Asymptotic behavior of solutions to space‐time fractional diffusion‐reaction equations

This article discusses the analyticity and the long‐time asymptotic behavior of solutions to space‐time fractional diffusion‐reaction equations in . By a Laplace transform argument, we prove that the decay rate of the solution as t→∞ is dominated by the order of the time‐fractional derivative. We consider the decay rate also in a bounded domain. Copyright © 2016 John Wiley & Sons, Ltd.     

Lot‐sizing policies for deterioration items under two‐level trade credit with partial trade credit to credit‐risk retailer and limited storage capacity

The main purpose of this article is to investigate the optimal wholesaler's replenishment decisions for deterioration items under two levels of the trade credit policy and two storage facilities in order to reflect the supply chain management situation within the economic order quantity framework. In this study, each of the following assumptions have been made: (1) The own warehouse with limited capacity always is not sufficient to store the order quantity, so that a rented warehouse is needed to store the excess units over the capacity of the own warehouse; (2) The wholesaler always obtains the partial trade credit, which is independent of the order quantity offered by the supplier, but the wholesaler offers the full trade credit to the retailer; (3) The wholesaler must take a loan to pay his or her supplier the partial payment immediately when the order is received and then pay off the loan with the entire revenue. Under these three conditions, the wholesaler can obtain the least costs. Furthermore, this study models the wholesaler's optimal replenishment decisions under the aforementioned conditions in the supply chain management. Two theorems are developed to efficiently determine the optimal replenishment decisions for the wholesaler. Finally, numerical examples are given to illustrate the theorems that are proven in this study, and the sensitivity analysis with respect to the major parameters in this study is performed. Copyright © 2016 John Wiley & Sons, Ltd.     

Oscillation criteria for higher‐order nonlinear dynamic equations with Laplacians and a deviating argument on time scales

In this paper, we study the n th‐order nonlinear dynamic equation with Laplacians and a deviating argument on an above‐unbounded time scale, where n ?2, New oscillation criteria are established for the cases when n is even and odd and when α  > γ ,α  = γ , and α  < γ , respectively, with α  = α ₁?α _{n  ? 1}. Copyright © 2017 John Wiley & Sons, Ltd.     

Existence and limit behavior of prescribed L2‐norm solutions for Schrödinger‐Poisson‐Slater systems in

In this paper, we study constraint minimizers of the following L ²?critical minimization problem: where E (u ) is the Schrödinger‐Poisson‐Slater functional and N denotes the mass of the particles in the Schrödinger‐Poisson‐Slater system. We prove that e (N ) admits minimizers for and, however, no minimizers for N >N ^?, where Q (x ) is the unique positive solution of in . Some results on the existence and nonexistence of minimizers for e (N ^?) are also established. Further, when e (N ^?) does not admit minimizers, the limit behavior of minimizers as N ↗N ^? is also analyzed rigorously.     

Cooperative Chemotaxis of Magnesium Microswimmers for Corrosion Spotting

Numerous artificial micro- and nanomotors, as well as various swimmers have been inspired by living organisms that are able to move in a coordinated manner. Their cooperation has also gained a lot of attention because the resulting clusters are able to adapt to changes in their environment and to perform complex tasks. However, mimicking such a collective behavior remains a challenge. In the present work, magnesium microparticles are used as chemotactic swimmers with pronounced collective features, allowing the gradual formation of macroscopic agglomerates. The formed clusters act like a single swimmer able to follow pH gradients. This dynamic behavior can be used to spot localized corrosion events in a straightforward way. The autonomous docking of the swimmers to the corrosion site leads to the formation of a local protection layer, thus increasing corrosion resistance and triggering partial self-healing.     

Triruthenium clusters containing mono and bidentate phosphines: Synthesis,structure, thermal reactivity and fluxional behavior

The syntheses, structures and thermal reactions of [Ru₃(CO)₉{P(C₄H₃E)₃}(μ-dppe)] (2, E = S; 3, E = O; dppe = 1,2-bis(diphenylphosphino)ethane) are described. These triphosphine-substituted clusters can be easily obtained in high yield from the Me₃NO initiated room temperature reaction between [Ru₃(CO)₁₀(μ-dppe)] (1) and P(C₄H₃E)₃. Both clusters have been structurally characterized which reveals that the functionalized phosphine P(C₄H₃E)₃ is coordinated to the remote ruthenium atom using the phosphorus atom, while the NMR spectroscopic data indicate that both clusters are fluxional in solution mainly due to the ring-flipping process involving the dppe ligand which has been probed by VT NMR spectroscopy. Thermolysis of 2 at 66 °C affords 1 via P(C₄H₃S)₃ dissociation, whilst that of 3 under similar experimental conditions also furnishes the diruthenium σ,π-furyl complex [Ru₂(CO)₆(μ,η²-C₄H₃O){μ-P(C₄H₃O)₂] (4) in addition to 1.     

压缩CO2中Co-N-C催化3-硝基苯乙烯选择性加氢反应动力学及相行为

对于苯环上含有各种可还原基团(如–C=C,–CN,–C≡C)的硝基芳烃,通过选择性加氢来制备芳香胺类化合物依然充满挑战.负载型纳米催化剂通常存在过度加氢的缺陷,虽然通过覆盖部分金属位点等方法可改善其选择性,但多是以牺牲催化活性为代价.得益于较高的原子利用率以及孤立的活性位结构,单原子催化剂在硝基芳烃选择性加氢反应中崭露头角.例如Pt1/FeOx单原子催化剂在3-硝基苯乙烯加氢反应中对目标产物的选择性高于99％,且转化频率(TOF)是Pt纳米催化剂的20倍以上.然而,已报道的单原子催化体系中,活性组分多为Pt族贵金属,且以有机溶剂为反应介质,不符合绿色化学理念.本文以环境友好型溶剂——压缩CO2为反应介质,以氮掺杂碳负载非贵金属Co单原子(Co-N-C)为催化剂,实现了3-硝基苯乙烯的选择性加氢,且反应体系中无任何有机溶剂和助剂.在温和(60 oC,3 MPa H2(RT),总压8.1 MPa)的反应条件下,3-硝基苯乙烯可完全转化,目标产物3-乙烯基苯胺的选择性达到>99％,且产物可通过简单卸压直接分离.Co-N-C单原子催化剂表现出较高的稳定性,循环使用4次以后活性并无明显降低.HAADF-STEM表征发现反应后的催化剂中,Co仍然呈单原子分散.研究发现,通过改变CO2压力(即CO2相行为)可调变H2在其中的溶解度以及在加氢反应中的反应级数,进而调变反应速率.通常认为,催化活性会随CO2压力增大呈线性增加,而本文中转化率却随CO2压力增加呈现"倒V型"曲线关系,即当体系总压为8.1 MPa(PCO2=5.0 MPa)时,转化率达到最大值(100％),而升高或降低CO2压力均会显著降低催化活性.为解释"倒V型"曲线的成因,通过含可视窗的高压釜研究了3-硝基苯乙烯/CO2/H2三元体系的相行为.发现当总压为13.4 MPa时,体系为均匀的一相(即3-硝基苯乙烯完全溶解在CO2中);而当总压为8.1 MPa时,却形成了气-液两相.用激光笔照射高压釜上部的气相时,出现了明显的丁达尔现象,说明其中溶解有少量的3-硝基苯乙烯,呈胶体分散;底部为CO2膨胀的3-硝基苯乙烯液相,且该膨胀行为通过硝基苯-CO2二元相行为研究得到证实(即在一定CO2压力下,6 mL硝基苯可被CO2膨胀至充满整个高压釜(容积为29.3 mL)).动力学研究发现,在不含CO2以及总压为11.2 MPa时,H2的反应级数为～0.5;而当总压为8.1 MPa(CO2压力为5.0 MPa)时,H2的级数降为0,说明该压力下H2的溶解度显著增加.通过Peng-Robinson方程计算了不同CO2压力下H2的溶解度,发现H2溶解度与CO2压力也呈"倒V型"曲线关系,且最高点对应的CO2压力与上述转化率-PCO2曲线一致.因此,当总压为8.1 MPa,CO2分压为5.0 MPa时形成了CO2膨胀的3-硝基苯乙烯液体,溶解入该膨胀液体的CO2促进了H2的溶解,进而使H2的反应级数降为0,从而促进了加氢反应的进行.综上,本文以压缩CO2为溶剂,以非贵金属基Co-N-C为催化剂,发展了一种3-硝基苯乙烯绿色选择性加氢途径.同时发现,改变CO2压力可调变反应体系的相行为及反应动力学行为,进而调变催化性能.该研究结果可为调变压缩CO2介质中进行的其它催化转化反应性能提供借鉴.     

The Shakhov model near a global Maxwellian

Shakhov model is a relaxation approximation of the Boltzmann equation proposed to overcome the deficiency of the original BGK model, namely, the incorrect production of the Prandtl number. In this paper, we address the existence and the asymptotic stability of the Shakhov model when the initial data is a small perturbation of global equilibrium. We derive a dichotomy in the coercive estimate of the linearized relaxation operator between zero and non-zero Prandtl number, and observe that the linearized relaxation operator is more degenerate in the former case. To remove such degeneracy and recover the full coercivity, we consider a micro–macro system that involves an additional non-conservative quantity related to the heat flux.