This work focuses on the temporal average of the backward Euler-Maruyama(BEM)method,which is used to approximate the ergodic limit of stochastic ordinary differential equations(SODEs).We give the central limit theorem...
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This work focuses on the temporal average of the backward Euler-Maruyama(BEM)method,which is used to approximate the ergodic limit of stochastic ordinary differential equations(SODEs).We give the central limit theorem(CLT)of the temporal average of the BEM method,which characterizes its asymptotics in *** the deviation order is smaller than the optimal strong order,we directly derive the CLT of the temporal average through that of original equations and the uniform strong order of the BEM *** the case that the deviation order equals to the optimal strong order,the CLT is established via the Poisson equation associated with the generator of original *** experiments are performed to illustrate the theoretical *** main contribution of this work is to generalize the existing CLT of the temporal average of numerical methods to that for SODEs with super-linearly growing drift coefficients.
In this paper,we investigate the existence of solutions and analyze the large-time behavior for Gurtin-Maccamy population model involving conformable fractional *** a preliminary step,we construct a generic structure ...
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In this paper,we investigate the existence of solutions and analyze the large-time behavior for Gurtin-Maccamy population model involving conformable fractional *** a preliminary step,we construct a generic structure of the solution associated with our proposed model by utilizing some basic properties and tools of conformable fractional *** establish the existence of a unique solution of the given model with the given initial *** last,by using the upper and lower solutions for the characteristic equation,we define the upper and lower boundaries for the obtained solution and describe the large-time behavior of the total population.
In the field of speech recognition, enhancing accuracy is paramount for diverse linguistic communities. Our study addresses this necessity, focusing on improving Amazigh speech recognition through the implementation o...
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The speeding-up and slowing-down(SUSD)direction is a novel direction,which is proved to converge to the gradient descent direction under some *** authors propose the derivative-free optimization algorithm SUSD-TR,whic...
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The speeding-up and slowing-down(SUSD)direction is a novel direction,which is proved to converge to the gradient descent direction under some *** authors propose the derivative-free optimization algorithm SUSD-TR,which combines the SUSD direction based on the covariance matrix of interpolation points and the solution of the trust-region subproblem of the interpolation model function at the current iteration *** analyze the optimization dynamics and convergence of the algorithm *** of the trial step and structure step are *** results show their algorithm’s efficiency,and the comparison indicates that SUSD-TR greatly improves the method’s performance based on the method that only goes along the SUSD *** algorithm is competitive with state-of-the-art mathematical derivative-free optimization algorithms.
In this paper, we investigate the approximate solutions for the fractional fuzzy acoustic wave equations. We use the Laplace transform and an iterative technique with the fractional Atangana–Baleanu–Caputo operator ...
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In this paper, we design and analyze a space-time spectral method for the subdiffusion ***, we are facing two difficulties. The first is that the solutions of this equation are usually singular near the initial time. ...
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In this paper, we design and analyze a space-time spectral method for the subdiffusion ***, we are facing two difficulties. The first is that the solutions of this equation are usually singular near the initial time. Consequently, traditional high-order numerical methods in time are inefficient. The second obstacle is that the resulting system of the space-time spectral approach is usually large and time-consuming to solve. We aim at overcoming the first difficulty by proposing a novel approach in time, which is based on variable transformation techniques. Suitable ψ-fractional Sobolev spaces and a new variational framework are introduced to establish the well-posedness of the associated variational problem. This allows us to construct our space-time spectral method using a combination of temporal generalized Jacobi polynomials(GJPs) and spatial Legendre polynomials. For the second difficulty, we propose a fast algorithm to effectively solve the resulting linear system. The fast algorithm makes use of a matrix diagonalization in space and QZ decomposition in time. Our analysis and numerical experiments show that the proposed method is exponentially convergent with respect to the polynomial degrees in both space and time directions, even though the exact solution has very limited regularity.
In this paper the author investigates the following predator-prey model with prey-taxis and rotational?ux terms■in a bounded domain with smooth *** presents the global existence of generalized solutions to the model...
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In this paper the author investigates the following predator-prey model with prey-taxis and rotational?ux terms■in a bounded domain with smooth *** presents the global existence of generalized solutions to the model■in any dimension.
In the present paper, we investigate the existence of solutions for coupled systems of ψ-Caputo semilinear fractional differential equations in Banach space with initial conditions. The stability of the relevant solu...
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In this study, we developed a speech recognition system for the Amazigh language, specifically targeting the recognition of the initial ten numbers. The system employs four Convolutional Neural Network (CNN) models, i...
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The field of speech recognition makes it simpler for humans and machines to engage with speech. Number-oriented communication, such as using a registration code, mobile number, score, or account number, can benefit fr...
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