Global stability for a model of competition in the chemostat with microbial inputs

We propose a model of competition of n species in a chemostat, with constant input of some species. We mainly emphasize the case that can lead to coexistence in the chemostat in a non-trivial way, i.e., where the n−1 less competitive species are in the input. We prove that if the inputs satisfy a constraint, the coexistence between the species is obtained in the form of a globally asymptotically stable (GAS) positive equilibrium, while a GAS equilibrium without the dominant species is achieved if the constraint is not satisfied. This work is round up with a thorough study of all the situations that can arise when having an arbitrary number of species in the chemostat inputs; this always results in a GAS equilibrium that either does or does not encompass one of the species that is not present in the input.     

Interaction between congo red and copper in a binary adsorption system: Spectroscopic and kinetic studies

This study focused on the competitive adsorption of congo red (CR) and copper by chitosan hydrogel beads in a binary adsorption system. Spectroscopic analysis, including Fourier transform infrared spectroscopy (FTIR) and X-ray photoelectron spectroscopy (XPS) were integrated with kinetic studies to elucidate the interaction. It was determined that chitosan hydrogel beads show better adsorption performance towards congo red and copper in single adsorption systems. The addition of copper caused a 25% reduction in congo red adsorption capacity, while copper adsorption was enhanced slightly by the presence of congo red. The adsorption results for binary adsorption systems seem due to competition for the present amine and hydroxyl groups that may occur between congo red and copper. A congo red–copper complex was formed in binary adsorption systems. Copper attached to chitosan hydrogel beads individually or was bound by the congo red–copper complex, which resulted in an increase in adsorption capacity. Chitosan exhibited higher adsorption selectivity to the free Cu²⁺ ion than the congo red–copper complex in the binary adsorption system. Adsorption of the congo red–copper complex indicated an inhibition in the attachment of the free Cu²⁺ ion in the form of Cu(II).     

竞争包结法研究β-环糊精及其衍生物对灯盏花乙素的选择键合

以酚酞作为光谱探针,采用紫外-可见光谱滴定法测定了β-环糊精(β-CD),单(6-脱氧-乙二胺)-β-环糊精(en-β-CD),单(6-脱氧-二乙基三胺)-β-环糊精(dien-β-CD),羟丙基-β-环糊精(HP-β-CD),磺丁基醚-β-环糊精(SBE-β-CD)在30℃时,pH=10.50的0.025mol/L缓冲液中与灯盏花乙素所形成超分子配合物的稳定常数。结果表明,多种弱相互作用力协同作用于环糊精的配位过程,主-客体间的尺寸匹配决定所形成配合物的稳定性,环糊精衍生物的取代基影响主体的配位能力。5种环糊精主体化合物对灯盏花乙素客体分子的包合能力大小为:β-CDSBE-β-CDen-β-CDdien-β-CDHP-β-CD。     

Removal of cationic dyes by modified waste biosorbent under continuous model: Competitive adsorption and kinetics

Modified waste sugarcane bagasse (SCB) was prepared to remove cationic dyes: methylene blue and rhodamine B from aqueous solution by using a continuous mode. Effects of flow rate on adsorption of the two dyes in fixed bed column were studied. Competitive adsorption kinetics of the two dyes in binary system was investigated in detail. Results showed that the adsorption capacities of the modified sorbent for methylene blue and rhodamine B in one component system were 1.7 and 0.4 mmol g^?1, respectively. Competitive adsorption process in the binary system could be divided into three phases: free adsorption, substitution adsorption and adsorption equilibrium. 0.19 mmol of rhodamine B absorbed was replaced by 0.35 mmol of methylene blue in the second phase. Simple modified Yoon–Nelson model was used to predict the adsorption kinetics for the first time. The obtained adsorption rate constants for the two dyes in the three phases both followed the order: phase I > phase III > phase II, demonstrating that substitution adsorption phase is the rate determining step. Desorption experiment showed that the loaded two dyes could be separated and recycled by using the mixture solution of HCl (0.1 mol L^?1) and ethanol as eluent. The prepared fixed bed column had great potential in industrial wastewater treatment.     

竞争光度法研究两种抗癌嘌呤类药物与β-环糊精衍生物的包合作用

利用酚酞作为光谱探针,竞争光度法研究了β-环糊精衍生物在室温下,pH=10.38的缓冲液中与硫唑嘌呤和巯嘌呤的包合性能。固定β-环糊精衍生物和酚酞的浓度,随着硫唑嘌呤和巯嘌呤两种药物浓度增大,酚酞的紫外吸收增加,表明β-环糊精衍生物与两种嘌呤类药物形成包合物并得出了包合常数。     

Borch’s theorem,equal margins,and efficient allocation

The economic concept of margin guides or justifies the sharing of risks and resources. Broadly, by Borch’s theorem, competing claimants, ends or users ought see equal margins along any efficient allocation.However helpful this maxim, its application is often hampered, and occasionally misguided, by concerns with the differentiability of objectives—or with the interiority of solutions. Circumventing such concerns, this paper introduces a quite applicable, generalized notion, called essential margin.Presuming transferable or quasi-linear utility, the coincidence of such margins supports efficiency, competitive equilibria, and core solutions. The said coincidence also defines deductibles and prioritized claims, seen in finance and insurance.     

Small into isomorphisms onL ∞ spaces

IfT is an isomorphism ofL (A, ) intoL (B, ) which satisfies the condition T T ^–11+, where (A, ) is a -finite measure space, thenT/T is close to an isometry with an error less than 4.     

竞争反应避免苯和苯酚的羟化反应中产生焦油

通过引入竞争反应, 彻底地抑止了以过氧化氢为氧化剂进行的苯和苯酚的羟化反应过程中焦油的产生, 从而使得反应活性和催化剂的使用寿命都显著提高.