Narrow Results

The complex system has been widely applied in aerospace, chemical industry, manufacturing, military equipment and other fields. To ensure its safe and reliable operation, it is necessary for technicians to grasp the health state of the system effectively. However, if there are perturbations in the observation data, the evaluation result may be inaccurate. Besides, the effectiveness of evaluation result can be affected by perturbation, which means that the threshold of perturbation intensity should be determined. To solve these problems, in this paper, a new health evaluation method of complex systems is proposed based on the evidential reasoning (ER) rule by considering perturbations. First, the structure of the evaluation model is constructed. Second, an ER rule-based health evaluation model is proposed, and the idea of perturbation analysis is introduced for the robustness analysis of the model. Third, a parameter optimization model is established, and the upper bound of perturbation intensity is estimated accurately. The threshold can measure the effectiveness of the evaluation result and the anti-perturbation ability of the system in engineering practice. Finally, a case study of the WD615 model diesel engine is conducted to validate the effectiveness of the proposed method.

Given a $\sigma$-compact and metrizable locally compact abelian (LCA) group $G$, we give new perturbation results for Riesz bases for the matrix-valued function space $L^2(G,{ℂ}^{s\times r})$, $s$ and $r\in \mathbb{N}$.

In this paper, we introduce a row version of Kadison and Kastler's metric on the set of C*-subalgebras of . By showing C*-algebras have row length (in the sense of Pisier) of at most 2 we show that the row metric is equivalent to the original Kadison–Kastler metric. Ino and Watatani have recently proved that in certain circumstances sufficiently close intermediate C*-algebras occur as small unitary perturbations. By adjusting their arguments to work with the row metric we are able to obtain universal constants independent of inclusions.

Dynamical degradation is inevitable when chaotic map is implemented on a device with limited precision. To mitigate the insecurity caused by dynamic degradation, an effective method based on linear feedback and parameter perturbation with previous variables is proposed in this paper. We apply this method on the basis of the most widely used one-dimensional logistic map. Through the numerical experiments, this model is proved to have good chaotic characteristics and strong competitiveness. In addition, in order to verify the practicability of this method, we design a simple process pseudo-random bit generator (PRBG), whose security completely depends on the improved logistic map. The results of NIST experiment show that the generated pseudo-random sequence has ideal randomness.

Recently, tensor complementarity problems are becoming more and more popular. There are various literatures considering all kinds of properties of tensor complementarity problems, however, the stability of solutions and the continuity of solution maps are rarely mentioned so far. In the present paper, we study these two properties for tensor complementarity problems. We propose conditions under which the solutions of tensor complementarity problems are stable with the help of the tensor variational inequality or structured tensors. We also show that the solution maps of tensor complementarity problems are upper semicontinuous with the involved tensors being $R_0$-tensors. Meanwhile, we establish the relationship between the uniqueness of solutions and the continuity of solution maps of tensor complementarity problems.

In this paper a quantum super-Yang–Mills theory perturbed by dilaton-coupled scalars, is considered. The induced effective action for such a theory is calculated on a dilaton-gravitational background using the conformal anomaly found via AdS/CFT correspondence. Considering such an effective action (using the large N method) as a quantum correction to the classical gravity action with cosmological constant we study the effect from dilaton to the scale factor (which corresponds to the inflationary universe without dilaton). It is shown that, depending on the initial conditions for the dilaton, the dilaton may slow down, or accelerate, the inflation process. At late times, the dilaton is decaying exponentially. At the end of this work, we consider the question how the perturbation of the solution for the scale factor affects the stability of the solution for the equations of motion and therefore the stability of the Inflationary Universe, which could be eternal.

In this paper, the linear stability of static Mandal–Sengupta–Wadia (MSW) black holes in (2 + 1)-dimensional gravity against circularly symmetric perturbations is studied. Our analysis only applies to non-extremal configurations, thus leaving out the case of the extremal (2 + 1) MSW solution. The associated fields are assumed to have small perturbations in these static backgrounds. We then consider the dilaton equation and specific components of the linearized Einstein equations. The resulting effective Klein–Gordon equation is reduced to the Schrödinger-like wave equation with the associated effective potential. Finally, it is shown that MSW black holes are stable against the small time-dependent perturbations.

We obtain the wave equation of the perturbation theory governing massless fields of spin 0, 1/2, 1, 3/2 and 2 in accelerating Kerr–Newman–(anti-)de Sitter black holes. We show that the wave equation is separable and the radial and angular equations can both be transformed into Heun’s equation. We approximate Heun’s equation and analyze the solution of radial function near the event horizon. It is worth pointing out that all the field equations collapse to a unique equation which means it can provide a possible way for the analog research between the gravitational field and those other fields.

This work deals with a cosmological model consisting of cold dark matter and dark energy without any interaction. The study has been done both at the background level and at the perturbative level for the homogeneous and isotropic FLRW spacetime. By suitable transformation of the variables, the cosmic evolution equations are converted into an autonomous system. A discrete dynamical system analysis has been employed for cosmic inferences.

We derive explicit analytic expressions for the lateral force for two different configurations with corrugations, parallel plates and concentric cylinders. By making use of the multiple scattering formalism, we calculate the force for a scalar field under the influence of a delta-function potential that has sinusoidal dependence in one direction simulating the corrugations. By making a perturbative expansion in the amplitude of the corrugation we find the leading order for the corrugated concentric cylinders and the next-to-leading order for the corrugated parallel plates.

Experiments on neutrino oscillations have uncovered several small parameters, θ₁₃ being a prominent one. Others are the solar mass splitting vis-à-vis the atmospheric one and the deviation of θ₂₃ from maximal mixing. In this talk, (talk given at the International Conference on Massive Neutrinos, Singapore, 9–13 February 2015) we elaborate on a neutrino mass model based on the see-saw mechanism in which the mixing angles to start with are either vanishing (θ₁₃ and θ₁₂) or π/4 (θ₂₃). The atmospheric mass splitting is taken as a part of this initial structure but the solar splitting is absent. A perturbative contribution, originating from a Type-I see-saw, results in nonzero values of θ₁₃, θ₁₂, , and shifts θ₂₃ slightly from π/4, interrelating them all. The model incorporates CP-violation, the phase δ being close to 3π/2 for (a) quasidegeneracy or (b) inverted mass ordering. It will be put to test as the neutrino parameters get better determined.

In this paper, we explore the zeta function arising from a small perturbation on a surface of revolution and the effect of this on the functional determinant and on the change of the Casimir energy associated with the surface.

The steady velocities and volume flow rates (up to the second order) of an Eyring-fluids along the cross-section of an (approximated) wavy-rough nanotube are obtained analytically by using the verified fluid model and boundary perturbation method. Our results show that the wavy-roughness could tune the flow rate especially for larger forcing due to the larger surface-to-volume ratio and slip-velocity effect. The effects of wave number and slip length are also addressed.

A recently proposed third order + second order perturbation density functional theory (DFT) approach is made self-contained by using a virial pressure from the Ornstein–Zernike integral equation theory as input to determine the numerical value of an associated physical parameter. An exacting examination is formulated by applying the self-contained perturbation DFT approach to a short-range square well fluid of low temperatures subject to various external fields and comparing the theoretical results for density profiles to the corresponding grand canonical ensemble Monte Carlo simulation results. The comparison seems favorable for the third order + second order perturbation DFT approach as a self-contained and accurate predictive approach. It is surprisingly found that this self-contained third order + second order perturbation DFT approach is displayed outstandingly even if a deep SW perturbation term is being accounted for by a second order perturbation expansion. A discussion is presented about potential opportunity for this perturbation scheme.

The perturbation of a uniformly tiled resistor network by adding an edge (a resistor) to the network is considered. The two-point resistance on the perturbed tiling in terms of that on the perfect tiling is obtained using Green’s function. Some theoretical results are presented for an infinite modified square lattice. These results are confirmed experimentally by constructing an actual resistor lattice of size 13 × 13.

In this paper, the problem of finding the velocity profile of fully developed laminar flows through ducts of arbitrary cross-sections is investigated. The method which is used is based on a perturbative approach, although some nonperturbative exact results are also obtained. The main quantity which is addressed is the specific conductivity. This is a dimensionless quantity, which is independent of the size of the duct and the properties of the fluid, depending on only the shape of the duct. Some examples are studied is detail, for which the numerical values of the specific conductivity are determined, in the form of perturbative or exact results.

In this paper, the dust acoustic wave is studied in conditions where the dust temperature is not constant. This model includes negatively charged dust particles and thermal ions. The reductive perturbation technique is used and the new point in this study is the nonuniformity of the plasma temperature. The nonconstancy of the temperature is entered as a first-order perturbation in the calculations, and finally the modified Korteweg–de Vries (mKdV) equation is derived. The solution of the modified KdV equation clarifies the change in soliton shape of the wave when it moves in the perturbation plasma. We show how the soliton wave undergoes deformation and amplitude reduction during propagation when it encounters a region with a different temperature. The output of this research can be effective to better understand the wave behavior in a real plasma with nonuniform temperature.

This paper is an extension of the brief study by Sarah Douglas et al. [Phys. Plasmas20 (2013) 114504] where in the study a sinusoidal perturbation of the heating power has been studied. In this paper a stepwise increase of the heating power and its influence on the $L$–$H$ transition are studied. Using a function, $Atanh(t/T)$ for the transition of input heating power for tokamak plasmas, i.e. the addition of the perturbation, $Atanh(t/T)$, to constant power $q_0$ is shown to promote the confinement, leading to the $L$–$H$ transition at a lower value of $q_0$, as compared to the case of constant $q_0$ without the $Atanh(t/T)$ perturbation. It is seen that the input heating power $Q$ that consists of constant part $q_0$ in addition to a function $Atanh(t/T)$ provides the $L$–$H$ transition for relatively small $A$ and much wider range values of $1/T$ as compared to Sarah Douglas et al. [Phys. Plasmas20 (2013) 114504].

This research paper is dedicated to the investigation of the optical soliton solutions with the power law of self-phase modulation (SPM) and the third-order dispersion (TOD), completely neglecting the chromatic dispersion (CD). The aim is focused on two main points. First, obtaining the straddled soliton solution which permits us to have bright and singular soliton by applying the new Kudryashov (nKM) scheme which was recently introduced as a simple, effective, and reliable method. Second, to observe the influences of the TOD, SPM, and inter-modal dispersion (IMD) on pure-cubic optical soliton dynamics in the absence of the CD.

Neural network technology has achieved good results in many tasks, such as image classification. However, for some input examples of neural networks, after the addition of designed and imperceptible perturbations to the examples, these adversarial examples can change the output results of the original examples. For image classification problems, we derive low-dimensional attack perturbation solutions on multidimensional linear classifiers and extend them to multidimensional nonlinear neural networks. Based on this, a new adversarial example generation algorithm is designed to modify a specified number of pixels. The algorithm adopts a greedy iterative strategy, and gradually iteratively determines the importance and attack range of pixel points. Finally, experiments demonstrate that the algorithm-generated adversarial example is of good quality, and the effects of key parameters in the algorithm are also analyzed.