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991.
We investigate the deductive strength of statements concerning vector spaces over specific fields in the hierarchy of various choice principles.  相似文献   
992.
Pengjian Shang  Aijing Lin 《Physica A》2009,388(5):720-726
The Detrended Fluctuation Analysis (DFA) and its extensions (MF-DFA) have been used extensively to determine possible long-range correlations in self-affine signals. However, recent studies have reported the susceptibility of DFA to trends which give rise to spurious crossovers and prevent reliable estimation of the scaling exponents. In this study, a smoothing algorithm based on the Chaotic Singular-Value Decomposition (CSVD) is proposed to minimize the effect of exponential trends and distortion in the log-log plots obtained by DFA techniques. The effectiveness of the technique is demonstrated on monofractal and multifractal data corrupted with exponential trends.  相似文献   
993.
994.
We are concerned with the existence of global in time solution for a semilinear heat equation with exponential nonlinearity
(P){?tu=Δu+eu,xRN,t>0,u(x,0)=u0(x),xRN,
where u0 is a continuous initial function. In this paper, we consider the case where u0 decays to ?∞ at space infinity, and study the optimal decay bound classifying the existence of global in time solutions and blowing up solutions for (P). In particular, we point out that the optimal decay bound for u0 is related to the decay rate of forward self-similar solutions of ?tu=Δu+eu.  相似文献   
995.
Let At=stF(Xs?,Xs) be a purely discontinuous additive functional of a subordinate Brownian motion X=(Xt,Px). We give a sufficient condition on the non-negative function F that guarantees that finiteness of A implies finiteness of its expectation. This result is then applied to study the relative entropy of Px and the probability measure induced by a purely discontinuous Girsanov transform of the process X. We prove these results under the weak global scaling condition on the Laplace exponent of the underlying subordinator.  相似文献   
996.
997.
A strongly damped wave equation involving a delay of neutral type in its second order derivative is considered. It is proved that solutions decay to zero exponentially despite the fact that delays are, in general, sources of instability.  相似文献   
998.
It is proved that every $(Q,T)$-affine-periodic differential equation has a $(Q,T)$-affine-periodic solution if the corresponding homogeneous linear equation admits exponential dichotomy or exponential trichotomy. This kind of ``periodic'' solutions might be usual periodic or quasi-periodic ones if $Q$ is an identity matrix or orthogonal matrix. Hence solutions also possess certain symmetry in geometry. The result is also extended to the case of pseudo affine-periodic solutions.  相似文献   
999.
By using the Krylov estimate, we prove the exponential ergodicity of the invariant measure for stochastic Langevin equation with singular coefficients, where the classical Lyapunov condition cannot be verified.  相似文献   
1000.
In this study, a mechanical system with linear deterioration and preventive maintenance is considered. The state of the system over time is represented by a semicontinuous stochastic process with dependent components. The system cycles through on and off periods during its lifetime. The state of the system deteriorates linearly as a function of the usage time during on periods. When the system is offline, preventive maintenance is conducted, which improves the system state by a random amount. The system's on and off times and random improvement amounts are assumed to have general distributions. For such a system, our objective is to determine the expected value and variance for the number of preventive maintenance activities needed during the system lifetime and to propose a novel replacement policy for the system based on delay‐time modeling. Finally, the effectiveness of the obtained asymptotic results and the proposed replacement policy are tested through simulation.  相似文献   
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