A partially isochronous splitting algorithm for three-block separable convex minimization problems

During the last decade, the state-of-the-art alternating direction method of multipliers (ADMM) has successfully been used to solve many two-block separable convex minimization problems arising from several applied areas such as signal/image processing and statistical and machine learning. It however remains an interesting problem of how to implement ADMM to three-block separable convex minimization problems as required by the situation where many objective functions in the above-mentioned areas are actually more conveniently decomposed to the sum of three convex functions, due also to the observation that the straightforward extension of ADMM from the two-block case to the three-block case is apparently not convergent. In this paper, we shall introduce a new algorithm that is called a partially isochronous splitting algorithm (PISA) in order to implement ADMM for the three-block separable model. The main idea of our algorithm is to incorporate only one proximal term into the last subproblem of the extended ADMM so that the resulting algorithm maximally inherits the promising properties of ADMM. A remarkable superiority over the extended ADMM is that we can simultaneously solve two of the subproblems, thereby taking advantages of the separable structure and parallel architectures. Theoretically, we will establish the global convergence of our algorithm under standard conditions, and also the O(1/t) rate of convergence in both ergodic and nonergodic senses, where t is the iteration counter. The computational competitiveness of our algorithm is shown by numerical experiments on an application to the well-tested robust principal component analysis model.     

Approximations to fixed points of contraction semigroups in hilbert spaces

Sequences (or curves) are constructed to approximate common fixed points of a pair of nonex-pansive mappings (or contraction semigroups) in Hilbert spaces. The obtained results extend the previously known results from a single mapping to a family of mappings.     

Electrical Current in Sinai Billiards Under General Small Forces

The Lorentz gas of $\mathbb{Z}^{2}$ -periodic scatterers (or the so called Sinai billiards) can be used to model motion of electrons on a metal. We investigate the linear response for the system under various external forces (during both the flight and the collision). We give some characterizations under which the forced system is time-reversible, and derive an estimate of the electrical current generated by the forced system. Moreover, applying Pesin entropy formula and Young dimension formula, we get several characterizations of the non-equilibrium steady state of the forced system.     

Synthesis of a Novel Phosphorus-Containing Curing Agent and Its Effects on the Flame Retardancy,and Thermal Stability of Epoxy Resins

Russian Journal of Applied Chemistry - A novel curing agent containing phosphorus and carboxyl group compound diphenyl(2,3-dicarboxylpropyl)phosphine oxide (DPDCPPO) was synthesized and used as a...     

硅基超薄多孔氧化铝膜的制备

将二次阳极氧化法应用于硅基铝膜的制备, 在草酸溶液中得到了厚度可控的硅基超薄多孔氧化铝膜(PAM), 厚度小于100 nm. 实验中记录了氧化电流随时间的实时变化曲线, 发现硅衬底的氧化电流在大幅下降前有一小幅波动. 对应于Al/Si界面的氧化过程中, 孔洞底部之间的残留铝岛被优先氧化, 可将此作为终止铝氧化的标志. 扫描电镜(SEM)观察表明, 二次氧化提高了孔洞分布的均匀性, 使得孔在一定的区域内呈现有序六角分布.这种模板可进一步用于硅基纳米器件和纳米结构的制备.     

Matrix approaches to approximate solutions of variational inequalities in Hilbert spaces

A matrix approach to approximating solutions of variational inequalities in Hilbert spaces is introduced. This approach uses two matrices: one for iteration process and the other for regularization. Ergodicity and convergence (both weak and strong) are studied. Our methods combine new or well-known iterative methods (such as the original Mann’s method) with regularized processes involved regular matrices in the sense of Toeplitz.     

Asymptotically strict pseudocontractive mappings in the intermediate sense

It is proved that the modified Mann iteration process: _xn+1=(1−_αn)_xn+_αnTⁿ_xn,n∈N$x_{n+1}=(1-{\alpha }_n)x_n+{\alpha }_n{T}^n{x}_n,n\in \mathbb{N}$, where {_αn}$\left\{{\alpha }_n\right\}$ is a sequence in (0, 1) with δ≤_αn≤1−κ−δ$\delta \le {\alpha }_n\le 1-\kappa -\delta$ for some δ∈(0,1)$\delta \in (0,1)$, converges weakly to a fixed point of an asymptotically κ$\kappa$-strict pseudocontractive mapping T$T$ in the intermediate sense which is not necessarily Lipschitzian. We also develop CQ method for this modified Mann iteration process which generates a strongly convergent sequence.     

A new process for preparing dialdehyde by catalytic oxidation of cyclic olefins with aqueous hydrogen peroxide

A. novel peroxo-niobophosphate was synthesized for the first time and used as a catalyst in the oxidation reaction of cyclic olefins with aqueous hydrogen peroxide to prepare dialdehy-des. The catalyst was characterized by elemental analysis, thermographic analyses, IR, UV/vis, 31P NMR and XPS spectra as [ π-C5H5N(CH2 )13 CH3 ]2 [ Nb4O6 (O2 )2 (PO4 )2 ] ·6H2O (PTNP). It showed high selectivity to glutaraldehyde in the catalytic oxidation of cyclopentene with aqueous hydrogen peroxide in ethanol.     

Flexible organic frameworks sequester neuromuscular blocking agents in vitro and reverse neuromuscular block in vivo

Supramolecular sequestration and reversal of neuromuscular block (NMB) have great clinical applications. Water-soluble flexible organic frameworks (FOFs) cross-linked by disulfide bonds are designed and prepared. Different linker lengths are introduced to FOFs to give them varied pore sizes. FOFs are anionic nanoscale polymers and capable of encapsulating cationic neuromuscular blocking agents (NMBAs), including rocuronium (Roc), vecuronium (Vec), pancuronium (Panc) and cisatracurium (Cis). A host–guest study confirms that FOFs bind NMBAs in water. The multivalency interaction between FOFs and NMBAs is able to sequester NMBAs, and prevent them from escaping. These FOFs are non-toxic and biocompatible. Animal studies show that FOFs are effective for the reversal of NMB induced by Roc, Vec and Cis, which shorten the time to a train-of-four ratio of 0.9 by 2.6, 3.8 and 5.7-fold compared to a placebo, respectively.

Water-soluble flexible organic frameworks are prepared and used to sequester neuromuscular blocking agents, and reverse their neuromuscular block in vivo.     

Catalyst Control of Interfacial Welding Mechanical Properties of Vitrimers

Chinese Journal of Polymer Science - Interfacial welding of thermosetting polymers has been a challenge, but vitrimers with dynamic covalent networks open numerous opportunities for welding and...