The existence of solutions for Sturm–Liouville differential equation with random impulses and boundary value problems

In this article, we consider the existence of solutions to the Sturm–Liouville differential equation with random impulses and boundary value problems. We first study the Green function of the Sturm–Liouville differential equation with random impulses. Then, we get the equivalent integral equation of the random impulsive differential equation. Based on this integral equation, we use Dhage’s fixed point theorem to prove the existence of solutions to the equation, and the theorem is extended to the general second order nonlinear random impulsive differential equations. Then we use the upper and lower solution method to give a monotonic iterative sequence of the generalized random impulsive Sturm–Liouville differential equations and prove that it is convergent. Finally, we give two concrete examples to verify the correctness of the results.

Existence and Stability Results for Second-Order Neutral Stochastic Differential Equations With Random Impulses and Poisson Jumps

The objective of this paper is to investigate the existence and stability results of secondorder neutral stochastic functional differential equations (NSFDEs) in Hilbert space. Initially, we establish the existence results of mild solutions of the aforementioned system using the Banach contraction principle. The results are formulated using stochastic analysis techniques. In the later part, we investigate the stability results through the continuous dependence of solutions on initial conditions.

Bearing Fault Diagnosis Based on Energy Spectrum Statistics and Modified Mayfly Optimization Algorithm

This study proposes a novel resonance demodulation frequency band selection method named the initial center frequency-guided filter (ICFGF) to diagnose the bearing fault. The proposed technology has a better performance on resisting the interference from the random impulses. More explicitly, the ICFGF can be summarized as two steps. In the first step, a variance statistic index is applied to evaluate the energy spectrum distribution, which can adaptively determine the center frequency of the fault impulse and suppress the interference from random impulse effectively. In the second step, a modified mayfly optimization algorithm (MMA) is applied to search the optimal resonance demodulation frequency band based on the center frequency from the first step, which has faster convergence. Finally, the filtered signal is processed by the squared envelope spectrum technology. Results of the proposed method for signals from an outer fault bearing and a ball fault bearing indicate that the ICFGF works well to extract bearing fault feature. Furthermore, compared with some other methods, including fast kurtogram, ensemble empirical mode decomposition, and conditional variance-based selector technology, the ICFGF can extract the fault characteristic more accurately.

Existence and Ulam-Hyers-Rassias stability of stochastic differential equations with random impulses

In this paper, we investigate the existence and Ulam-Hyers-Rassias stability of solutions for stochastic differential equations with random impulses. Based on the Krasnoselskii?s fixed point theorem, we perform investigations on the existence of solutions to the system of stochastic differential equations with random impulses. We apply the integral inequality of Gronwall type to the equations and study their Ulam-Hyers-Rassias stability.

Coexistence of Random Subharmonic Solutions of Random Impulsive Differential Equations and Inclusions on a Circle

The coexistence of random periodic solutions with various periods (i.e. subharmonics) is proved to random differential equations on a circle with random impulses of all integer orders. One of the theorems is also extended to random differential inclusions on a circle with multivalued deterministic impulses. These results can be roughly characterized as a further application of the randomized Sharkovsky type theorems to random impulsive differential equations and inclusions on a circle.

Nuets responsivitet – når det fremmede og det uperfekte setter premissen! Et filosofisk essay om musikalsk improvisasjon

As we improvise in music and become increasingly engrossed in the activity, we are intuitively engaged in a playful negotiation of various aesthetic possibilities in the Now. We are in a state where random impulses and irrational, unintentional actions become key premise providers along with everything we have learned through knowledge and experience. This essay reflects on the responsiveness of the Now in musical improvisation. We ask: What does the experience of the Now offer? Does it come with any kind of ethics and accountability and, if so, what kind and to whom does it apply? In our elaborations we are influenced by our own experiences of, and reflections on, compositional and music therapeutic practice. We refer to the theory of musical improvisation and early interaction, and also philosophical texts, especially those by Mikhail Bakhtin. We suggest that the responsiveness of the Now in musical improvisation is a mindset that challenges us both ethically and aesthetically. It does so by seeking creative satisfaction, joy and insight, taking shape through sensory perception that is close to intuition, mimesis and imagination. Its meaning remains unfinalised and foreign to us. It is also risky and is situated on the boundary between music and performer, between performer and other performers, and between the past and future of our actions. The ideal is to strive for a Now that can be experienced as the right now but also as a Now that suits the responses we try to find room for when we improvise.