Fixed Points,Continuous Selections,and Existence of Solution of Optimization-Related Problems

We propose a definition of a generalized type of Knaster–Kuratowski–Mazurkiewicz (KKM) mappings, called a weak T-KKM mapping, and a corresponding weak KKM property. A new extension of the Fan–Glicksberg fixed-point theorem is established. Sufficient conditions for the existence of a continuous selection, a fixed point of a composition, and a coincidence point are also provided. Then, we use the obtained results to study the existence of solutions to various optimization-related problems. Discussions and detailed examples are included as well to compare our results with existing ones and to explain their advantages in many situations.     

Side Information Generation Scheme Based on Coefficient Matrix Improvement Model in Transform Domain Distributed Video Coding

In order to effectively improve the quality of side information in distributed video coding, we propose a side information generation scheme based on a coefficient matrix improvement model. The discrete cosine transform coefficient bands of the Wyner–Ziv frame at the encoder side are divided into entropy coding coefficient bands and distributed video coding coefficient bands, and then the coefficients of entropy coding coefficient bands are sampled, which are divided into sampled coefficients and unsampled coefficients. For sampled coefficients, an adaptive arithmetic encoder is used for lossless compression. For unsampled coefficients and the coefficients of distributed video coding coefficient bands, the low density parity check accumulate encoder is used to calculate the parity bits, which are stored in the buffer and transmitted in small amount upon decoder request. At the decoder side, the optical flow method is used to generate the initial side information, and the initial side information is improved according to the sampled coefficients by using the coefficient matrix improvement model. The experimental results demonstrate that the proposed side information generation scheme based on the coefficient matrix improvement model can effectively improve the quality of side information, and the quality of the generated side information is improved by about 0.2–0.4 dB, thereby improving the overall performance of the distributed video coding system.     

Stochastic systems with memory and jumps

Stochastic systems with memory naturally appear in life science, economy, and finance. We take the modelling point of view of stochastic functional delay equations and we study these structures when the driving noises admit jumps. Our results concern existence and uniqueness of strong solutions, estimates for the moments and the fundamental tools of calculus, such as the Itô formula. We study the robustness of the solution to the change of noises. Specifically, we consider the noises with infinite activity jumps versus an adequately corrected Gaussian noise. The study is presented in two different frameworks: we work with random variables in infinite dimensions, where the values are considered either in an appropriate $L^p$-type space or in the space of càdlàg paths. The choice of the value space is crucial from the modelling point of view, as the different settings allow for the treatment of different models of memory or delay. Our techniques involve tools of infinite dimensional calculus and the stochastic calculus via regularisation.     

Stochastic delay foraging arena predator–prey system with Markov switching

Abstract

In this paper, we introduce white noise, telegraph noise and time delay to the two-dimensional foraging arena population system describing the prey and predator abundance. The aim is to find out how the interactions between white noise, telegraph noise and time delay affect the dynamics of the population system. Firstly, the existence of a global positive solution is verified. Then the long-time properties including the stochastically ultimate boundedness, extinction and some other asymptotic pathwise estimation of this population system are studied. Finally, the main results are illustrated by two examples.     

具有非线性传染率和时滞的随机SIQR计算机病毒模型的渐近行为

研究了一类具有非线性发生率和时滞的随机SIQR计算机病毒模型.首先证明了该系统具有唯一的全局正解,然后通过构造适当的Lyapunov函数并利用伊藤公式,分析了该模型的解在无病平衡点附近及地方病平衡点附近的渐近行为,最后通过数值模拟对随机系统解的渐近行为做了进一步的分析并给出了结论.     

Synergistic Effects of Pseudocolor Imaging,Differentiation, and Square and Logarithmic Conversion on Accuracy of Quantification of Chemical Characteristics Using Test Strips and Similar Products

Test strips and similar products are highly feasible tools for the rapid and approximate determination of chemical characteristics. Although the application of both the quantitative observation of coloration and regression modeling has recently enabled these products to become quantitative tools, their precision and accuracy may be further improved. In this study, the pseudocolor imaging of the coloration image, derivative spectrophotometry-like differentiation of the coloration values, and logarithmic conversion of the raw and derivative values were compared in terms of the precision and accuracy of the quantitative determination of corrosiveness, glucose, nitrate, and pH using the products. The best regression models for the determination were provided by the combination of pseudocolor imaging and differentiation (nitrate and pH); pseudocolor imaging, differentiation, and square-conversion (corrosiveness); or all of the techniques (glucose). When compared to the use of the original 10 raw coloration variables of red-green-blue, cyan-magenta-yellow-key black, and L*a*b* color models only, the above combinations improved the normalized mean absolute error from 14.8% to 3.09% (corrosiveness), 6.33% to 3.15% (glucose), 7.46% to 4.56% (nitrate), and 3.22% to 0.94% (pH). These achievements were largely attributed to the combination of multiple variables that have non-linear and nonmonotonic relationships with the chemical characteristics.     

Rapid Generation and Safe Use of Carbenes Enabled by a Novel Flow Protocol with In‐line IR spectroscopy

A powerful new continuous process for the formation and use of donor/acceptor‐substituted carbenes is described. The safety profile of diazo group transfer on methyl phenylacetate was determined including kinetic studies in batch and in flow using in‐line IR analysis. Batch work‐up and liquid chromatography were circumvented by developing an optimized liquid/liquid flow separation method providing aryl diazoacetates in high purity. Fast screening of reaction conditions in flow with in‐line IR analysis allowed rapid reaction optimization. Finally, a multistep process of diazo group transfer, extraction, separation and subsequent diazo decomposition combined with multiple X?H insertion reactions was established.     

Highly Productive Oxidative Biocatalysis in Continuous Flow by Enhancing the Aqueous Equilibrium Solubility of Oxygen

We report a simple, mild, and synthetically clean approach to accelerate the rate of enzymatic oxidation reactions by a factor of up to 100 when compared to conventional batch gas/liquid systems. Biocatalytic decomposition of H₂O₂ is used to produce a soluble source of O₂ directly in reaction media, thereby enabling the concentration of aqueous O₂ to be increased beyond equilibrium solubility under safe and practical conditions. To best exploit this method, a novel flow reactor was developed to maximize productivity (g product L^?1 h^?1). This scalable benchtop method provides a distinct advantage over conventional bio‐oxidation in that no pressurized gas or specialist equipment is employed. The method is general across different oxidase enzymes and compatible with a variety of functional groups. These results culminate in record space‐time yields for bio‐oxidation.     

Morphology,rheology property,and crystallization behavior of PLLA/OMMT nanocomposites prepared by an innovative eccentric rotor extruder

An innovative eccentric rotor extruder, which can generate continuous elongation flow, was used to fabricate the poly(L‐lactide) (PLLA)/organo‐modified montmorillonite (OMMT) nanocomposites in different OMMT concentrations. The morphology of the nanocomposites was characterized by thermal gravimetric analyzer, X‐ray diffractometer, and transmission electron microscope. The results showed that the OMMT nanoparticles were uniformly dispersed in the PLLA matrix and mainly existed in intercalation mode. The intercalation and exfoliation process of OMMT in the eccentric rotor extruder may be a double‐side exfoliation, which is more effective than the layer‐by‐layer peeling mechanism based on the shear flow. The influence of OMMT on the rheological behavior of PLLA was investigated by dynamic rheological measurements, showing greater improvement of rheological properties for the nanocomposites. The thermo‐mechanical properties analysis indicated that significant enhancement of E′ can be seen for all the nanocomposites. Presence of intercalated OMMT platelets did not lead to a significant shift of the E″ and tan δ curves compared with that of pure PLLA. The crystallization and melting behavior was studied by differential scanning calorimetry, which indicated that the incorporation of OMMT nanoparticles slightly increased the crystallinity of PLLA matrix. The polarizing microscope was further carried out and showed that the dispersed OMMT nanoparticles acted as a heterogeneous nucleating agent to promote the crystallization of PLLA.