Jacobi Collocation Methods for Solving Generalized Space-Fractional Burgers Equations

The aim of this paper is to obtain the numerical solutions of generalized space-fractional Burgers' equations with initial-boundary conditions by the Jacobi spectral collocation method using the shifted Jacobi-Gauss-Lobatto collocation points. By means of the simplifed Jacobi operational matrix, we produce the diferentiation matrix and transfer the space-fractional Burgers' equation into a system of ordinary diferential equations that can be solved by the fourth-order Runge-Kutta method. The numerical simulations indicate that the Jacobi spectral collocation method is highly accurate and fast convergent for the generalized space-fractional Burgers' equation.

Uncertainty Calculation of Roundness Assessment by Automatic Differentiation in Coordinate Metrology

Reomtly, Coordinate bieasuring Machines （CMMs） are widely used to measure roundness errors. Roundness is calculated from a large number of points collected from the profiles of the parts. According to the Guide to the Expression of Uncertainty in Measta- meat （GUM）, all measurement results must have a stated uncertainty associated the titan. However, no CMMs give the uncertainty value of the roundness, because no suitable measrement uncertainty calculation procedure exists. In the case of roundness raeasurement in coordinate metrology, this paper suggests the algorithms for the calculation of the measurement uncertainty of the roudness deviation based on the two mainly used association criteria, LSC and MZC. The calculation of the sensitivity coefficients for the uncertainty calculatiion can be done by autnatic differentiation, in order to avoid introducing additional emars by the traditional difference quotient approxima- tions. The proposed methods are exact and need input data only as the nrasured coordinates of the data points and their associated un- certainties.

GENERAL COUPLED MEAN-FIELD REFLECTED FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

In this paper we consider general coupled mean-field reflected forward-backward stochastic differential equations(FBSDEs),whose coefficients not only depend on the solution but also on the law of the solution.The first part of the paper is devoted to the existence and the uniqueness of solutions for such general mean-field reflected backward stochastic differential equations(BSDEs)under Lipschitz conditions,and for the one-dimensional case a comparison theorem is studied.With the help of this comparison result,we prove the existence of the solution for our mean-field reflected forward-backward stochastic differential equation under continuity assumptions.It should be mentioned that,under appropriate assumptions,we prove the uniqueness of this solution as well as that of a comparison theorem for mean-field reflected FBSDEs in a non-trivial manner.

A High-Order Scheme for Fractional Ordinary Differential Equations with the Caputo-Fabrizio Derivative

In this paper, we consider numerical solutions of fractional ordinary diferential equations with the Caputo-Fabrizio derivative, and construct and analyze a high-order time-stepping scheme for this equation. The proposed method makes use of quadratic interpolation function in sub-intervals, which allows to produce fourth-order convergence. A rigorous stability and convergence analysis of the proposed scheme is given. A series of numerical examples are presented to validate the theoretical claims. Traditionally a scheme having fourth-order convergence could only be obtained by using block-by-block technique. The advantage of our scheme is that the solution can be obtained step by step, which is cheaper than a block-by-block-based approach.

Revaluating coal permeability-gas pressure relation under various gas pressure differential conditions

Identifying changes in coal permeability with gas pressure and accurately codifying mean efective stresses in laboratory samples are crucial in predicting gas-fow behavior in coal reservoirs. Traditionally, coal permeability to gas is assessed using the steady-state method, where the equivalent gas pressure in the coal is indexed to the average of upstream and downstream pressures of the coal, while ignoring the nonlinear gas pressure gradient along the gas fow path. For the fow of a compressible gas, the traditional method consistently underestimates the length/volume-averaged pressure and overestimates mean efective stress. The higher the pressure diferential within the sample, the greater the error between the true mean pressure for a compressible fuid and that assumed as the average between upstream and downstream pressures under typical reservoir conditions. A correction coefcient for the compressible fuid pressure asymptotes to approximately 1.3%, representing that the error in mean pressure and efective stress can be on the order of approximately 30%, particularly for highly pressure-sensitive permeabilities and compressibilities, further amplifying errors in evaluated reservoir properties. We utilized this volume-averaged pressure and efective stress to correct permeability and compressibility data reported in the literature. Both the corrected initial permeability and the corrected pore compressibility were found to be smaller than the uncorrected values, due to the underestimation of the true mean fuid pressure, resulting in an overestimation of reservoir permeability if not corrected. The correction coefcient for the initial permeability ranges from 0.6 to 0.1 (reservoir values are only approximately 40% to 90% of laboratory values), while the correction coefcient for pore compressibility remains at approximately 0.75 (reservoir values are only approximately 25% of laboratory value). Errors between the uncorrected and corrected parameters are quantifed under various factors, such as confning pressure, gas sorption, and temperature. By analyzing the evolutions of the initial permeability and pore compressibility, the coupling mechanisms of mechanical compression, adsorption swelling, and thermal expansion on the pore structure of the coal can be interpreted. These fndings can provide insights that are useful for assessing the sensitivity of coal permeability to gas pressure as truly representative of reservoir conditions.

Trotter–Kato Approximations of Impulsive Neutral SPDEs in Hilbert Spaces

This paper studies a class of impulsive neutral stochastic partial differential equations in real Hilbert spaces.The main goal here is to consider the Trotter-Kato approximations of mild solutions of such equations in the pth-mean(p≥2).As an application,a classical limit theorem on the dependence of such equations on a parameter is obtained.The novelty of this paper is that the combination of this approximating system and such equations has not been considered before.

Related-Key Impossible Diferential Attack on Reduced-Round LBlock

LBlock is a 32-round lightweight block cipher with 64-bit block size and 80-bit key. This paper identifies 16- round related-key impossible differentials of LBlock, which are better than the 15-round related-key impossible differentials used in the previous attack. Based on these 16-round related-key impossible differentials, we can attack 23 rounds of LBlock while the previous related-key impossible differential attacks could only work on 22-round LBlock. This makes our attack on LBlock the best attack in terms of the number of attacked rounds.

Quantum federated learning through blind quantum computing

Private distributed learning studies the problem of how multiple distributed entities collaboratively train a shared deep network with their private data unrevealed. With the security provided by the protocols of blind quantum computation, the cooperation between quantum physics and machine learning may lead to unparalleled prospect for solving private distributed learning tasks.In this paper, we introduce a quantum protocol for distributed learning that is able to utilize the computational power of the remote quantum servers while keeping the private data safe. For concreteness, we first introduce a protocol for private single-party delegated training of variational quantum classifiers based on blind quantum computing and then extend this protocol to multiparty private distributed learning incorporated with diferential privacy. We carry out extensive numerical simulations with diferent real-life datasets and encoding strategies to benchmark the efectiveness of our protocol. We find that our protocol is robust to experimental imperfections and is secure under the gradient attack after the incorporation of diferential privacy. Our results show the potential for handling computationally expensive distributed learning tasks with privacy guarantees, thus providing a valuable guide for exploring quantum advantages from the security perspective in the field of machine learning with real-life applications.

Satellite integrity monitoring for satellite-based augmentation system:an improved covariance-based method

Satellite integrity monitoring is vital to satellite-based augmentation systems,and can provide the confdence of the diferential corrections for each monitored satellite satisfying the stringent safety-of-life requirements.Satellite integrity information includes the user diferential range error and the clock-ephemeris covariance which are used to deduce integrity probability.However,the existing direct statistic methods sufer from a low integrity bounding percentage.To address this problem,we develop an improved covariance-based method to determine satellite integrity information and evaluate its performance in the range domain and position domain.Compared with the direct statistic method,the integrity bounding percentage is improved by 24.91%and the availability by 5.63%.Compared with the covariance-based method,the convergence rate for the user diferential range error is improved by 8.04%.The proposed method is useful for the satellite integrity monitoring of a satellite-based augmentation system.

EXPONENTIAL STABILITY TO A NEUTRAL DIFFERENTIAL EQUATION OF FIRST ORDER WITH DELAY

In this paper, we study the exponential stability of the zero solution to a neutral diferential equation. By applying the Lyapunov-Krasovskiì functional approach, we prove a result on the stability of the zero solution. The result we obtained extends and generalizes the existing ones in the previous literature. Comparing with the previous results, our result is new and complements some known results.

LIMIT CYCLES FOR A CLASS OF SECOND ORDER DIFFERENTIAL EQUATIONS AND DUFFING EQUATIONS

By the averaging method of frst order, we study in this work the limit cycles for a class of second order diferential equations and Dufng diferential equations which can be seen as a particular perturbation of the harmonic oscillator.

EXISTENCE OF MILD SOLUTION TO NONLINEAR NEUTRAL STOCHASTIC DIFFERENTIAL SYSTEM WITH DELAY

This paper is concerned with the existence of solution to a nonlinear neutral stochastic diferential system with delay in a Hilbert Space. Sufcient conditions for the existence are obtained using the Schaefer fxed point theorem.

EXISTENCE OF ANTI-PERIODIC MILD SOLUTIONS TO FRACTIONAL DIFFERENTIAL EQUATIONS OF ORDER α∈(0,1)

In this paper, by Schauder’s fxed point theorem and the contraction mapping principle, we consider the existence and stability of T-anti-periodic solutions to fractional diferential equations of order α∈(0,1). An example is given to illustrate the main results.

EXISTENCE AND UNIQUENESS OF SOLUTIONS TO A BACKWARD STOCHASTIC DIFFERENTIAL EQUATION

A backward stochastic diferential equation is discussed in this paper. Under some weaker conditions than uniformly Lipschitzian condition given by Pardoux and Peng(1990), using Picard interaction and Cauchy sequence, the existence and uniqueness of the solutions to the backward stochastic diferential equation.

HYERS-ULAM-RASSIAS STABILITY OF SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS

In this paper, using Banach’s contraction principle, we consider the Hyers-UlamRassias stability of nonlinear partial diferential equations. An example is given to demonstrate the applicability of our results.

THREE POSITIVE SOLUTIONS TO SECOND-ORDER IMPULSIVE NEUMANN BOUNDARY VALUE PROBLEM

Using the fve functionals fxed point theorem, in this paper we present some criteria which guarantee the existence of three positive solutions to second order impulsive Neumann boundary value problem.