve as a validation method for future active and passive satellite observational systems.

The importance of various markers such as sclerostin, Dickkopf-1 (DKK-1), Irisin, receptor activator of NF-kB ligand (RANKL), and Vitamin D have been well studied in bone metabolism. Additionally, inflammatory cytokines such as tumor necrosis factor-alpha (TNF-α) and Interleukine-6 (IL-6) have been identified to hinder muscle protein synthesis, leading to the loss of muscle and strength. However, a research gap exists in the understanding their role in muscle function and physical activity. Therefore, this study aims to explore the serum levels of sclerostin, DKK-1, irisin, IL-6, RANKL, Vitamin D, and TNF-α and assess their relationships with upper and lower body strength in young adults. In this study, 38 college-aged students 18-23 years participated and completed the protocols. The participants’ lower and upper body strength were assessed by the vertical jump test (Just Jump, Probotic, AL) with a Tendo FitroDyne (Tendo Sports Machines, Trencin, Slovak Republic) and handgrip (HG) dynamometry (Takei Scientific Instruments, Yashiroda, Japan), respectively. Fasting morning blood samples were analyzed for serum levels of the biomarkers by ELISA. The results indicate significant sex differences in sclerostin, DKK-1, irisin, and vitamin D levels (p<0.05). Furthermore, a positive association was observed between sclerostin, DKK-1, and vitamin D, with lower body muscle performance variables (p<0.05). Conversely, a significant negative correlation was observed between TNF-α and upper-body muscle performance variables (p<0.05). The results suggest that these markers may have a distinct effect on muscle performance, underscoring the need for further investigation to elucidate the concept of muscle-bone crosstalk.

Background/Aim: Rapid onset of facial ptosis can impact physical appearance and compromise the outcomes of facelift procedures. The level of vitamin D has a potential correlation with collagen formation and its deficiency with inflammatory processes that affect the breakdown of hyaluronic acid. This study aims to investigate the potential relationship between accentuated facial ptosis in women and low levels of vitamin D. Furthermore, it aims to explore preventive measures or strategies to slow down facial ptosis and enhance the longevity of facelift results. Materials and Methods: The study was focused on monitoring the vitamin D levels in women and men with advanced facial ptosis and comparing them with a control group. Results: Notably, a direct association between gender and serum vitamin D levels was observed, indicating less sustainable outcomes in women. Conclusion: Women face additional challenges in the aging process due to hormonal shifts after menopause or premenopausal, which are associated with osteoporosis and lower vitamin D levels.

Optimization of Magnetohydrodynamics parameters on the velocity profile and temperature distribution of incompressible fluid flow on a porous channel was evaluated. The fluid flow was considered to be unsteady, incompressible and flowing in 2-D in porous channel. The effects of magnetic parameter, Darcy’s number and fluid pressure on velocity profiles, and the effect of variable viscosity and Eckert number on temperature distribution in incompressible fluid flow were determined. The flow was considered to be in a channel running along the x-axis on which the magnetic field exist and finally along the y-axis on the porous part of the channel. The resulting model equations were solved by Finite Difference Method (FDM) in MATLAB software. Analysis of results indicated that increasing Darcy’s number and fluid pressure leads to increase in fluid velocity profile, while increasing magnetic parameter decreases fluid velocity profile. Also, it was observed that increase in both Eckert number and fluid viscosity lead to increase in temperature distribution. Optimization in temperature was achieved by increasing the magnetic field while viscosity was optimized by increasing the length of the porous part of the channel. This study will helpful to contribute alternative equations and methodology to engineering and in factories where getting the MHD parameters optimally is the main objective, particularly on temperature, velocity and pressure.

Cancer diseases lead to the second-highest death rate all over the world. The dynamics of invasion of cancer cells into the human body tissues and metastasis are the main causes of death in patients with cancer. This study deals with theoretical investigation of the dynamics of invasion of cancer cells for tumour growths in human body tissues using discretized Cahn-Hilliard, concentration and reaction-diffusion equations which were solved by Finite Difference Method with the aid of MATLAB computer software. A Crank-Nicolson numerical scheme was developed for the discretized model equations. The numerical result obtained was used to describe the dynamics of cancer invasion of tissues with respect to cancer cells density on tumour growth, turbulence and mobility and equilibrium between charge and discharge of cancer cells. The results of the study provide new insights into combating cancer disease by providing mitigating and intervention measures to this major health problem.

We employ another approach to quantize electromagnetic fields in the coordinate space, instead of the mode (or Fourier) space, such that local features of photons can be efficiently, physically, and more intuitively described. To do this, coordinate-ladder operators are defined from mode-ladder operators via the unitary transformation of systems involved in arbitrary inhomogeneous dielectric media. Then, one can expand electromagnetic field operators through the coordinate-ladder operators weighted by non-orthogonal and spatially-localized bases, which are propagators of initial quantum electromagnetic (complex-valued) field operators. Here, we call them QEM-CV-propagators. However, there are no general closed form solutions available for them. This inspires us to develop a quantum finite-difference time-domain (Q-FDTD) scheme to numerically time evolve QEM-CV-propagators. In order to check the validity of the proposed Q-FDTD scheme, we perform computer simulations to observe the Hong-Ou-Mandel effect resulting from the destructive interference of two photons in a 50/50 quantum beam splitter.

A finite-difference approach with non-uniform meshes was presented for simulating magnetotelluric responses in 2D structures. We presented the formulation of this scheme and gave some sights into its successful implementation, and compared finite-difference solution with known numerical results and simple analytical solutions. First, a homogeneous half-space model was tested and the finite-difference approach can provide very good accuracy for 2D magnetotelluric modeling. Then we compared to the analytical solutions for the two-layered model, the relative errors of the apparent resistivity and the impedance phase were both increased when the frequency was increased. In the end, we compare our finite-difference simulation results with COMMEMI 2D-0 model with the finite-element solutions. Both results are in close agreement to each other. These comparisons confirm the validity and reliability of our finite-difference algorithm.

Calculus, as a starting point to everyone's study of mathematics, was developed along with classical mechanics. Though not rigorously formulated, the intuition for differential form and infinitesimal motion makes calculus not hard to understand. And hence it does not require great effort to grasp the principles of classical mechanics. However, the situation becomes quite different when it comes to the quantum world. Given a particle system, what of interest is always the physical quantity of this system, such as energy, position, momentum, entropy, etc. But it is no longer straightforward.

Molecular studies regarding regulatory elements such as small ncRNAs and their mechanisms are poorly understood in infectious diseases. Tuberculosis is one of the oldest infectious diseases of humanity, and it is still a challenge to prevent and treat it. The control of the infection as well as its diagnosis are still complex, and treatments used are linked to several side effects. This study aimed to investigate miRNA’s expression profile to identify possible biomarkers for tuberculosis. We applied NGS techniques to investigate miRNA’s global expression profile from blood samples of infected patients with tuberculosis, their respective healthy physicians, and external healthy individuals as controls. Samples from 22 individuals run through a differential expression, target genes, gene set enrichment, and miRNA-gene network analysis. We observed 153 altered miRNAs, among which, only three DEmiRNAs (hsa-let-7g-5p, hsa-miR-486-3p and hsa-miR-4732-5p) were found between the investigated patients and their respective physicians. These DEmiRNAs are suggested to play an important role in granuloma regulation and their immune physiopathology. Our results propose that miRNAs may be involved in immune modulation, regulating the repertoire of genes expressed in the immune system’s cells. Our findings encourage the application of miRNAs as potential biomarkers for tuberculosis.

Agricultural activities are the second largest source of greenhouse gas emissions, and carbon emissions from agricultural land use (CEALU) have become a hot issue across the world. However, few scholars explored the impact of agricultural land policies on carbon emissions, such as the High-standard farmland construction(HSFC) in China.Thus，by relying on provincial panel data for China for the period 2005-2017, the effect of the high-standard basic farmland construction policy on carbon emissions from agricultural land use per unit area and its regional differences were quantitatively analyzed using the difference-in-difference (DID) model. The results showed that: 1) China's CEALU per unit area presented a fluctuating upward trend during the period 2005-2017, from 392.58 kg/ha to 457.72 kg/ha, with an average annual growth rate of 1.31%. 2) The high-standard farmland construction(HSFC) policy produced a significant carbon emission reduction effect in agricultural land use, and reduced the CEALU per unit area by 10.80% on average. With the promotion of this policy, its carbon emission reduction effect in agricultural land use presented an overall increasing trend. 3) The carbon emission reduction effect of the high-standard farmland construction policy in agricultural land use was significant in central China, but non-significant in eastern China and western China.

We provide methodology and numerical results for the Hattendorff differential equa- tion for the continuous time evolution of the variance of L(j)t , the loss at time t random variable for a multi-state process, given that the state at time t is j.

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

The sonification of data to communicate information to a user is a relatively new approach that established itself around the 1990s. To date many researchers design their individual sonification from scratch. There are no standards in sonification design and evaluation. But researchers and practitioners have formulated several requirements and established several methods. There is wide consensus that psychoaocustics could play an important role in the sonification design and evaluation phase. But this requires an adaption of psychoacoustic methods to the signal types and the requirements of sonification. In this method paper we present PAMPAS, a PsychoAcoustical Method for the Perceptual Analysis of multidimensional Sonification. A well-defined and well-established, efficient, reliable and replicable Just Noticeable Difference experiment using the Maximum Likelihood Procedure serves as the basis to achieve linearity of parameter mapping during the sonification design stage and to identify and quantify perceptual effects during the sonification evaluation stage, namely the perceptual resolution, hysteresis effects and perceptual interferences. The experiment results are universal scores from a standardized data space and a standardized procedure. These scores can serve to compare multiple sonification designs of a single researcher, or even between different research groups. The method can supplement other sonification design and evaluation methods from a perceptual viewpoint.