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This paper investigates the one-bit function perturbation (OBFP) impact on the robust set stability of Boolean networks with disturbances (DBNs). Firstly, the dynamics of these networks are converted into the algebraic forms utilizing the semi-tensor product (STP) method. Secondly, OBFP’s impact on the robust set stability of DBNs is divided into two situations. Then, by constructing a state set and defining an index vector, several necessary and sufficient conditions to guarantee that a DBN under OBFP can stay robust set stable unchanged are provided. Finally, a biological example is proposed to demonstrate the effectiveness of the obtained theoretical results.

In this paper, we are interested with a new class of perturbation named the Φ-perturbation function which allowing us to derive some advances on the semi-Browder and Browder operators theory acting in Banach spaces. More precisely, sufficient conditions are investigated to reach the stability analysis of perturbed semi-Browder and Browder operators via such approach of perturbation. Our mainly results are subsequently used to develop a new characterization of Browder’s spectra of linear operators on the Φ-perturbation function based approach. Furthermore, illustrative examples are presented to enrich the validity of our theoretical results.

We examine in this paper the stability analysis in f ( R , T , R μ ν T μ ν ) modified gravity, where R and T are the Ricci scalar and the trace of the energy-momentum tensor, respectively. By considering the flat Friedmann universe, we obtain the corresponding generalized Friedmann equations and we evaluate the geometrical and matter perturbation functions. The stability is developed using the de Sitter and power-law solutions. We search for application the stability of two particular cases of f ( R , T , R μ ν T μ ν ) model by solving numerically the perturbation functions obtained.

The convergence rate of the augmented Lagrangian method (ALM) for solving the nonlinear semidefinite optimization problem is studied. Under the Jacobian uniqueness conditions, when a multiplier vector (π,Y) and the penalty parameter σ are chosen such that σ is larger than a threshold σ*>0 and the ratio ∥(π,Y)−(π*,Y*)∥/σ is small enough, it is demonstrated that the convergence rate of the augmented Lagrange method is linear with respect to ∥(π,Y)−(π*,Y*)∥ and the ratio constant is proportional to 1/σ, where (π*,Y*) is the multiplier corresponding to a local minimizer. Furthermore, by analyzing the second-order derivative of the perturbation function of the nonlinear semidefinite optimization problem, we characterize the rate constant of local linear convergence of the sequence of Lagrange multiplier vectors produced by the augmented Lagrange method. This characterization shows that the sequence of Lagrange multiplier vectors has a Q-linear convergence rate when the sequence of penalty parameters {σk} has an upper bound and the convergence rate is superlinear when {σk} is increasing to infinity.

This paper studies the robust stabilization of impulsive Boolean control networks (IBCNs) with function perturbation. A Boolean control network (BCN) with a state-dependent impulsive sequence is converted to an equivalent BCN by the semi-tensor product method. Based on the equivalence of stabilization between the IBCN and the corresponding BCN, several criteria are proposed for the robust stabilization of IBCNs. Furthermore, when the IBCN is not robustly stabilizable after the function perturbation, an algorithm is presented to modify the control or the impulse-triggered set. Finally, an example is given to verify the obtained results.

This paper is concerned with a unified duality theory for a constrained extremum problem. Following along with the image space analysis, a unified duality scheme for a constrained extremum problem is proposed by virtue of the class of regular weak separation functions in the image space. Some equivalent characterizations of the zero duality property are obtained under an appropriate assumption. Moreover, some necessary and sufficient conditions for the zero duality property are also established in terms of the perturbation function. In the accompanying paper, the Lagrange-type duality, Wolfe duality and Mond–Weir duality will be discussed as special duality schemes in a unified interpretation. Simultaneously, three practical classes of regular weak separation functions will be also considered.

In this paper, a class of smooth penalty functions is proposed for constrained optimization problem. It is put forward based on L p , a smooth function of a class of exact penalty function ℓ p p ∈ ( 0 , 1 ] . Based on the class of penalty functions, a penalty algorithm is presented. Under the very weak condition, a perturbation theorem is set up. The global convergence of the algorithm is derived. This result generalizes some existing conclusions. Finally, numerical experiments on two examples demonstrate the effectiveness and efficiency of our algorithm.

The asymptotic behavior of the secular perturbation function expanded in a power series in μ, the ratio of the semimajor axes of the massless point (asteroid) and Jupiter, is studied in the restricted spatial circular three-body problem. It is assumed that (internal case). A new derivation of the expansion of a secular perturbation function into a power series with coefficients expressed through Gauss and Clausen functions is described based on Parseval’s formula. For different values of μ at fixed values of the Lidov-Kozai constant, the radius of convergence of the reduced series, the areas of convergence and divergence are described in the plane of osculating elements e , ω. It is shown that power series is asymptotic in the sense of Poincaré in divergence regions, and that truncating the series after a 70 number of terms provides an high value approximation to a secular perturbation function. It is shown that the asymptotic properties of the series deteriorate on the nonanalyticity curves of secular perturbation function and completely disappear in a small neighborhood of . The asymptotic nature of the series allows, using ordinary methods of perturbation theory, to study the evolution of Keplerian orbital elements for all values of from the interval [0, 1), excluding the case .

This paper develops a parameter tuning method for solving the set restabilization problem of perturbed Boolean control networks (BCNs). First, the absorbable attractor, which we previously proposed, is recalled. Based on the relationship between attractors, a necessary and sufficient restabilizability criterion is derived. This criterion is used to check whether a perturbed BCN can be stabilized to the original target set by modifying the least number of parameters to the old controller. Furthermore, a constructive method for fine-tuning the old controller is provided if the criterion condition derived above is satisfied. Compared with the existing relevant results, ours have clear advantages, since they can address the set restabilization problem of BCNs subject to multi-column function perturbations, which has not been solved yet. Finally, two examples are employed to show the effectiveness and advantages of our results.

This article uses the sailfish outline as an airfoil profile to create a dual vertical-axis water turbine model for capturing wave and tidal current energy. A parametric water turbine model is built with the shape function perturbation and characteristic parameter description methods. Optimized by the multi-island genetic algorithm on the Isight platform, a CNC sample of the optimized model is made. Its torque and pressure are measured in a wind tunnel and compared with CFD numerical analysis results. The results show small differences between the numerical and experimental results. Both indicate that the relevant performance parameters of the turbine improved after optimization. During constant flow velocity measurement, the optimized axial-flow turbine has a pressure increase of 55% and a torque increase of 40%, while for the centrifugal turbine, the pressure increases by 60% and the torque by 12.5%. During constant rotational speed measurement, the axial-flow turbine’s pressure increases by 16.7%, with an unobvious torque increase. The Q-criterion diagram shows more vortices after optimization. This proves the method can quickly and effectively optimize the dual vertical-axis water turbine.