On a class of least-element complementarity problems

The present paper studies the linear complementarity problem of finding vectorsx andy inR ₊ ⁿ such thatc + Dx + y 0,b – x 0 andx ^T (c + Dx + y) = y ^T (b – x) = 0 whereD is aZ-matrix andb > 0. Complementarity problems of this nature arise, for example, from the minimization of certain quadratic functions subject to upper and lower bounds on the variables. Two least-element characterizations of solutions to the above linear complementarity problem are established first. Next, a new and direct method to solve this class of problems, which depends on the idea of least-element solution is presented. Finally, applications and computational experience with its implementation are discussed.Research partially supported by the National Science Foundation Grant MCS 71-03341 A04 and the Air Force Office of Scientific Research Contract F 44620 14 C 0079.     

Existence of positive stationary solutions for a diffusive variable-territory prey–predator model

This paper concerns the existence of positive stationary solutions for a diffusive variable-territory prey–predator model, and completely settles an open problem of Wang and Pang (2009). The main result closes a gap in an earlier result (2011) by the authors.     

Production, Characterization, and Application of an Organic Solvent-Tolerant Lipase Present in Active Inclusion Bodies

An organic solvent-tolerant lipase from Serratia marcescens ECU1010 (rSML) was overproduced in Escherichia coli in an insoluble form. High concentrations of both biomass (50 g cell wet weight/L culture broth) and inclusion bodies (10.5 g/L) were obtained by applying a high-cell-density cultivation procedure. Activity assays indicated that the enzymatic activity of rSML reached 600 U/L. After treatment with isopropyl ether for 12 h, the maximum lipase activity reached 6,000 U/L. Scanning electron microscopy and Fourier transform infrared microspectroscopy revealed the activation mechanism of rSML in the presence of organic solvents. rSML was stable in broad ranges of temperatures and pH values, as well as in a series of organic solvents. Besides, rSML showed the best enantioselectivity for the kinetic resolution of (±)-trans-3-(4-methoxyphenyl)glycidic acid methyl ester. These features render the S. marcescens ECU1010 lipase attractive for biotechnological applications in the field of organic synthesis and pharmaceutical industry.     

A Normal Criterion Concerning Omitted Holomorphic Function

In this paper, we continue to discuss the normality concerning omitted holomorphic function and get the following result. Let F be a family of meromorphic functions on a domain D, k ≥ 4 be a positive integer, and let a(z) and b(z) be two holomorphic functions on D, where a(z) 0 and f(z) ≠ ∞ whenever a(z)=0. If for any f ∈ F, f'(z) -a(z)f^k(z) ≠ b(z), then F is normal on D.     

Nickel Oxide/Graphene Composites: Synthesis and Applications

Nickel oxide (NiO) has emerged as one of the most promising transition-metal oxides (TMOs) for electrochemical capacitors, batteries, catalysis, and electrochromic films, owing to its cost-effectiveness, abundance, and well-defined electrochemical properties. Recent studies have identified that mixing NiO with graphene or graphene derivatives results in novel composites with synergistic effects and superior electrochemical performance. This review summarizes the latest advances in composites of NiO with graphene or graphene derivatives. The synthetic strategies, morphologies, and electrochemical performance of these composites are introduced, as well as their electrochemical applications in supercapacitors, batteries, sensors, catalysis, and so forth. Finally, tentative conclusions and assessments regarding the opportunities and challenges for the future development of these composites and other TMOs/graphene or graphene-derived composites are presented.     

Hyperbolic metric and normal family

In this paper, we study the normality of the family of meromorphic functions from the viewpoint of hyperbolic metric. Then, a new sufficient and necessary condition is obtained, which can determine a given family of meromorphic functions is normal or not.     

CaPtAs: A new noncentrosymmetric superconductor

We report the discovery of a new noncentrosymmetric superconductor CaPtAs.It crystallizes in a tetragonal structure(space group I41md,No.109),featuring three dimensional honeycomb networks of Pt-As and a much elongated c-axis(a=b=4.18?,and c=43.70?).The superconductivity of CaPtAs with Tc=1.47 K was characterized by means of electrical resistivity,specific heat,and ac magnetic susceptibility.The electronic specific heat Ce(T)/T shows evidence for a deviation from the behavior of a conventional BCS superconductor,and can be reasonably fitted by a p-wave model.The upper critical fieldμ0Hc2 of CaPtAs exhibits a moderate anisotropy,with an in-plane value of around 204 mT and an out-of-plane value of 148 mT.Density functional theory calculations indicate that the Pt-5 d and As-4 p orbitals mainly contribute to the density of states near the Fermi level,showing that the Pt-As honeycomb networks may significantly influence the superconducting properties.