Decomposition of the convex simplex method

Rutenberg (Ref. 1) provided a decomposition method to solve the problem of minimizing a separable, nonlinear objective function with large-scale linear constraints by using the convex simplex method (Ref. 2). However, there seem to be some errors in his paper (Ref. 3). This paper will rebuild the method by using more convenient and consistent notation.     

Spin-glass state and ferromagnetic order in Cu(II)－Fe(III) cyanides

The static and dynamic magnetic properties of a Prussian blue analogue, molecular magnet Cu^Ⅱ_{3}[Fe^Ⅲ(CN)_6]_2·3NH_3·6H_2O were investigated in detail. The H dependence of the linear AC susceptibility, the irreversibility in the field-cooled (FC)/zero-field-cooled (ZFC) magnetization (M_{FC}/M_{ZFC}) and the relaxation of M_{ZFC} suggest that the magnetic system can be visualized as containing a ferromagnetic cluster of spin below T_C, mixed with small spin-glass clusters formed below temperature T_g less than T_C. The observed magnetic properties are explained with a ferromagnetic-spin-glass phase model. The magnetic ordering of the sample occurs below 19.8K.     

Ultrathin Hexagonal Hybrid Nanosheets Synthesized by Graphene Oxide‐Assisted Exfoliation of β‐Co(OH)2 Mesocrystals

In the present study, we report the synthesis of a high‐quality, single‐crystal hexagonal β‐Co(OH)₂ nanosheet, exhibiting a thickness down to ten atomic layers and an aspect ratio exceeding 900, by using graphene oxide (GO) as an exfoliant of β‐Co(OH)₂ nanoflowers. Unlike conventional approaches using ionic precursors in which morphological control is realized by structure‐directing molecules, the β‐Co(OH)₂ flower‐like superstructures were first grown by a nanoparticle‐mediated crystallization process, which results in large 3D superstructure consisting of ultrathin nanosheets interspaced by polydimethoxyaniline (PDMA). Thereafter, β‐Co(OH)₂ nanoflowers were chemically exfoliated by surface‐active GO under hydrothermal conditions into unilamellar single‐crystal nanosheets. In this reaction, GO acts as a two‐dimensional (2D) amphiphile to facilitate the exfoliation process through tailored interactions between organic and inorganic molecules. Meanwhile, the on‐site conjugation of GO and Co(OH)₂ promotes the thermodynamic stability of freestanding ultrathin nanosheets and restrains further growth through Oswald ripening. The unique 2D structure combined with functionalities of the hybrid ultrathin Co(OH)₂ nanosheets on rGO resulted in a remarkably enhanced lithium‐ion storage performance as anode materials, maintaining a reversible capacity of 860 mA h g^?1 for as many as 30 cycles. Since mesocrystals are ubiquitous and rich in morphological diversity, the strategy of the GO‐assisted exfoliation of mesocrystals developed here provides an opportunity for the synthesis of new functional nanostructures that could bear importance in clean renewable energy, catalysis, photoelectronics, and photonics.     

Regularity for diffuse reflection boundary problem to the stationary linearized Boltzmann equation in a convex domain

We investigate the regularity issue for the diffuse reflection boundary problem to the stationary linearized Boltzmann equation for hard sphere potential, cutoff hard potential, or cutoff Maxwellian molecular gases in a strictly convex bounded domain. We obtain pointwise estimates for first derivatives of the solution provided the boundary temperature is bounded differentiable and the solution is bounded. This result can be understood as a stationary version of the velocity averaging lemma and mixture lemma.     

A Mössbauer investigation of the amorphous Tin-Antimony oxide films

The Tin-Antimony oxide films SN_1-xSb_xO₂ (x=0.00-0.66) with thickness about 1100Å have been prepared on glass substrates by CVD and studied by using CEMS and XRD. The broad line widths of Mössbauer spectra and of X-ray diffraction patterns indicate a distribution of the hyperfine parameters due to the distortion of the rutile lattice. A distribution fitting program has been used to evaluate the distribution of quadrupole splitting QS and of isomer shift IS in the samples studied.     

Mössbauer studies of hemoglobin of the patients with liver cancer and cirrhosis

Red blood cells (RBC) of the patients with primary liver cancer and with cirrhosis were investigated by using Mössbauer spectroscopy. Control measurements were carried out on RBC from normal adults. The Mössbauer spectra of normal RBC are composed of two doublets corresponding to deoxy-Hb and Oxy-Hb. Besides disappearance or a decrease of the doublets corresponding to deoxy-Hb, no additional peak was detected in the samples from the patients.     

Lagrange multiplier theorem of multiobjective programming problems with set functions

In this paper, Lagrange multiplier theorems are developed for the cases of single-objective and multiobjective programming problems with set functions. Properly efficient solutions are also characterized by subdifferentials and zero-like functions.The authors greatly appreciate helpful and valuable comments and suggestions received from the referee.