The nonlinear fractional diffusion equations with Nagumo-type sources and perturbed orders

**solution**of the problems with respect to perturbed fractional orders. For $t=0$, we show that the final value problem is instable and deduce that the problem is ill-posed. A regularization method is proposed to recover the initial data from the inexact fractional orders and the final data. By some regularity assumptions of the exact

**solutions**of the problems, we obtain an error estimate of H\"older type.

6/10 relevant

arXiv

Sub-method, partial behavioral reflection with Reflectivity: Looking back on 10 years of use

**solutions**, but which introduced a semantic gap between the code that requires adaptation and the expression of the partial behavior. Expand abstract.

**solution**. As validation over the practical use of Reflectivity in dynamic object-oriented languages, the API has been ported to Python. Finally, the AST annotation feature of Reflectivity opens new experimentation opportunities about the control that developers could gain on the behavior of their own software.

4/10 relevant

arXiv

Explicit Multi-objective Model Predictive Control for Nonlinear Systems Under Uncertainty

**solutions**, we include an additional online optimization step, which is considerably cheaper than the original multi-objective optimization problem. Expand abstract.

**solutions**can degrade in quality or even become infeasible. Thus, there is the need to design methods that can handle uncertainty. In this work, we consider nonlinear multi-objective optimal control problems with uncertainty on the initial conditions, and in particular their incorporation into a feedback loop via model predictive control (MPC). In multi-objective optimal control, an optimal compromise between multiple conflicting criteria has to be found. For such problems, not much has been reported in terms of uncertainties. To address this problem class, we design an offline/online framework to compute an approximation of efficient control strategies. This approach is closely related to explicit MPC for nonlinear systems, where the potentially expensive optimization problem is solved in an offline phase in order to enable fast

**solutions**in the online phase. In order to reduce the numerical cost of the offline phase, we exploit symmetries in the control problems. Furthermore, in order to ensure optimality of the solutions, we include an additional online optimization step, which is considerably cheaper than the original multi-objective optimization problem. We test our framework on a car maneuvering problem where safety and speed are the objectives. The multi-objective framework allows for online adaptations of the desired objective. Alternatively, an automatic scalarizing procedure yields very efficient feedback controls. Our results show that the method is capable of designing driving strategies that deal better with uncertainties in the initial conditions, which translates into potentially safer and faster driving strategies.

6/10 relevant

arXiv

On the asymptotic behavior of **solutions** to time-fractional elliptic
equations driven a multiplicative white noise

**solutions**. Expand abstract.

**solutions**to scalar stochastic fractional differential equations, Ito's formula and establishing a new weighted norm associated with a Lyapunov-Perron operator defined from this representation of solutions, we show the asymptotic behaviour of

**solutions**to these systems in mean square sense. As a consequence, we also prove existence, uniqueness and the convergence rate of their

**solutions**.

5/10 relevant

arXiv

Traveling waves in a mean field learning model

**solutions**and their propagation speed on various economic parameters of the system. Expand abstract.

**solutions**to this system. They correspond to what is known in economics as balanced growth path

**solutions**. We also study the dependence of the

**solutions**and their propagation speed on various economic parameters of the system.

6/10 relevant

arXiv

Geometrically Nonlinear Response of a Fractional-Order Nonlocal Model of Elasticity

**solution**of the integro-differential nonlinear governing equations. Expand abstract.

**solution**which is consistent across loading and boundary conditions. The governing equations and the corresponding boundary conditions of the geometrically nonlinear and nonlocal Euler-Bernoulli beam are obtained using variational principles. Further, a nonlinear finite element model for the fractional-order system is developed in order to achieve the numerical

**solution**of the integro-differential nonlinear governing equations. Following a thorough validation with benchmark problems, the fractional finite element model (f-FEM) is used to study the geometrically nonlinear response of a nonlocal beam subject to various loading and boundary conditions. Although presented in the context of a 1D beam, this nonlinear f-FEM formulation can be extended to higher dimensional fractional-order boundary value problems.

4/10 relevant

arXiv

Machine Learning Algorithms for Predicting Coronary Artery Disease: Efforts Toward an Open Source **Solution**

**solution**for predicting the presence of coronary artery disease in a given population and present a workflow model for implementing a possible solution. Expand abstract.

**solution**for predicting the presence of coronary artery disease in a given population and present a workflow model for implementing a possible

**solution**.

7/10 relevant

bioRxiv

Food waste and dynamic complex systems: The case of Peru and a **solution** model proposal Part 1: Peruvian Anchoveta (Engraulis ringens)

5/10 relevant

PsyArXiv

Asymptotic completeness of a scalar quasilinear wave equation satisfying the weak null condition

**solution**which agrees with the approximate solution at infinite time. Expand abstract.

**solution**which agrees with the approximate

**solution**at infinite time.

4/10 relevant

arXiv

Existence and smoothness of the **solution** to the Navier-Stokes

**solution**exists for the Navier-Stokes equations in three dimensions. In this paper we shall study this problem. The Navier-Stokes equations are given by: $u_{it}(x,t)-\rho\triangle u_i(x,t)-u_j(x,t) u_{ix_j}(x,t)+p_{x_i}(x,t)=f_i(x,t)$ , $div\textbf{u}(x,t)=0$ with initial conditions $\textbf{u}|_{(t=0)\bigcup\partial\Omega}=0$. We introduce the unknown vector-function: $\big(w_i(x,t)\big)_{i=1,2,3}: u_{it}(x,t)-\rho\triangle u_i(x,t)-\frac{dp(x,t)}{dx_i}=w_i(x,t)$ with initial conditions: $u_i(x,0)=0,$ $u_i(x,t)\mid_{\partial\Omega}=0$. The

**solution**$u_i(x,t)$ of this problem is given by: $u_i(x,t)=\int_0^t\int_{\Omega}G(x,t;\xi,\tau)~\Big(w_i(\xi,\tau)+\frac{dp(\xi,\tau)}{d\xi_i}\Big)d\xi d\tau$ where $G(x,t;\xi,\tau)$ is the Green function. We consider the following N-Stokes-2 problem: find a

**solution**$\textbf{w}(x,t)\in \textbf{L}_2(Q_t), p(x,t): p_{x_i}(x,t)\in L_2(Q_t)$ of the system of equations: $w_i(x,t)-G\Big(w_j(x,t)+\frac{dp(x,t)}{dx_j}\Big)\cdot G_{x_j}\Big(w_i(x,t)+\frac{dp(x,t)}{dx_i}\Big)=f_i(x,t)$ satisfying almost everywhere on $Q_t.$ Where the v-function $\textbf{p}_{x_i}(x,t)$ is defined by the v-function $\textbf{w}_i(x,t)$. Using the following estimates for the Green function: $|G(x,t;\xi ,\tau)| \leq\frac{c}{(t-\tau)^{\mu}\cdot |x-\xi|^{3-2\mu}}; |G_{x}(x,t;\xi,\tau)|\leq\frac{c}{(t-\tau)^{\mu}\cdot|x-\xi|^{3-(2\mu-1)}}(1/2

8/10 relevant

arXiv