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Flexibility of statistical properties for smooth systems satisfying the central limit theorem
We exhibit new classes of smooth systems which satisfy the Central Limit Theorem (CLT) and have (at least) one of the following properties:
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Probabilistic stability analysis of tunnel roof in two-layer soil mass combining upper bound theorem and response surface method
In this work, with reference to the nonlinear Mohr–Coulomb failure criterion and upper bound theorem of limit analysis, two-dimensional (2D) collapse...
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Upper Bound Limit Analysis for the Stability of Elliptical Tunnels Based on the Node-Based Smoothed Finite Element Method and Second Order Cone Programming
The stability of 2D elliptical tunnels in cohesive-frictional soils are studied by using upper bound approach of limit analysis based on smoothed...
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Functional Central Limit Theorem via Nonstationary Projective Conditions
In this paper we survey some recent progress on the Gaussian approximation for nonstationary dependent structures via martingale methods. First, we...
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Example of a Differential System with Complete Perron and Upper-Limit Instability but Massive Partial Stability
AbstractIt is constructively proved that the complete Perron and upper-limit instability (in contrast to the Lyapunov instability) of a...
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Stability of Gypseous Soil Slopes Using the Upper Bound Theorem of Limit Analysis
The upper bound theorem of limit analysis is utilized to study the stability of gypseous soil slopes. A simplified equation is proposed to estimate...
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Frobenius’ Theorem
This chapter focuses on the Frobenius theorem, which plays a major role in economics. This chapter, explicitly states Frobenius theorem when extended...
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Central limit theorem and cohomological equation on homogeneous spaces
The dynamics of one-parameter diagonal group actions on finite volume homogeneous spaces has a partially hyperbolic feature. In this paper we extend...
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Estimates of the Rate of Convergence in the Limit Theorem for Negative Binomial Random Sums
New practically applicable estimates are constructed for the accuracy of approximation to the distributions of negative binomial random sums in the...
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Central limit theorem for linear processes generated by IID random variables under the sub-linear expectation
In this paper, we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently...
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Face Stability of Tunnel in Multi-stratum: Limit Analysis and Numerical Simulation
Under multiple-stratum conditions, the stability of the tunnel face must be maintained by a reasonable support pressure. Through the combination of...
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A fixed point theorem for measurable selection valued correspondences induced by upper Caratheodory correspondences
We show that any measurable selection valued correspondence induced by the composition of an m -tuple of real-valued Caratheodory functions with an...
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A simple characterization of the existence of upper semicontinuous order-preserving functions
We introduce an upper semicontinuity condition concerning a not necessarily total preorder on a topological space, namely strong upper semicontinuity ,...
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The limit cycle bifurcations of a whirling pendulum with piecewise smooth perturbations
This paper deals with the problem of limit cycles for the whirling pendulum equation ẋ = y, ẏ = sin x (cos x − r ) under piecewise smooth perturbations...
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A Limit Theorem on Fuzzy Set-Valued Random Variables in Fuzzy Metric Space
In this paper, we shall give the definition of fuzzy metric for fuzzy sets and discuss its properties. Then we prove a limit theorem of compact fuzzy...
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Upper Domination Parameters
In this chapter, we study the upper core domination parameters, namely the upper domination number, the upper total domination number, and the...