Global-in-time solvability and blow-up for a non-isospectral two-component cubic Camassa-Holm system in a critical Besov space

In this paper, we prove the global Hadamard well-posedness of strong solutions to a non-isospectral two-component cubic Camassa-Holm system in the critical Besov space $B_{2,1}^{\frac{1}{2}}(\mathbb{T})$. Our results shows that in comparison with the well-known work for classic Camassa-Holm-type equations, the existence of global solution only relies on the $L^1$-integrability of the variable coefficients $\alpha(t)$ and $\gamma(t)$, but nothing to do with the shape or smoothness of the initial data. The key ingredient of the proof hinges on the careful analysis of the mutual effect among two component forms, the uniform bound of approximate solutions, and several crucial estimates of cubic nonlinearities in low-regularity Besov spaces via the Littlewood-Paley decomposition theory. A reduced case in our results yields the global existence of solutions in a Besov space for two kinds of well-known isospectral peakon system with weakly dissipative terms.} Moreover, we derive two kinds of precise blow-up criteria for a strong solution in both critical and non-critical Besov spaces, as well as providing specific characterization for the lower bound of the blow-up time, which implies the global existence with additional conditions on the time-dependent parameters $\alpha(t)$ an $\gamma(t)$

Global-in-time solvability and blow-up for a non-isospectral two-component cubic Camassa-Holm system in a critical Besov space

In this paper, we prove the global Hadamard well-posedness of strong solutions to a non-isospectral two-component cubic Camassa-Holm system in the critical Besov space B2,11/2(T). Our results show that in comparison with the well-known work for classic Camassa-Holm-type equations, the existence of global solution only relies on the L1-integrability of the variable coefficients α(t) and γ(t), but nothing to do with the shape of the initial data. The key ingredient of the proof hinges on the careful analysis of the mutual effect among two component forms, the uniform bound of approximate solutions, and several crucial estimates of cubic nonlinearities in low-regularity Besov spaces via the Littlewood-Paley decomposition theory. A reduced case in our results yields the global existence of solutions in a Besov space for two kinds of well-known isospectral peakon system with weakly dissipative terms. Moreover, we derive two kinds of precise blow-up criteria for a strong solution in both critical and non-critical Besov spaces, as well as providing specific characterization for the lower bound of the blow-up time, which implies the global existence with additional conditions on the time-dependent parameters α(t) an γ(t)

Reduce NOx Emissions by Adsorber-Reduction Catalyst on Lean Burn Engine

 The effect of a new catalyst system composed of traditional three way catalyst converter and adsorber-reduction catalysis converter on the emission characteristics and BSFC (Breake Specific Fuel Consumption- BSFC)of a lean burn gasoline engine operated were investigated in this paper under different schemes of catalyst converter arrangement and different speeds and loads. The results show that the position of Three Way Catalyst is before the NOx adsorber Catalyst was the best scheme of catalyst converter arrangement. Which has the highest converter efficiency of reduction NOx emission in lean burn gasoline engine. The effects of speed on the exhaust emission and BSFC were also related to the ratio of lean burn time to rich burn time and the absolute value of both time of the adsorber-reduction catalyst converter. The load of the engine was the main influential factor to the exhaust emission characteristics and BSFC of lean burn gasoline engine, and the more load of the engine was, the more NOx emission, the less NOx conversion rate (CNOx) and the better BSFC were

Análise de elasticidade para sistemas agrícolas da planície do norte da China baseada em um modelo dinâmico de sistema

Este trabalho se refere a um estudo de caso da teoria de elasticidade para entender sistemas agrícolas na província de Luancheng na planície do norte da China. Foi construído um modelo de sistema dinâmico acoplado a subsistemas agrícolas sociais, econômicos e ecológicos para a província de Luancheng com um intervalo de tempo de um mês. O modelo inclui cinco componentes principais: recursos hídricos, rentabilidade, irrigação, produção agrícola e área. O lençol freático simulado, a área e a produção de trigo, a área e produção de milho e a transferência de mão de obra refletiram a tendência geral dos resultados observados com coeficientes de determinação maiores que 0.88. A elasticidade dos sistemas agrícolas, indicada pela rentabilidade e segurança alimentar, foi explorada para a província de Luancheng, que mostrou que inicialmente os investimentos em agricultura tiveram sua elasticidade aumentada rapidamente. Entretanto, com a degradação dos recursos e o aumento do investimento agrícola, o custo da produção agrícola tornou-se muito alto para obtenção de lucro. O aumento de população aumenta o risco de segurança alimentar. Como resultado, a elasticidade dos sistemas agrícolas decresceu gradualmente. A província de Luancheng encontra-se agora na fase conservativa do ciclo de adaptação. Ajustes parciais deveriam ser implementados para impulsionar sua elasticidade e promover o desenvolvimento contínuo dos sistemas agrícolas.This paper presents a case study of resilience theory to understand agricultural systems in the Luancheng County of the North China Plain. A dynanic system model coupled with social, economic and ecological subsystems of agriculture for the Luancheng County was constructed with a time step of one month. The model includes five main components, water resources, profitability, irrigation, crop yield and area. The simulated groundwater table, wheat area and yield, maize area and yield, and rural labor transfer reflected the general trend of the observed data, with calculated determination coefficients higher than 0.88. Resilience of agricultural systems, as indicated by agricultural profitability and food security, were explored for the Luancheng County. Initially, investments in agriculture increased its resilience rapidly. However, with the degradation of resources and the increases in agricultural investment, the cost of agricultural production became too high to gain profit. The rise in population increases the risk of food security. As a result, the resilience of agricultural systems decreased gradually. The Luancheng County is now in the conservation phase of the adaptive cycle. Partial adjustments should be introduced to enhance its resilience and promote the continuing development of the agricultural systems

Research on Polling Control System in Wireless Sensor Networks

To solve the problem of multi-priority and multi-business tasks in wireless sensor networks, a two-level polling control system is proposed based on the basic polling system. The system divides the sites into ordinary sites and high-priority site according to business priorities. The ordinary sites use gated services, and the high-priority sites use exhaustive services. The mathematical model of the system is established by using the method of Markov chain and probability generating function, and the important parameters such as query period, throughput, average queue length and average delay are obtained. The simulation results are approximately equal to the theoretical calculation results, which shows that the theoretical analysis method is correct and effective. While distinguishing priority services, the system ensures the delay of users and improves the quality of service of the polling system

Improved resolution optical time stretch imaging based on high efficiency in-fiber diffraction

Most overlooked challenges in ultrafast optical time stretch imaging (OTSI) are sacrificed spatial resolution and higher optical loss. These challenges are originated from optical diffraction devices used in OTSI, which encode image into spectra of ultrashort optical pulses. Conventional free-space diffraction gratings, as widely used in existing OTSI systems, suffer from several inherent drawbacks: limited diffraction efficiency in a non-Littrow configuration due to inherent zeroth-order reflection, high coupling loss between free-space gratings and optical fibers, bulky footprint, and more importantly, sacrificed imaging resolution due to non-full-aperture illumination for individual wavelengths. Here we report resolution-improved and diffraction-efficient OTSI using in-fiber diffraction for the first time to our knowledge. The key to overcome the existing challenges is a 45° tilted fiber grating (TFG), which serves as a compact in-fiber diffraction device offering improved diffraction efficiency (up to 97%), inherent compatibility with optical fibers, and improved imaging resolution owning to almost full-aperture illumination for all illumination wavelengths. 50 million frames per second imaging of fast moving object at 46 m/s with improved imaging resolution has been demonstrated. This conceptually new in-fiber diffraction design opens the way towards cost-effective, compact and high-resolution OTSI systems for image-based high-throughput detection and measurement

Phase Field Model for Non-equilibrium Interface Conditions

This article presents a new phase-field formulation for non-equilibrium interface conditions in rapid phase transformations. With a particular way of defining concentration fields, the classical sharp and diffuse (thick) interface theories are unified into the present phase-field model. Each point inside the diffuse interface is comparable to the classical sharp interface model, governed by phase boundary migration and short-range atomic exchanges and connected by long-range diffusion. Their thermodynamic forces and fluxes are following the Onsager reciprocal relation and consistent with the classical irreversible thermodynamics. Furthermore, we establish the balance of driving forces and energy dissipations for both the diffuse interface and the single point inside it. The model is then validated by rapid solidification of Al-Cu alloys. With an effective mobility of considering non-equilibrium long-range diffusion, the model represents the main characteristics of non-equilibrium interface kinetics, i.e., solute trapping and solute drag. Especially, we reproduce the complete trapping at the high-velocity regime and provide a thermodynamic consistent description of the partial drag phenomena at the low-velocity region. Moreover, the dissipation analysis indicates that even the far-from-equilibrium diffuse interface is composed of numerous representative volume elements near the equilibrium, providing a new understanding of non-equilibrium interfaces.Comment: 51 Pages, 122 Equations, 12 Figure

Interactions Between Product and Labour Market Reforms

Labour market reforms face very often opposition from the employed workers, because it normally reduces their wages. Also product market regulations are regularly biased towards too much benefitting the firms. As a result there remain many frictions in both the labour and product markets that hinder an optimal functioning of the economy. These issues have recently received a lot of attention in the economics literature and scholars have been looking for politically viable reforms in both markets. However, despite its potential importance, there has been done virtually no research on the interaction between reforms in product and labour markets. We find that when combining reforms, the opposition for reforms decreases considerably. This is because there exist complementarities and the gains in total welfare can be more evenly distributed over the interest groups. Moreover, the interaction of reforms offers a way out for the so-called 'sclerosis' effect