Crosslinking network of bio‐based bis‐functional epoxides derived from trans‐limonene oxide

The thiol‐ene reaction between trans‐limonene oxide (trans‐LO) and ethane‐1,2‐dithiol in the presence of triethylborane affords a bio‐based bis‐functional epoxide (bis‐trans‐LO). The crosslinking reaction of bis‐trans‐LO with branched polyethyleneimine (BPEI; M_n = 600; BPEI₆₀₀) at a feed ratio of bis‐trans‐LO/BPEI₆₀₀ = 57/43 (wt/wt) yields the corresponding network polymer with T_d10 (10% thermal decomposition temperature) of 304.7 °C in 98% yield. In contrast, negligible amounts of network polymer are obtained by the reaction of bis‐LO (bis‐functional epoxide derived from cis and trans‐LO) and BPEI₆₀₀ regardless of the feed ratio. The mechanical strengths as measured by direct tensile tests of the network polymers derived from bis‐trans‐LO and BPEI_600,1800 (M_n = 600 and 1800) were approximately 16 and 11 times higher than that of bis‐LO and BPEI₁₈₀₀, respectively. The tensile shear strengths of the metal‐to‐metal adhesive bonds induced by bis‐trans‐LO and BPEI_600,1800 were 9.5 and 14.1 MPa, respectively. DMA revealed that the storage modulus of the network polymer derived from bis‐trans‐LO and BPEI₁₈₀₀ in the rubber region was higher than that of the material prepared from bis‐LO and BPEI₁₈₀₀, indicating higher crosslink density of the bis‐trans‐LO/BPEI₁₈₀₀ system. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 2466–2473     

Stochastic optimization of forward recursive functions

This note solves a finite-horizon stochastic optimization problem with forward recursive criterion through dynamic programming. The forward recursive criterion is wide; it includes additive (discounted), multiplicative (discounted risk-sensitive), minimum and terminal criteria. The basic idea is to apply invariant imbedding method for the stochastic optimization. The method incorporates recursive accumulation process into dynamics by expanding the original state space.     

Modelling of a single drop impact onto liquid film using particle method

The process of single liquid drop impact on thin liquid surface is numerically simulated with moving particle semi‐implicit method. The mathematical model involves gravity, viscosity and surface tension. The model is validated by the simulation of the experimental cases. It is found that the dynamic processes after impact are sensitive to the liquid pool depth and the initial drop velocity. In the cases that the initial drop velocity is low, the drop will be merged with the liquid pool and no big splash is seen. If the initial drop velocity is high enough, the dynamic process depends on the liquid depth. If the liquid film is very thin, a bowl‐shaped thin crown is formed immediately after the impact. The total crown subsequently expands outward and breaks into many tiny droplets. When the thickness of the liquid film increases, the direction of the liquid crown becomes normal to the surface and the crown propagates outward. It is also found that the radius of the crown is described by a square function of time: r_C = [c(t ? t₀)]^0.5. When the liquid film is thick enough, a crown and a deep cavity inside it are formed shortly after the impact. The bottom of the cavity is initially oblate and then the base grows downward to form a sharp corner and subsequently the corner moves downward. Copyright © 2004 John Wiley & Sons, Ltd.     

Facilitated sulfate transfer across the nitrobenzene-water interface as mediated by hydrogen-bonding ionophores.

Facilitated SO4(2-) transfers by hydrogen bond-forming ionophores are investigated across the nitrobenzene (NB)-water interface by using polarography with a dropping electrolyte electrode. Bis-thiourea 1, alpha,alpha'-bis(N'-p-nitrophenylthioureylene)-m-xylene, is found to significantly facilitate the transfer of the highly hydrophilic SO4(2-) whereas its counterpart, N-(p-nitrophenyl)-N'-propylthiourea (ionophore 2), cannot. In contrast to the predominant formation of a 1:1 complex with SO4(2-) in the bulk NB phase, the SO4(2-) transfer assisted by 1 is indeed based on the formation of a 1:2 complex between SO4(2-) and ionophore, even under the condition of [SO4(2-)]aq > [1]org. Such an exclusive formation of the 1:2 (SO4(2-) to ionophore) complex at the NB-water interface is not observed with structurally similar bis-thiourea 3, alpha,alpha'-bis(N'-phenylthioureylene)-m-xylene, where p-nitrophenyl moietes of bis-thiourea 1 are simply replaced by phenyl groups. The facilitated transfer of SO4(2-) with bis-thiourea 1 is further compared to that of HPO4(2-) and H2PO4- across the NB-water interface, which was previously shown to be assisted by 1 through the formation of the 1:1 and 2:1 (anion to ionophore) complexes, respectively. On the basis of these examinations, unique binding behaviors of hydrogen bond-forming ionophores at the NB-water interface are discussed, with a view towards development of ionophore-based anion-selective chemical sensors.     

A fully linear-time approximation algorithm for grammar-based compression

A linear-time approximation algorithm for the grammar-based compression is presented. This is an optimization problem to minimize the size of a context-free grammar deriving a given string. For each string of length n, the algorithm guarantees approximation ratio without suffix tree construction.     

Symmetry-Breaking Phenomena in an Optimization Problem for some Nonlinear Elliptic Equation

Let $\Omega$ be a bounded domain in ${\bf R^n}$ with Lipschitz boundary, $\lambda >0,$ and $1\le p \le (n+2)/(n-2)$ if $n\ge 3$ and $1\le p< +\infty$ if $n=1,2$. Let $D$ be a measurable subset of $\Omega$ which belongs to the class $ {\cal C}_{\beta}=\{D\subset \Omega \quad | \quad |D|=\beta\} $ for the prescribed $\beta\in (0, |\Omega|).$ For any $D\in{\cal C}_{\beta}$, it is well known that there exists a unique global minimizer $u\in H^1_0(\Omega)$, which we denote by $u_D$, of the functional \[\quad J_{\Omega,D}(v)=\frac12\int_{\Omega}|\nabla v|^2\, dx+\frac{\lambda}{p+1}\int_{\Omega}|v|^{p+1}\, dx -\int_{\Omega}\chi_Dv\,dx \] on $H^1_0(\Omega)$. We consider the optimization problem $ E_{\beta,\Omega}=\inf_{D\in {\cal C}_{\beta}} J_D(u_D) $ and say that a subset $D^*\in {\cal C}_{\beta}$ which attains $E_{\beta,\Omega}$ is an optimal configuration to this problem. In this paper we show the existence, uniqueness and non-uniqueness, and symmetry-preserving and symmetry-breaking phenomena of the optimal configuration $D^*$ to this optimization problem in various settings.