This paper concerns the nonlinear Schrödinger equation in the Bopp-Podolsky electrodynamics. By considering a minimization problem related to the virial identity, we prove the existence of the ground ...state. In our approach we use the linear profile decomposition to recover compactness, which is distinguished with the mostly used mountain pass theorem. By doing a variational estimate below the ground state, we give the dichotomy of global boundedness and blow-up for solutions with energy below the ground state. As a consequence of the dichotomy, we show the strong instability of the standing wave. In the last part, the non-existence of scattering state will be proved based on the latest result of Murphy-Nakanishi.
C-reactive protein (CRP) is an inflammatory biomarker with associated clinical utility in a wide number of inflammatory disorders, including rheumatoid arthritis (RA). The interaction of CRP with ...pro-inflammatory cytokines has been explored before, however its role in complement regulation is more subtle, where CRP is capable of both up and downregulating the complement cascade. CRP is produced in a pentameric form and can dissociate to a monomeric form in circulation which has significant implications for its ability to interact with receptors and binding partners. This dichotomy of CRP structure could have relevance in patients with RA who have significant dysfunction in their complement cascade and also widely varying CRP levels including at the time of flare. This review aims to bring together current knowledge of CRP in its various forms, its effects on complement function and how this could influence pathology in the context of RA.
•CRP shows differential activity in monomeric & pentameric forms throughout the immunity including complement activation.•The complement system is differentially activated in Rheumatoid Arthritis patient subsets.•Differential activation of complement by CRP may be structurally specific with different sites available in different forms.
In this paper we investigate some free boundary problems for the Lotka–Volterra type prey–predator model in one space dimension. The main objective is to understand the asymptotic behavior of the two ...species (prey and predator) spreading via a free boundary. We prove a spreading–vanishing dichotomy, namely the two species either successfully spread to the entire space as time t goes to infinity and survive in the new environment, or they fail to establish and die out in the long run. The long time behavior of solution and criteria for spreading and vanishing are also obtained. Finally, when spreading successfully, we provide an estimate to show that the spreading speed (if exists) cannot be faster than the minimal speed of traveling wavefront solutions for the prey–predator model on the whole real line without a free boundary.
Among Zeno paradoxes the most known are Dichotomy, Achilles, Arrow, and Stadium. These argumentations state that movement is impossible since it is not thinkable. According to the ascendant form of ...dichotomy, a mobile cannot touch its destination since it always must to reach the half of the distance. The solutions of Diogenes, Aristotle and mathematical analysis are not satisfactory. Finally, the difference between rest and movement can be only conventionally established.
The brake system requires careful attention for continuous monitoring as a vital module. This study specifically focuses on monitoring the hydraulic brake system using vibration signals through ...experimentation. Vibration signals from the brake pad assembly of commercial vehicles were captured under both good and defective conditions. Relevant histograms and wavelet features were extracted from these signals. The selected features were then categorized using Nested dichotomy family classifiers. The accuracy of all the algorithms during categorization was evaluated. Among the algorithms tested, the class-balanced nested dichotomy algorithm with a wavelet filter achieved a maximum accuracy of 99.45%. This indicates a highly effective method for accurately categorizing the brake system based on vibration signals. By implementing such a monitoring system, the reliability of the hydraulic brake system can be ensured, which is crucial for the safe and efficient operation of commercial vehicles in the market.
Hydraulic brakes in automobiles play a vital role for the safety on the road; therefore vital components in the brake system should be monitored through condition monitoring techniques. Condition ...monitoring of brake components can be carried out by using the vibration characteristics. The vibration signals for the different fault conditions of the brake were acquired from the fabricated hydraulic brake test setup using a piezoelectric accelerometer and a data acquisition system. Condition monitoring of brakes was studied using machine learning approaches. Through a feature extraction technique, descriptive statistical features were extracted from the acquired vibration signals. Feature classification was carried out using nested dichotomy, data near balanced nested dichotomy and class balanced nested dichotomy classifiers. A Random forest tree algorithm was used as a base classifier for the nested dichotomy (ND) classifiers. The effectiveness of the suggested techniques was studied and compared. Amongst them, class balanced nested dichotomy (CBND) with the statistical features gives better accuracy of 98.91% for the problem concerned.
For linear nonautonomous differential equations we introduce a new family of spectrums defined with general nonuniform dichotomies: for a given growth rate μ in a large family of growth rates, we ...consider a notion of spectrum, named nonuniform μ-dichotomy spectrum. This family of spectrums contain the nonuniform dichotomy spectrum as the very particular case of exponential growth rates. For each growth rate μ, we describe all possible forms of the nonuniform μ-dichotomy spectrum, relate its connected components with adapted notions of Lyapunov exponents, and use it to obtain a reducibility result for nonautonomous linear differential equations. We also give illustrative examples where the spectrum is obtained, including a situation where a normal form is obtained for polynomial behavior.
We introduce and study a class of free boundary models with “nonlocal diffusion”, which are natural extensions of the free boundary models in 16 and elsewhere, where “local diffusion” is used to ...describe the population dispersal, with the free boundary representing the spreading front of the species. We show that this nonlocal problem has a unique solution defined for all time, and then examine its long-time dynamical behavior when the growth function is of Fisher-KPP type. We prove that a spreading-vanishing dichotomy holds, though for the spreading-vanishing criteria significant differences arise from the well known local diffusion model in 16.
We study the diffusive logistic equation with a free boundary in time-periodic environment. Such a model may be used to describe the spreading of a new or invasive species, with the free boundary ...representing the expanding front. For time independent environment, in the cases of one space dimension, and higher space dimensions with radial symmetry, this free boundary problem has been studied in Du and Lin (2010) 12, Du and Guo (2011) 9. In both cases, a spreading–vanishing dichotomy was established, and when spreading occurs, the asymptotic spreading speed was determined. In this paper, we show that the spreading–vanishing dichotomy is retained in time-periodic environment, and we also determine the spreading speed. The former is achieved by further developing the earlier techniques, and the latter is proved by introducing new ideas and methods.
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