A Study on Cooperative Continuous Static Games without Differentiability under Fuzzy Environment

In this study, a fuzzy cooperative continuous static game (PQFCCSG) with n players having fuzzy parameters in all of the cost functions and the right- hand-side of constraints is characterized. Their fuzzy parameters are represented by piecewise quadratic fuzzy numbers. The α-pareto optimal solution concept is specified. In addition, the stability sets of the first and second kind without differentiability are conceptualized and established. An illustrated numerical example is discussed for proper understanding and interpretation of the proposed concept.

Linear and brute force stability of orthogonal moment multiple-relaxation-time lattice Boltzmann methods applied to homogeneous isotropic turbulence

Multiple-relaxation-time (MRT) lattice Boltzmann methods (LBM) based on orthogonal moments exhibit lattice Mach number dependent instabilities in diffusive scaling. The present work renders an explicit formulation of stability sets for orthogonal moment MRT LBM. The stability sets are defined via the spectral radius of linearized amplification matrices of the MRT collision operator with variable relaxation frequencies. Numerical investigations are carried out for the three-dimensional Taylor–Green vortex benchmark at Reynolds number 1600. Extensive brute force computations of specific relaxation frequency ranges for the full test case are opposed to the von Neumann stability set prediction. Based on that, we prove numerically that a scan over the full wave space, including scaled mean flow variations, is required to draw conclusions on the overall stability of LBM in turbulent flow simulations. Furthermore, the von Neumann results show that a grid dependence is hardly possible to include in the notion of linear stability for LBM. Lastly, via brute force stability investigations based on empirical data from a total number of 22 696 simulations, the existence of a deterministic influence of the grid resolution is deduced. This article is part of the theme issue ‘Progress in mesoscale methods for fluid dynamics simulation’.

The IκB-protein BCL-3 controls Toll-like receptor-induced MAPK activity by promoting TPL-2 degradation in the nucleus

Proinflammatory responses induced by Toll-like receptors (TLRs) are dependent on the activation of the NF-ĸB and mitogen-activated protein kinase (MAPK) pathways, which coordinate the transcription and synthesis of proinflammatory cytokines. We demonstrate that BCL-3, a nuclear IĸB protein that regulates NF-ĸB, also controls TLR-induced MAPK activity by regulating the stability of the TPL-2 kinase. TPL-2 is essential for MAPK activation by TLR ligands, and the rapid proteasomal degradation of active TPL-2 is a critical mechanism limiting TLR-induced MAPK activity. We reveal that TPL-2 is a nucleocytoplasmic shuttling protein and identify the nucleus as the primary site for TPL-2 degradation. BCL-3 interacts with TPL-2 and promotes its degradation by promoting its nuclear localization. As a consequence,Bcl3−/−macrophages have increased TPL-2 stability following TLR stimulation, leading to increased MAPK activity and MAPK-dependent responses. Moreover, BCL-3–mediated regulation of TPL-2 stability sets the MAPK activation threshold and determines the amount of TLR ligand required to initiate the production of inflammatory cytokines. Thus, the nucleus is a key site in the regulation of TLR-induced MAPK activity. BCL-3 links control of the MAPK and NF-ĸB pathways in the nucleus, and BCL-3–mediated TPL-2 regulation impacts on the cellular decision to initiate proinflammatory cytokine production in response to TLR activation.

On stability sets for numerical discretizations of neutral delay differential equations

The paper discusses the -method discretization of the neutral delay differential equation y'(t) = ay (t) + by (t - τ) + cy' (t - τ), t > 0, where a, b, c are real constant coefficients and is a positive real lag. Using recent developments on stability of appropriate delay difference equations we give a complete description of stability sets for this discretization. Some of their properties and related comparisons with the stability set for the underlying neutral differential equation are discussed as well.

Asymptotic Stability Of Dynamic Equations With Two Fractional Terms: Continuous Versus Discrete Case

The paper discusses asymptotic stability conditions for the linear fractional difference equation∇with real coefficients a, b and real orders α > β > 0 such that α/β is a rational number. For given α, β, we describe various types of discrete stability regions in the (a, b)-plane and compare them with the stability regions recently derived for the underlying continuous patternDinvolving two Caputo fractional derivatives. Our analysis shows that discrete stability sets are larger and their structure much more rich than in the case of the continuous counterparts.