A priori error estimates of finite volume element method for bilinear parabolic optimal control problem

In this paper, we study the finite volume element method of bilinear parabolic optimal control problem. We will use the optimize-then-discretize approach to obtain the semi-discrete finite volume element scheme for the optimal control problem. Under some reasonable assumptions, we derive the optimal order error estimates in $L^2(J; L^2)$ and $L^\infty(J; L^2)$-norm. We use the backward Euler method for the discretization of time to get fully discrete finite volume element scheme for the optimal control problem, and obtain some error estimates. The approximate order for the state, costate and control variables is $O(h^{3/2}+\triangle t)$ in the sense of $L^2(J; L^2)$ and $L^\infty(J; L^2)$-norm. Finally, a numerical experiment is presented to test these theoretical results

The morphological dependent Tully-Fisher relation of spiral galaxies

The Tully-Fisher relation of spiral galaxies shows notable dependence on morphological types, with earlier type spirals having systematically lower luminosity at fixed maximum rotation velocity $V_{max}$. This decrement of luminosity is more significant in shorter wavelengths. By modeling the rotation curve and stellar population of different morphological type spiral galaxies in combination, we find the $V_{max}$ of spiral galaxies is weakly dependent on the morphological type, whereas the difference of the stellar population originating from the bulge disk composition effect mainly account for the morphological type dependence of the Tully-Fisher relation.Comment: 8 pages, 3 figures, ApJ accepte

A Novel Fire Risk Assessment Approach for Large-Scale Commercial and High-Rise Buildings Based on Fuzzy Analytic Hierarchy Process (FAHP) and Coupling Revision

In recent years, much more emphasis than before has been placed on fire safety regulations by the local and central authorities of China, which makes fire risk assessments more important. In this paper we propose a new fire risk assessment approach for large-scale commercial and high-rise buildings that aims to evaluate the performances of their fire safety systems; this should improve the fire risk management and public safety in those buildings. According to the features of large-scale commercial and high-rise buildings, a fire-risk indexing system was built, and based on it we established a scientific fire risk evaluation system. To this end, the fuzzy analytic hierarchy process (FAHP) was used to assign a reasonable weight to each fire risk factor in the evaluation system. In addition, we revised the original scores by analyzing the coupling relationships among the fire risk factors. To validate our system, we selected 11 buildings in Shandong province and collected their fire safety data. Then, we calculated the final scores for the fire safety management of those buildings, and the results show that: (1) our fire risk evaluation system can assign reasonable weights; (2) the proposed evaluation system is comprehensive and has strong interpretability, since it exploits the coupling relationships among the risk factors. The novelty of the proposed approach lies in that it integrates opinions from multiple experts and utilizes coupling relationships among the factors. Further, the feedback from the approach can find not only the weaknesses in fire risk management, but also the potential causes of fires. As a result, the feedback from our assessment can assist the safety chiefs and inspectors with improving fire risk management

A differential game analysis of multi-regional coalition for transboundary pollution problems

Basin water pollution control problem has become a real and serious challenge to build an environment-friendly and resource-conserving society. Since the water environment is quasi-public property, regional cooperation across upstream and downstream regions is critical for pollution control. Employing the differential game theory, we establish four differential game models of transboundary pollution with multi-regional coalitions. Optimal control theory was used to explore the optimal feedback Nash equilibriums solutions of the four models. Our analysis suggests that cooperation among the three regions is more effective in pollution control. The upstream and midstream cooperation can help the upstream region to increase the pollution abatement level, decrease the pollution emission level and pollution stock. The cooperation between the midstream region and both the upstream and downstream regions can help the midstream region to increase the pollution abatement level and decrease the pollution emission level

Interactions among microorganisms functionally active for electron transfer and pollutant degradation in natural environments

Compared to single microbial strains, complex interactions between microbial consortia composed of various microorganisms have been shown to be effective in expanding ecological functions and accomplishing biological processes. Electroactive microorganisms (EMs) and degradable microorganisms (DMs) play vital roles in bioenergy production and the degradation of organic pollutants hazardous to human health. These microorganisms can strongly interact with other microorganisms and promote metabolic cooperation, thus facilitating electricity production and pollutant degradation. In this review, we describe several specific types of EMs and DMs based on their ability to adapt to different environments, and summarize the mechanism of EMs in extracellular electron transfer. The effects of interactions between EMs and DMs are evaluated in terms of electricity production and degradation efficiency. The principle of the enhancement in microbial consortia is also introduced, such as improved biomass, changed degradation pathways, and biocatalytic potentials, which are directly or indirectly conducive to human health

Conceptual Framework and Computational Research of Hierarchical Residential Household Water Demand

Although the quantity of household water consumption does not account for a huge proportion of the total water consumption amidst socioeconomic development, there has been a steadily increasing trend due to population growth and improved urbanization standards. As such, mastering the mechanisms of household water demand, scientifically predicting trends of household water demand, and implementing reasonable control measures are key focuses of current urban water management. Based on the categorization and characteristic analysis of household water, this paper used Maslow’s Hierarchy of Needs to establish a level and grade theory of household water demand, whereby household water is classified into three levels (rigid water demand, flexible water demand, and luxury water demand) and three grades (basic water demand, reasonable water demand, and representational water demand). An in-depth analysis was then carried out on the factors that influence the computation of household water demand, whereby equations for different household water categories were established, and computations for different levels of household water were proposed. Finally, observational experiments on household water consumption were designed, and observation and simulation computations were performed on three typical households in order to verify the scientific outcome and rationality of the computation of household water demand. The research findings contribute to the enhancement and development of prediction theories on water demand, and they are of high theoretical and realistic significance in terms of scientifically predicting future household water demand and fine-tuning the management of urban water resources

Laparoscopic versus open radical cystectomy for elderly patients over 75-year-old: a single center comparative analysis.

PURPOSE: To explore the morbidity, mortality and oncological results of laparoscopic radical cystectomy (LRC) in the elderly patients over 75-year-old in contrast with open radical cystectomy (ORC). MATERIALS AND METHODS: We analyzed 46 radical cystectomies from January 2009 to December 2013 in patients over 75-year-old in our institute, 21 patients in the LRC group and 25 in the ORC group. Demographic parameters, operative variables and perioperative outcome were retrospectively collected and analyzed between the two groups. Perioperative morbidity and mortality were categorized as early (within 90 days after surgery) or late (more than 90 days) according to the time of occurrence. RESULTS: Patients in both groups had comparable preoperative characteristics. A significant longer operative time (418 vs. 337 min, p = 0.018) and less estimated blood loss (400 vs. 500 ml p = 0.038) were observed in LRC group compared with ORC group. Infection and ileus were the most common early complications after surgery. Patients underwent ORC suffered from significantly more postoperative ileus (28.0% vs. 4.8%, P = 0.038) and infection (40% vs. 9.5%, P = 0.019) than LRC group within 90 days after surgery. The mortality rate was 4.7% (1/21) and 4% (1/25) for LRC group and ORC group respectively. At a median follow-up of 21 months (range 2-61 months), the Kaplan-Meier survival curves and log-rank analysis demonstrate that there were no significant differences between the LRC and ORC groups in the 3-year overall, cancer-specific, or recurrence-free survival rates. CONCLUSIONS: It is suggested that LRC should be recommended as the primary intervention to treat muscle invasive or high risk non-muscle invasive bladder cancer in elderly patients with a relative long life expectancy