Global infimum of strictly convex quadratic functions with bounded perturbations

The problem of minimizing [(f)\tilde]=f+p{\tilde f=f+p} over some convex subset of a Euclidean space is investigated, where f(x) = x ^T Ax + b ^T x is strictly convex and |p| is only assumed to be bounded by some positive number s. It is shown that the function [(f)\tilde]{\tilde f} is strictly outer γ-convex for any γ > γ*, where γ* is determined by s and the smallest eigenvalue of A. As consequence, a γ*-local minimal solution of [(f)\tilde]{\tilde f} is its global minimal solution and the diameter of the set of global minimal solutions of [(f)\tilde]{\tilde f} is less than or equal to γ*. Especially, the distance between the global minimal solution of f and any global minimal solution of [(f)\tilde]{\tilde f} is less than or equal to γ*/2. This property is used to prove a roughly generalized support property of [(f)\tilde]{\tilde f} and some generalized optimality conditions.     

Higher-order optimality conditions in set-valued optimization using radial sets and radial derivatives

We propose higher-order radial sets and corresponding derivatives of a set-valued map and prove calculus rules for sums and compositions, which are followed by direct applications in discussing optimality conditions for several particular optimization problems. Our main results are both necessary and sufficient higher-order conditions for weak efficiency in a general set-valued vector optimization problem without any convexity assumptions. Many examples are provided to explain advantages of our results over a number of existing ones in the literature.     

Facile synthesis of SnO2–ZnO core–shell nanowires for enhanced ethanol-sensing performance

The design of core–shell heteronanostructures is powerful tool to control both the gas selectivity and the sensitivity due to their hybrid properties. In this work, the SnO₂–ZnO core–shell nanowires (NWs) were fabricated via two-step process comprising the thermal evaporation of the single crystalline SnO₂ NWs core and the spray-coating of the grainy polycrystalline ZnO shell for enhanced ethanol sensing performance. The as-obtained products were investigated by X-ray diffraction, scanning electron microscopy, and photoluminescence. The ethanol gas-sensing properties of pristine SnO₂ and ZnO–SnO₂ core–shell NW sensors were studied and compared. The gas response to 500 ppm ethanol of the core–shell NW sensor increased to 33.84, which was 12.5-fold higher than that of the pristine SnO₂ NW sensor. The selectivity of the core–shell NW sensor also improved. The response to 100 ppm ethanol was about 14.1, whereas the response to 100 ppm liquefied petroleum gas, NH₃, H₂, and CO was smaller, and ranged from 2.5 to 5.3. This indicates that the core–shell heterostructures have great potential for use as gas sensing materials.     

Trade-off between diffraction efficiency and uniformity for design of binary diffractive laser beam shaper

The trade-off between diffraction efficiency and uniformity is studied when a binary phase-only diffractive optical element (DOE) is designed for transforming a Gaussian beam to an expanded squared uniform intensity distribution. The simulated annealing (SA) algorithm and Fresnel diffraction theory are applied in our design. Two types of cost functions are utilized in the SA algorithm, and the cases of different incident Gaussian diameters and bright-area sizes of the target patterns are studied. The mechanisms of reducing nonuniformity by the two cost functions are essentially different, and the mechanism combining nonuniformity and the intensity difference between the reconstructed and target patterns has better results. Satisfactory performance can be obtained under the trade-off between them.     

Coherent potential approximation study of the Mott transition in optical lattice system with site-dependent interactions

We study the Mott transition in the half-filled Hubbard model with spatially alternating interactions by means of the coherent potential approximation. The phase boundary between metallic and insulating phases at zero temperature is derived and the nature of the Mott states is also considered. Our results are in good agreement with the ones recently obtained by the two-site dynamical mean-field theory.     

A backward parabolic equation with a time-dependent coefficient: Regularization and error estimates

We consider the problem of determining the temperature u(x,t)$u(x,t)$, for (x,t)∈[0,π]×[0,T)$(x,t)\in [0,\pi ]\times [0,T)$ in the parabolic equation with a time-dependent coefficient. This problem is severely ill-posed, i.e., the solution (if it exists) does not depend continuously on the given data. In this paper, we use a modified method for regularizing the problem and derive an optimal stability estimation. A numerical experiment is presented for illustrating the estimate.     

Loewy Modules with Finite Loewy Invariants and Max Modules with Finite Radical Invariants

Over a commutative ring R, a module is artinian if and only if it is a Loewy module with finite Loewy invariants [5 Facchini , A. ( 1981 ). Loewy and artinian modules over commutative rings . Ann. Mat. Pura Appl. 128 : 359 – 374 .[Crossref], [Web of Science ®] , [Google Scholar]]. In this paper, we show that this is not necesarily true for modules over noncommutative rings R, though every artinian module is always a Loewy module with finite Loewy invariants. We prove that every Loewy module with finite Loewy invariants has a semilocal endomorphism ring, thus generalizing a result proved by Camps and Dicks for artinian modules [3 Camps , R. , Dicks , W. ( 1993 ). On semilocal rings . Israel J. Math. 81 : 203 – 211 .[Crossref], [Web of Science ®] , [Google Scholar]]. Finally, we obtain similar results for the dual class of max modules.     

Solution/Ammonolysis Syntheses of Unsupported and Silica-Supported Copper(I) Nitride Nanostructures from Oxidic Precursors

Herein we describe an alternative strategy to achieve the preparation of nanoscale Cu₃N. Copper(II) oxide/hydroxide nanopowder precursors were successfully fabricated by solution methods. Ammonolysis of the oxidic precursors can be achieved essentially pseudomorphically to produce either unsupported or supported nanoparticles of the nitride. Hence, Cu₃N particles with diverse morphologies were synthesized from oxygen-containing precursors in two-step processes combining solvothermal and solid−gas ammonolysis stages. The single-phase hydroxochloride precursor, Cu₂(OH)₃Cl was prepared by solution-state synthesis from CuCl₂·2H₂O and urea, crystallising with the atacamite structure. Alternative precursors, CuO and Cu(OH)₂, were obtained after subsequent treatment of Cu₂(OH)₃Cl with NaOH solution. Cu₃N, in the form of micro- and nanorods, was the sole product formed from ammonolysis using either CuO or Cu(OH)₂. Conversely, the ammonolysis of dicopper trihydroxide chloride resulted in two-phase mixtures of Cu₃N and the monoamine, Cu(NH₃)Cl under similar experimental conditions. Importantly, this pathway is applicable to afford composite materials by incorporating substrates or matrices that are resistant to ammoniation at relatively low temperatures (ca. 300 °C). We present preliminary evidence that Cu₃N/SiO₂ nanocomposites (up to ca. 5 wt.% Cu₃N supported on SiO₂) could be prepared from CuCl₂·2H₂O and urea starting materials following similar reaction steps. Evidence suggests that in this case Cu₃N nanoparticles are confined within the porous SiO₂ matrix.     

Activated Carbon by KOH and NaOH Activation: Preparation and Electrochemical Performance in K2SO4 and Na2SO4 Electrolytes

Russian Journal of Electrochemistry - Activated carbons were successfully prepared from rice husk (RH) by chemical activation using KOH (RH-K4) or NaOH (RH-N3) as activating agents and...     

Fabrication of Nano Flower‐shaped Platinum on Glassy Carbon Electrode as a Sensitive Sensor for Lead Electrochemical Analysis

Platinum nanoflowers modified glassy carbon electrodes (PtNFs/GCE) was fabricated simply for lead determination in water samples. The modified electrodes were prepared by electrodeposition in hexachloroplatinic acid solution at constant potential. The influence of deposition time and potential on surface morphology, chemical composition, electrochemical properties of electrode were investigated. At ?0.2 V of potential and 150 s of deposition duration, platinum developed as nanoflower shape and scattered densely all over the glassy carbon surface, producing the largest electrochemically active surface areas. The highest differential pulse stripping voltammetry (DPSV) signal of lead was obtained by using the prepared electrode. Under optimized experimental condition of electrolyte, accumulation potential and time, the peak current was found to be linear proportion to lead concentration in range of 1 to 100 μg L^?1 (slope=0.371) with a limit of detection of 0.398 μg L^?1. The method has good repeatability and reproducibility with relative standard deviations of 1.47 % and 4.83 %, respectively. The modified PtNFs/GCE also demonstrated an excellent long‐term stability with only 9 % decrease in Pb peak current over 30 days. Moreover, the performance of the modified PtNFs/GCE in determination of Pb(II) in two industrial wastewaters was good agreement with data obtained by a graphite furnace atomic absorption spectrometry (GFAAS) method.