A novel method for simulating nuclear explosion with chemical explosion to form an approximate plane wave: Field test and numerical simulation

A nuclear explosion in the rock mass medium can produce strong shock waves,seismic shocks,and other destructive effects,which can cause extreme damage to the underground protection infrastructures.With the increase in nuclear explosion power,underground protection engineering enabled by explosion-proof impact theory and technology ushered in a new challenge.This paper proposes to simulate nuclear explosion tests with on-site chemical explosion tests in the form of multi-hole explosions.First,the mechanism of using multi-hole simultaneous blasting to simulate a nuclear explosion to generate approximate plane waves was analyzed.The plane pressure curve at the vault of the underground protective tunnel under the action of the multi-hole simultaneous blasting was then obtained using the impact test in the rock mass at the site.According to the peak pressure at the vault plane,it was divided into three regions:the stress superposition region,the superposition region after surface reflection,and the approximate plane stress wave zone.A numerical simulation approach was developed using PFC and FLAC to study the peak particle velocity in the surrounding rock of the underground protective cave under the action of multi-hole blasting.The time-history curves of pressure and peak pressure partition obtained by the on-site multi-hole simultaneous blasting test and numerical simulation were compared and analyzed,to verify the correctness and rationality of the formation of an approximate plane wave in the simulated nuclear explosion.This comparison and analysis also provided a theoretical foundation and some research ideas for the ensuing study on the impact of a nuclear explosion.

Approximately Bi-Similar Symbolic Model for Discretetime Interconnected Switched System

Dear Editor,This letter concerns the development of approximately bi-similar symbolic models for a discrete-time interconnected switched system(DT-ISS).The DT-ISS under consideration is formed by connecting multiple switched systems known as component switched systems(CSSs).Although the problem of constructing approximately bi-similar symbolic models for DT-ISS has been addressed in some literature,the previous works have relied on the assumption that all the subsystems of CSSs are incrementally input-state stable.

A signal coordination algorithm for two adjacent intersections based on approximate dynamic programming

To reduce vehicle emissions in road networks, a new signal coordination algorithm based on approximate dynamic programming （ADP） is developed for two intersections. Taking the Jetta car as an experimental vehicle, field tests are conducted in Changchun Street of Changchun city and vehicle emission factors in complete stop and uniform speed states are collected. Queue lengths and signal light colors of approach lanes are selected as state variables, and green switch plans are selected as decision variables of the system. Then the calculation model of the optimization index during the planning horizon is developed based on the basis function method of the ADP. The temporal-difference algorithm is employed to update the weighting factor vector of the approximate function. Simulations are conducted in Matlab and the results show that the established algorithm outperforms the conventional coordination algorithm in reducing vehicle emissions by 8.2%. Sensitive analysis of the planning horizon length on the evaluation index is also conducted and the statistical results show that the optimal length of the planning horizon is directly proportional to the traffic load.

APPROXIMATE QUERY AND CALCULATION OF RNN_k BASED ON VORONOI CELL

Reverse k nearest neighbor （RNNk） is a generalization of the reverse nearest neighbor problem and receives increasing attention recently in the spatial data index and query. RNNk query is to retrieve all the data points which use a query point as one of their k nearest neighbors. To answer the RNNk of queries efficiently, the properties of the Voronoi cell and the space-dividing regions are applied. The RNNk of the given point can be found without computing its nearest neighbors every time by using the rank Voronoi cell. With the elementary RNNk query result, the candidate data points of reverse nearest neighbors can he further limited by the approximation with sweepline and the partial extension of query region Q. The approximate minimum average distance （AMAD） can be calculated by the approximate RNNk without the restriction of k. Experimental results indicate the efficiency and the effectiveness of the algorithm and the approximate method in three varied data distribution spaces. The approximate query and the calculation method with the high precision and the accurate recall are obtained by filtrating data and pruning the search space.

Comparison of two kinds of approximate proximal point algorithms for monotone variational inequalities

This paper proposes two kinds of approximate proximal point algorithms （APPA） for monotone variational inequalities, both of which can be viewed as two extended versions of Solodov and Svaiter＇s APPA in the paper ＂Error bounds for proximal point subproblems and associated inexact proximal point algorithms＂ published in 2000. They are both prediction- correction methods which use the same inexactness restriction; the only difference is that they use different search directions in the correction steps. This paper also chooses an optimal step size in the two versions of the APPA to improve the profit at each iteration. Analysis also shows that the two APPAs are globally convergent under appropriate assumptions, and we can expect algorithm 2 to get more progress in every iteration than algorithm 1. Numerical experiments indicate that algorithm 2 is more efficient than algorithm 1 with the same correction step size,

APPROXIMATE DUALITY OF g-FRAMES IN HILBERT SPACES

In this article, we introduce and characterize approximate duality for g-frames. We get some important properties and applications of approximate duals. We also obtain some new results in approximate duality of frames, and generalize some of the known results in approximate duality of frames to g-frames. We also get some results for fusion frames, and perturbation of approximately dual g-frames. We show that approximate duals are stable under small perturbations and they are useful for erasures and reconstruction.

Application of approximate entropy on dynamic characteristics of epileptic absence seizure

Electroencephalogram signals are time-varying complex electrophysiological signals. Existing studies show that approximate entropy, which is a nonlinear dynamics index, is not an ideal method for electroencephalogram analysis. Clinical electroencephalogram measurements usually contain electrical interference signals, creating additional challenges in terms of maintaining robustness of the analytic methods. There is an urgent need for a novel method of nonlinear dynamical analysis of the electroencephalogram that can characterize seizure-related changes in cerebral dynamics. The aim of this paper was to study the fluctuations of approximate entropy in preictal, ictal, and postictal electroencephalogram signals from a patient with absence seizures, and to improve the algorithm used to calculate the approximate entropy. The approximate entropy algorithm, especially our modified version, could accurately describe the dynamical changes of the brain during absence seizures. We could also demonstrate that the complexity of the brain was greater in the normal state than in the ictal state. The fluctuations of the approximate entropy before epileptic seizures observed in this study can form a good basis for further study on the prediction of seizures with nonlinear dynamics.

Operators of Approximations and Approximate Power Set Spaces

Boundary inner and outer operators are introduced, and union, intersection, complement operators of approximations are redefined. The approximation operators have a good property of maintaining union, intersection, complement operators, so the rough set theory has been enriched from the operator-oriented and set-oriented views. Approximate power set spaces are defined, and it is proved that the approximation operators are epimorphisms from power set space to approximate power set spaces. Some basic properties of approximate power set space are got by epimorphisms in contrast to power set space.

Three-dimensional gravity inversion based on sparse recovery iteration using approximate zero norm

This research proposes a novel three-dimensional gravity inversion based on sparse recovery in compress sensing. Zero norm is selected as the objective function, which is then iteratively solved by the approximate zero norm solution. The inversion approach mainly employs forward modeling; a depth weight function is introduced into the objective function of the zero norms. Sparse inversion results are obtained by the corresponding optimal mathematical method. To achieve the practical geophysical and geological significance of the results, penalty function is applied to constrain the density values. Results obtained by proposed provide clear boundary depth and density contrast distribution information. The method's accuracy, validity, and reliability are verified by comparing its results with those of synthetic models. To further explain its reliability, a practical gravity data is obtained for a region in Texas, USA is applied. Inversion results for this region are compared with those of previous studies, including a research of logging data in the same area. The depth of salt dome obtained by the inversion method is 4.2 km, which is in good agreement with the 4.4 km value from the logging data. From this, the practicality of the inversion method is also validated.

A new method to obtain approximate symmetry of nonlinear evolution equation from perturbations

A novel method for obtaining the approximate symmetry of a partial differential equation with a small parameter is introduced. By expanding the independent variable and the dependent variable in the small parameter series, we obtain more affluent approximate symmetries. The method is applied to two perturbed nonlinear partial differential equations and new approximate solutions are derived.

Using approximate dynamic programming for multi-ESM scheduling to track ground moving targets

This paper researches the adaptive scheduling problem of multiple electronic support measures(multi-ESM) in a ground moving radar targets tracking application. It is a sequential decision-making problem in uncertain environment. For adaptive selection of appropriate ESMs, we generalize an approximate dynamic programming(ADP) framework to the dynamic case. We define the environment model and agent model, respectively. To handle the partially observable challenge, we apply the unsented Kalman filter(UKF) algorithm for belief state estimation. To reduce the computational burden, a simulation-based approach rollout with a redesigned base policy is proposed to approximate the long-term cumulative reward. Meanwhile, Monte Carlo sampling is combined into the rollout to estimate the expectation of the rewards. The experiments indicate that our method outperforms other strategies due to its better performance in larger-scale problems.

Approximate solutions of the Alekseevskii–Tate model of long-rod penetration

The Alekseevskii–Tate model is the most successful semi-hydrodynamic model applied to long-rod penetration into semi-infinite targets. However, due to the nonlinear nature of the equations, the rod(tail) velocity, penetration velocity, rod length, and penetration depth were obtained implicitly as a function of time and solved numerically By employing a linear approximation to the logarithmic relative rod length, we obtain two sets of explicit approximate algebraic solutions based on the implicit theoretica solution deduced from primitive equations. It is very convenient in the theoretical prediction of the Alekseevskii–Tate model to apply these simple algebraic solutions. In particular, approximate solution 1 shows good agreement with the theoretical(exact) solution, and the first-order perturbation solution obtained by Walters et al.(Int. J. Impac Eng. 33:837–846, 2006) can be deemed as a special form of approximate solution 1 in high-speed penetration. Meanwhile, with constant tail velocity and penetration velocity approximate solution 2 has very simple expressions, which is applicable for the qualitative analysis of long-rod penetration. Differences among these two approximate solutions and the theoretical(exact) solution and their respective scopes of application have been discussed, and the inferences with clear physical basis have been drawn. In addition, these two solutions and the first-order perturbation solution are applied to two cases with different initial impact velocity and different penetrator/target combinations to compare with the theoretical(exact) solution. Approximate solution 1 is much closer to the theoretical solution of the Alekseevskii–Tate model than the first-order perturbation solution in both cases, whilst approximate solution 2 brings us a more intuitive understanding of quasi-steady-state penetration.

EXTENSION OF CONVEX MODELS AND ITS IMPROVEMENT ON THE APPROXIMATE SOLUTION

In this paper, by means of combining non-probabilistic convex modeling with perturbation theory, an improvement is made on the first order approximate solution in convex models of uncertainties. Convex modeling is extended to largely uncertain and non-convex sets of uncertainties and the combinational convex modeling is developed. The presented method not only extends applications of convex modeling, but also improves its accuracy in uncertain problems and computational efficiency. The numerical example illustrates the efficiency of the proposed method.

An Approximate Analytical Propagation Formula for Gaussian Beams through a Cat-Eye Optical Lens under Large Incidence Angle Condition

Based on the generalized diffraction integral formula and the idea that the angle misalignment of the cat-eye optical lens can be transformed into the displacement misalignment,an approximate analytical propagation formula for Gaussian beams through a cat-eye optical lens under large incidence angle condition is derived.Numerical results show that the diffraction effect of the apertures of the cat-eye optical lens becomes stronger along with the increase in incidence angle.The results are also compared with those from using an angular spectrum diffraction integral and experiment to illustrate the applicability and validity of our theoretical formula.It is shown that the approximate extent is good enough for the application of a cat-eye optical lens with a radius of 20 mm and a propagation distance of 100 m,and the approximate extent becomes better along with the increase in the radius of the cat-eye optical lens and the propagation distance.

EXISTENCE OF SOLUTION AND APPROXIMATE CONTROLLABILITY OF A SECOND-ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATION WITH STATE DEPENDENT DELAY

This paper has two sections which deals with a second order stochastic neutral partial differential equation with state dependent delay. In the first section the existence and uniqueness of mild solution is obtained by use of measure of non-compactness. In the second section the conditions for approximate controllability are investigated for the distributed second order neutral stochastic differential system with respect to the approximate controllability of the corresponding linear system in a Hilbert space. Our method is an extension of co-author N. Sukavanam’s novel approach in [22]. Thereby, we remove the need to assume the invertibility of a controllability operator used by authors in [5], which fails to exist in infinite dimensional spaces if the associated semigroup is compact. Our approach also removes the need to check the invertibility of the controllability Gramian operator and associated limit condition used by the authors in [20], which are practically difficult to verify and apply. An example is provided to illustrate the presented theory.

Fully implicational methods for approximate reasoning based on interval-valued fuzzy sets

The aim of this paper is to discuss the approximate rea- soning problems with interval-valued fuzzy environments based on the fully implicational idea. First, this paper constructs a class of interval-valued fuzzy implications by means of a type of impli- cations and a parameter on the unit interval, then uses them to establish fully implicational reasoning methods for interval-valued fuzzy modus ponens （IFMP） and interval-valued fuzzy modus tel- lens （IFMT） problems. At the same time the reversibility properties of these methods are analyzed and the reversible conditions are given. It is shown that the existing unified forms of α-triple I （the abbreviation of triple implications） methods for FMP and FMT can be seen as the particular cases of our methods for IFMP and IFMT.

Approximate Controllability of Second-Order Neutral Stochastic Differential Equations with Infinite Delay and Poisson Jumps

The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the possibility of sudden price variations （jumps） resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the Poisson random measure. Many popular economic and financial models described by stochastic differential equations with Poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and Poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory.

Dynamic characteristics of resonant gyroscopes study based on the Mathieu equation approximate solution

Dynamic characteristics of the resonant gyroscope are studied based on the Mathieu equation approximate solution in this paper.The Mathieu equation is used to analyze the parametric resonant characteristics and the approximate output of the resonant gyroscope.The method of small parameter perturbation is used to analyze the approximate solution of the Mathieu equation.The theoretical analysis and the numerical simulations show that the approximate solution of the Mathieu equation is close to the dynamic output characteristics of the resonant gyroscope.The experimental analysis shows that the theoretical curve and the experimental data processing results coincide perfectly,which means that the approximate solution of the Mathieu equation can present the dynamic output characteristic of the resonant gyroscope.The theoretical approach and the experimental results of the Mathieu equation approximate solution are obtained,which provides a reference for the robust design of the resonant gyroscope.

Sampled-data Observer Design for a Class of Stochastic Nonlinear Systems Based on the Approximate Discrete-time Models

In this paper,we studied the approximate sampleddata observer design for a class of stochastic nonlinear systems.Euler-Maruyama approximation was investigated in this paper because it is the basis of other higher precision numerical methods,and it preserves important structures of the nonlinear systems.Also,the form of Euler-Maruyama model is simple and easy to be calculated.The results provide a reference for sampled-data observer design method for such stochastic nonlinear systems,and may be useful to many practical control applications,such as tracking control in mechanical systems.And the effectiveness of the approach is demonstrated by a simulation example.

Approximate trace and singleton failures equivalences for transition systems

Established system equivalences for transition systems, such as trace equivalence and failures equivalence, require the ob- servations to be exactly identical. However, an accurate measure- ment is impossible when interacting with the physical world, hence exact equivalence is restrictive and not robust. Using Baire met- ric, a generalized framework of transition system approximation is proposed by developing the notions of approximate language equivalence and approximate singleton failures （SF） equivalence. The framework takes the traditional exact equivalence as a special case. The approximate language equivalence is coarser than the approximate Slc equivalence, just like the hierarchy of the exact ones. The main conclusion is that the two approximate equiva- lences satisfy the transitive property, consequently, they can be successively used in transition system approximation.