Explicit Conditions Research Articles

Bistable traveling waves for time periodic reaction-diffusion equations in strip with Dirichlet boundary condition

We study the existence of bistable traveling wave solutions for time periodic reaction-diffusion equations in straight strips subject to the Dirichlet boundary condition. We first employ a monotone dynamical system framework to establish the existence of such a wave by assuming a bistability structure in terms of multiplicity and stability of periodic solutions in the section of the strip, which is then realized under a set of sufficient explicit conditions; in particular, the bistability structure appears if the reaction term is a time periodic smooth perturbation of the nonlinearity λu(1−u)(u−a) when a∈(0,1/2) and λ>λ⁎ for some λ⁎>0.

Quadratic Privacy-Signaling Games and the MMSE Information Bottleneck Problem for Gaussian Sources

We investigate a privacy-signaling game problem in which a sender with privacy concerns observes a pair of correlated random vectors which are modeled as jointly Gaussian. The sender aims to hide one of these random vectors and convey the other one whereas the objective of the receiver is to accurately estimate both of the random vectors. We analyze these conflicting objectives in a game theoretic framework with quadratic costs where depending on the commitment conditions (of the sender), we consider Nash or Stackelberg (Bayesian persuasion) equilibria. We show that a payoff dominant Nash equilibrium among all admissible policies is attained by a set of explicitly characterized linear policies. We also show that a payoff dominant Nash equilibrium coincides with a Stackelberg equilibrium. We formulate the information bottleneck problem within our Stackelberg framework under the mean squared error distortion criterion where the information bottleneck setup has a further restriction that only one of the random variables is observed at the sender. We show that this MMSE Gaussian Information Bottleneck Problem admits a linear solution which is explicitly characterized in the paper. We provide explicit conditions on when the optimal solutions, or equilibrium solutions in the Nash setup, are informative or noninformative.

Converter-Based Moving Target Defense Against Deception Attacks in DC Microgrids

With the rapid development of information and communications technology in DC microgrids (DCmGs), the deception attacks, which typically include false data injection and replay attacks, have been widely recognized as a significant threat. However, existing literature ignores the possibility of the intelligent attacker, who could launch deception attacks once obtaining necessary information by exploiting zero-day vulnerabilities or bribing insiders, to affect the system in an unforeseeable manner. In this paper, based on the observation that the primary control law of the power converter device in DCmGs is usually programmable, we propose a novel converter-based moving target defense (CMTD) strategy by proactively perturbing the primary control gains to defend against deception attacks. First, we study the impact of perturbing the primary control gains on the voltage stability in DCmGs and provide explicit conditions for the perturbation magnitude and frequency under which the voltage stability can be ensured. Then, we investigate the improved detectability against deception attacks under CMTD and present sufficient conditions under which these attacks can be detected. Finally, we conduct extensive MATLAB SIMULINK/PLECS based simulations and systematic hardware-in-the-loop based experiments to validate the effectiveness of CMTD.

REMARKS ON HILBERT’S TENTH PROBLEM AND THE IWASAWA THEORY OF ELLIPTIC CURVES

AbstractLet E be an elliptic curve with positive rank over a number field K and let p be an odd prime number. Let $K_{\operatorname {cyc}}$ be the cyclotomic $\mathbb {Z}_p$ -extension of K and $K_n$ its nth layer. The Mordell–Weil rank of E is said to be constant in the cyclotomic tower of K if for all n, the rank of $E(K_n)$ is equal to the rank of $E(K)$ . We apply techniques in Iwasawa theory to obtain explicit conditions for the rank of an elliptic curve to be constant in this sense. We then indicate the potential applications to Hilbert’s tenth problem for number rings.

Non-homogeneous Dirichlet-transmission problems for the anisotropic Stokes and Navier-Stokes systems in Lipschitz domains with transversal interfaces

This paper is build around the stationary anisotropic Stokes and Navier-Stokes systems with an L^infty -tensor coefficient satisfying an ellipticity condition in terms of symmetric matrices in {mathbb {R}}^{ntimes n} with zero matrix traces. We analyze, in L^2-based Sobolev spaces, the non-homogeneous boundary value problems of Dirichlet-transmission type for the anisotropic Stokes and Navier-Stokes systems in a compressible framework in a bounded Lipschitz domain with a transversal Lipschitz interface in {mathbb {R}}^n, nge 2 (n=2,3 for the nonlinear problems). Thus, the interface intersects transversally the boundary of the Lipschitz domain and divides the domain into two Lipschitz sub-domains. First, we use a mixed variational approach to prove the well-posedness of linear problems related to the anisotropic Stokes system. Then we show the existence of a weak solution to the Dirichlet and Dirichlet-transmission problems for the nonlinear anisotropic Navier-Stokes system. This is done by implementing the Leray-Schauder fixed point theorem and using various results and estimates from the linear case, as well as the Leray-Hopf and some other norm inequalities. Explicit conditions for uniqueness of solutions to the nonlinear problems are also provided.

Speed selection of wavefronts for lattice Lotka-Volterra competition system in a time periodic habitat

In this paper, the speed selection for the time periodic traveling wave solutions of a two-species competition lattice model of diffusive Lotka-Volterra type is investigated. By using the upper-lower solution method, an abstract result and several explicit sufficient conditions for linear selection are established. Moreover, a general condition for nonlinear selection is also obtained, which indicates that the minimal speed is nonlinearly selected if the system admits a lower solution with faster decay at the far end. Based on this result, some explicit conditions for nonlinear selection are found by constructing novel lower solutions.

Estimation Strategy Selection Is Modulated by Snapshot Emotional Priming, but Not Math Anxiety.

The present study explored the role of snapshot emotional priming and math anxiety in estimation strategy selection. Participants were asked to complete a two-digit multiplication estimation task (e.g., 34 × 67) under explicit (Experiment 1) and implicit (Experiment 2) snapshot emotional priming conditions by freely choosing to use DU (down-up, e.g., doing 30 × 70 = 2100 for 34 × 67) or UD (up-down, e.g., doing 40 × 60 = 2400 for 34 × 67) strategies to arrive as close as possible to the correct answer. In Experiment 1, individuals’ estimation performance was positively influenced by explicit happy priming (shorter RT (reaction time)), while not affected by explicit fear priming. In Experiment 2, individuals’ estimation ACC (accuracy) when using the UD strategy was negatively affected by both implicit happy and fear priming, but their RT when using DU and UD strategies was positively impacted by implicit happy priming. In both experiments, the correlations between math anxiety and estimation performance (ACC, RT, and strategy selection adaptivity) was not significant. The present study suggests that fear priming was not always detrimental to individuals’ estimation performance, and happy priming did not always universally improve individuals’ estimation performance. Additionally, estimation strategy selection was not influenced by math anxiety.

Decay Conditions for Antiplane Shear of a High-Contrast Multi-Layered Semi-Infinite Elastic Strip

The antiplane shear of a semi-infinite multi-layered elastic strip with traction free faces and edges subject to prescribed stress is studied. A high contrast is assumed in the stiffnesses of two types of homogeneous isotropic layers. Explicit conditions on the edge load are derived, ensuring the decay of stress components at the distance of order strip thickness. One of these conditions corresponds to the canonical Saint-Venant’s principle, manifesting the self-equilibrium of the load. The rest of the decay conditions consider the presence of high contrast and are of an asymptotic nature, in contrast to the exact former condition. The number of asymptotic conditions is the same as that of soft layers. An example of the implementation of the proposed decay conditions for calculating the solution for the interior (outside of a boundary layer zone) domain of a three-layered semi-strip, considering geometric asymmetry, is presented.

دور القاضي في إعمال الشرط الفاسخ والرقابة عليه خلال جائحة كورونا

Individuals are free to choose the contracts that they conclude based on the principle of the supremacy of the will that transcends in the field of contracts. which would include what it deems appropriate of terms in those contracts, without interference by the legislator, who grants them complete freedom in the same field. Among the common conditions in the field of contracts is the revocable or explicit condition as being clearly stated in the contract. It leads to the termination of the contract and the return of the contracting parties to the state they were in before the contract, taking into account the consequences and effects of the termination. We are in the process of explaining the judicial authority and its role in the event that the revocable condition is fulfilled, in light of the spread of the Corona epidemic (Covid 19), which stopped all life facilities and the accompanying general ban in most countries of the world. It is expected to intervene by the legislator to organize the proper legal description of the pandemic and controls or instructions to guide them in various legal fields, to stabilize transactions and achieve balance in contracts.

Quantitative statistical properties of two-dimensional partially hyperbolic systems

We study a class of two-dimensional partially hyperbolic systems, not necessarily skew products, in an attempt to develop a general theory. As a main result, we provide explicit conditions for the existence of finitely many physical measures (and SRB) and prove exponential decay of correlations for mixing measures. In addition, we obtain precise information on the regularity of such measures (they are absolutely continuous with respect to Lebesgue with density in some Sobolev space). To illustrate the scope of the theory, we show that our results apply to the case of fast-slow partially hyperbolic systems, and for such systems we obtain more precise results on the structure of the SRB measures.

Differential Operator Approximation Based Tightly Coupled Multiphysics Solver Using Cascaded Fourier Network

AbstractCalculating the unknown coupled multiphysics fields from the known boundary condition is of great significance in computational physics. Existing classical algorithms are usually time consuming and resource demanding. Explosive growth in deep learning (DL) has provided a substitutive way to accelerate the calculation process by fully making use of the parallel computing capability of the graphics processing unit. In this work, a cascaded DL framework is presented to compute the coupled multiphysics fields related to electrical potential, temperature, velocity, etc. The whole framework is comprised of an input module and several Fourier modules, which achieves to acquire the coupled fields from the explicit boundary conditions. Compared with conventional networks, the Fourier network emerges consistent average error among different resolutions which saves training costs. As a result, a fully trained network can obtain the expected physics fields in real time, offering rosy prospects for practical scenarios.

Scaling limits of branching random walks and branching-stable processes

AbstractBranching-stable processes have recently appeared as counterparts of stable subordinators, when addition of real variables is replaced by branching mechanisms for point processes. Here we are interested in their domains of attraction and describe explicit conditions for a branching random walk to converge after a proper magnification to a branching-stable process. This contrasts with deep results obtained during the past decade on the asymptotic behavior of branching random walks and which involve either shifting without rescaling, or demagnification.

Boundedness and asymptotic stability in a chemotaxis model with indirect signal production and logistic source

This article concerns the chemotaxis-growth system with indirect signal production $$\displaylines{ u_t=\Delta u-\nabla\cdot(u\nabla v)+\mu u(1-u),\quad x\in \Omega,\; t>0,\cr 0=\Delta v-v+w,\quad x\in \Omega,\; t>0,\cr w_t=-\delta w+u,\quad x\in\Omega,\; t>0, }$$ on a smooth bounded domain \(\Omega\subset \mathbb{R}^n\) (\(n\geq1\) with homogeneous Neumann boundary condition, where the parameters \(\mu, \delta>0\). It is proved that if \(n\leq 2\) and \(\mu>0\), for all suitably regular initial data, this model possesses a unique global classical solution which is uniformly-in-time bounded. While in the case \(n\geq 3\), we show that if \(\mu\) is sufficiently large, this system possesses a global bounded solution. Furthermore, the large time behavior and rates of convergence have also been considered under some explicit conditions.

Asymptotic behaviour of solutions to non-commensurate fractional-order planar systems

This paper is devoted to studying non-commensurate fractional order planar systems. Our contributions are to derive sufficient conditions for the global attractivity of non-trivial solutions to fractional-order inhomogeneous linear planar systems and for the Mittag-Leffler stability of an equilibrium point to fractional order nonlinear planar systems. To achieve these goals, our approach is as follows. Firstly, based on Cauchy’s argument principle in complex analysis, we obtain various explicit sufficient conditions for the asymptotic stability of linear systems whose coefficient matrices are constant. Secondly, by using Hankel type contours, we derive some important estimates of special functions arising from a variation of constants formula of solutions to inhomogeneous linear systems. Then, by proposing carefully chosen weighted norms combined with the Banach fixed point theorem for appropriate Banach spaces, we get the desired conclusions. Finally, numerical examples are provided to illustrate the effect of the main theoretical results.

Asymptotic accuracy of the saddlepoint approximation for maximum likelihood estimation

The saddlepoint approximation gives an approximation to the density of a random variable in terms of its moment generating function. When the underlying random variable is itself the sum of n unobserved i.i.d. terms, the basic classical result is that the relative error in the density is of order 1/n. If instead the approximation is interpreted as a likelihood and maximised as a function of model parameters, the result is an approximation to the maximum likelihood estimate (MLE) that can be much faster to compute than the true MLE. This paper proves the analogous basic result for the approximation error between the saddlepoint MLE and the true MLE: subject to certain explicit identifiability conditions, the error has asymptotic size O(1/n2) for some parameters and O(1/n3/2) or O(1/n) for others. In all three cases, the approximation errors are asymptotically negligible compared to the inferential uncertainty. The proof is based on a factorisation of the saddlepoint likelihood into an exact and approximate term, along with an analysis of the approximation error in the gradient of the log-likelihood. This factorisation also gives insight into alternatives to the saddlepoint approximation, including a new and simpler saddlepoint approximation, for which we derive analogous error bounds. As a corollary of our results, we also obtain the asymptotic size of the MLE approximation error when the saddlepoint approximation is replaced by the normal approximation.

Quantum transfer of interacting qubits

The transfer of quantum information between different locations is key to many quantum information processing tasks. Whereas, the transfer of a single qubit state has been extensively investigated, the transfer of a many-body system configuration has insofar remained elusive. We address the problem of transferring the state of n interacting qubits. Both the exponentially increasing Hilbert space dimension, and the presence of interactions significantly scale-up the complexity of achieving high-fidelity transfer. By employing tools from random matrix theory and using the formalism of quantum dynamical maps, we derive a general expression for the average and the variance of the fidelity of an arbitrary quantum state transfer protocol for n interacting qubits. Finally, by adopting a weak-coupling scheme in a spin chain, we obtain the explicit conditions for high-fidelity transfer of three and four interacting qubits.

The continuous delayed distribution problem

Nowadays, decision makers (DMs) at companies have access to extensive and accurate data, which means they have the opportunity to grow and improve if they use the latent potential effectively. We address the complex problem of optimizing decisions in a multi-period one-warehouse multi-retailer inventory system with stochastic continuous demand and an option of delayed distributions. At the beginning of each period, the DM determines each retailer’s target stock levels, as well as the number of items to be held back at a central location for later distribution(s). Such a policy offers partial inventory pooling through the holdback quantity. The decisions in each period are data-driven, i.e., made based on sales data available through an information system up to that point in time.We model the problem as a multi-stage stochastic program with recourse. For the general case, we develop a new recursive solution algorithm, which is based on subgradient optimization and an analysis of system dynamics. For the special case of two identical retailers and two periods, we provide explicit optimality conditions based on the subgradients. Using a large numerical study, we evaluate the performance of our proposed policy and compare it to two benchmark policies. We also demonstrate the impact of various problem parameters on the optimal solution and objective value.

Entropy stable and positivity preserving Godunov-type schemes for multidimensional hyperbolic systems on unstructured grid

This paper describes a novel subface flux-based Finite Volume (FV) method for discretizing multi-dimensional hyperbolic systems of conservation laws of general unstructured grids. The subface flux numerical approximation relies on the notion of simple Eulerian Riemann solver introduced in the seminal work [Gallice (2003) [18]]. The Eulerian Riemann solver is constructed from its Lagrangian counterpart by means of the Lagrange-to-Euler mapping. This systematic procedure ensures the transfer of good properties such as positivity preservation and entropy stability. In this framework, the conservativity and the entropy stability are no more locally face-based but result respectively from a node-based vectorial equation and a scalar inequation. The corresponding multi-dimensional FV scheme is characterized by an explicit time step condition ensuring positivity preservation and entropy stability. The application to gas dynamics provides an original multi-dimensional conservative and entropy-stable FV scheme wherein the numerical fluxes are computed through a nodal solver which is similar to the one designed for Lagrangian hydrodynamics. The robustness and the accuracy of this novel FV scheme are assessed through various numerical tests. We observe its insensitivity to the numerical pathologies that plague classical face-based contact discontinuity preserving FV formulations.

Bloch waves in high contrast electromagnetic crystals

Analytic representation formulas and power series are developed describing the band structure inside non-magnetic periodic photonic three-dimensional crystals made from high dielectric contrast inclusions. Central to this approach is the identification and utilization of a resonance spectrum for quasiperiodic source-free modes. These modes are used to represent solution operators associated with electromagnetic and acoustic waves inside periodic high contrast media. A convergent power series for the Bloch wave spectrum is recovered from the representation formulas. Explicit conditions on the contrast are found that provide lower bounds on the convergence radius. These conditions are sufficient for the separation of spectral branches of the dispersion relation for any fixed quasi-momentum.

Conditions on which cokriging does not do better than kriging

There is a vast literature on analyzing univariate spatial data by modeling, inference, and prediction in the past decades. While statistical modeling and inference with multivariate spatial data have been well developed, spatial prediction using multivariate spatial data called cokriging is relatively less investigated. Cokriging is usually considered to be superior to kriging, but there are not many theoretical studies that investigate how good cokriging is over kriging or when cokriging does not better than kriging. In this work, we provide explicit conditions on the covariance parameters and sampling schemes under an intrinsic coregionalization covariance model, with which cokriging does not better than kriging. Simulation studies and real data examples are also introduced to support our theoretical findings.