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This paper is concerned with the following L 2 -subcritical Kirchhoff-type equation − a + b ∫ R 2 | ∇ u | 2 d x s Δ u + V (x) u = μ u + β | u | 2 u , x ∈ R 2 , with ∫ R 2 | u | 2 d x = 1 . We give a detailed analysis of the limit property of the L 2 -normalized solution when exponent s tends toward 0 from the right (i.e., s ↘ 0 ). Our research extends previous works, in which the authors have displayed the limit behavior of L 2 -normalized solutions when s = 1 as a ↘ 0 or b ↘ 0 . [ABSTRACT FROM AUTHOR]

This paper is devoted to studying constraint minimizers for a class of elliptic equations with two nonlocal terms. Using the methods of constrained variation and energy estimation, we analyze the existence, non-existence, and limit behavior of minimizers for the related minimization problem. Our work extends and enriches the study of bi-nonlocal problems. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying a type of elliptic equation that contains a varying nonlocal term. We provide a detailed analysis of the existence, non-existence, and blow-up behavior of L 2 -norm solutions for the related equation when the potential function V (x) fulfills an appropriate choice. [ABSTRACT FROM AUTHOR]

In this paper, we study the constrained minimization problem for an energy functional which is related to a Kirchhoff-type equation. For s = 1 , there many articles have analyzed the limit behavior of minimizers when η > 0 as b → 0 + or b > 0 as η → 0 + . When the equation involves a varying non-local term ∫ R 3 | ∇ u | 2 d x s , we give a detailed limit behavior analysis of constrained minimizers for any positive sequence { η k } with η k → 0 + . The present paper obtains an interesting result on this topic and enriches the conclusions of previous works. [ABSTRACT FROM AUTHOR]

Marine ecosystem is a large and complex and changeable system; especially in the context of the rapid development of marine economy, the changes of marine ecological environment system have a great impact on the development of human and marine utilization. Biometrics is a recognition technology based on biological inherent physiological and action characteristics. In recent years, the coastal biometric technology has made great progress. In order to make bioassay practical from theoretical research, many scientific research institutions need to break through a series of important technologies to solve. Modern logistics is a new industry in China. So far, there is no regulation and accounting system of financial management of modern logistics enterprises. In order to meet the needs of financial accounting in accounting, the theoretical research and practical discussion on the method of calculating logistics enterprise cost are not enough. Logistics research field is devoted to the direction of logistics management, but only carries out the accounting treatment of logistics cost scattered, stays at the research level of the method of providing cost information for logistics cost management, and can not provide the theoretical basis and practical guide for logistics enterprises to calculate the external financial reporting cost. Therefore, according to their understanding of the concept of logistics cost, each logistics enterprise uses traditional cost calculation method to calculate the cost of enterprises. Due to the lack of rigorous cost calculation and the limitation of previous cost calculation methods, the cost information of logistics enterprises is lack of accuracy and comparative possibility. The paper puts forward the cost calculation method suitable for logistics enterprises, establishes a unified accounting cost calculation system suitable for Chinese logistics enterprises, and plays an active role in promoting the matching and common development of logistics accounting and logistics industry. [ABSTRACT FROM AUTHOR]

We study the Bose–Einstein condensates with attractive interaction in a bounded domain Ω ⊂ R 2 , described by Gross–Pitaevskii energy functional. We prove that there exists a constant a ∗ > 0 , such that minimizers exist if and only if 0 < a < a ∗ . As a ↗ a ∗ , the limit behavior of minimizers is also analyzed, where the mass must concentrate at the global minimum points of the trapping potential V (x). In particular, if V (x) has the flattest global minimum points both at the interior and the boundary of Ω, we prove that the mass must concentrate at an inner minimum point of Ω, rather than the neighborhood of the boundary minimum points. [ABSTRACT FROM AUTHOR]

This paper is concerned with constraint minimizers of an L2-critical minimization problem (1) in RN (N ≥ 1) under an L2-subcritical perturbation. We prove that the problem admits minimizers with mass ρN/2 if and only 4 if 0 ≤ ρ < ρ* := ‖Q‖24/N for b ≥ 0 and 0 < ρ ≤ ρ* for b < 0, where the constant b comes from the coefficient of the perturbation term, and Q is the unique positive radically symmetric solution of Δu(x) - u(x) + u1+ 4/N (x) = 0 in RN . Furthermore, we analyze rigorously the concentration behavior of minimizers as ρ /' ρ* for the case where b > 0, which shows that the concentration rates are determined by the subcritical perturbation, instead of the local profiles of the potential V (x). [ABSTRACT FROM AUTHOR]

In this paper, we study constraint minimizers of the following L2−critical minimization problem: [ABSTRACT FROM AUTHOR]

Biologically-treated municipal solid waste (MSW) leachate still contains many kinds of bio-recalcitrant organic matter. A new plate and frame electrochemical reactor was designed to treat these materials under flow conditions. In the electrochemical oxidation process, NH 3 and color could be easily removed by means of electro-generated chlorine/hypochlorite within 20 min. The effects of major process parameters on the removal of organic pollutants were investigated systematically. Under experimental conditions, the optimum operation parameters were current density of 65 mA/cm 2 , flow velocity of 2.6 cm/sec in electrode gap, and initial chloride ion concentration of 5000 mg/L. The COD in the leachate could be reduced below 100 mg/L after 1 hr of treatment. The kinetics and mechanism of COD removal were investigated by simultaneously monitoring the COD change and chlorine/hypochlorite production. The kinetics of COD removal exhibited a two-stage kinetic model, and the decrease of electro-generated chlorine/hypochlorite production was the major mechanism for the slowing down of the COD removal rate in the second stage. The narrowing of the electrode gap is beneficial for COD removal and energy consumption. [ABSTRACT FROM AUTHOR]