Wiener’s criterion for the unique solvability of the Dirichlet problem in arbitrary open sets with non-compact boundaries

This paper establishes a necessary and sufficient condition for the existence of a unique bounded solution to the classical Dirichlet problem in arbitrary open subset of R^N${\mathbb{R}}^N$ (N≥3$N\ge 3$) with a non-compact boundary. The criterion is the exact analogue of Wiener’s test for the boundary regularity of harmonic functions and characterizes the “thinness” of a complementary set at infinity. The Kelvin transformation counterpart of the result reveals that the classical Wiener criterion for the boundary point is a necessary and sufficient condition for the unique solvability of the Dirichlet problem in a bounded open set within the class of harmonic functions having a “fundamental solution” kind of singularity at the fixed boundary point. Another important outcome is that the classical Wiener’s test at the boundary point presents a necessary and sufficient condition for the “fundamental solution” kinds of singularities of the solution to the Dirichlet problem to be removable.     

A numerical study of turbulent opposed impinging jets issuing from triangular nozzles with different geometries

In present research, two turbulent opposed impinging air jets issuing from triangular nozzles with fixed and variable exit velocity ratios and different nozzle-to-nozzle distances have been studied numerically and then compared with rectangular and circular nozzles. The finite volume method has been applied for solving mass and momentum equations. The turbulence model being used here is k-ε RNG. Distributions of pressure, turbulence, kinetic energy and its dissipation rate in various regions especially on the impingement regions have been obtained with high accuracy. Study of the nozzle geometries has shown the advantage of triangular nozzles over other geometries. First, the triangle’s base in nozzle geometry has an important role in our study case which, mixing two flows and regions with high turbulence intensity, directly depends on it. Second, our results show that circular and rectangular nozzles have less efficiency than triangular nozzles in mixing applications. Third and last, it was found that the radial jet being created by opposed jets has some similarities to free jets. In this investigation, air in standard atmospheric pressure has been applied as working fluid.     

A new MIP model for mine equipment scheduling by minimizing maintenance cost

Mining investment has been recognized as capital intensive due mainly to the cost of large equipment. Equipment capital costs for a given operation are usually within the order of hundreds of million dollars but may reach to billion dollars for large companies operating multiple mines. Such large investments require the optimum usage of equipment in a manner that the operating costs are minimized and the utilization of equipment is maximized through optimal scheduling. This optimum usage is required to ensure that the business remains sustainable and financially stable. Most mining operations utilize trucks to haul the mined material. Maintenance is one of the major operating cost items for these fleets as it can reach approximately one hundred million dollars yearly. There is no method or application in the literature that optimizes the utilization for truck fleet over the life of mine. A new approach based on mixed integer programming (MIP) techniques is used for annually scheduling a fixed fleet of mining trucks in a given operation, over a multi-year time horizon to minimize maintenance cost. The model uses the truck age (total hours of usage), maintenance cost and required operating hours to achieve annual production targets to produce an optimum truck schedule. While this paper focuses on scheduling trucks for mining operation, concept can be used in most businesses using equipment with significant maintenance costs. A case study for a large scale gold mine showed an annual discounted (10% rate) maintenance cost saving of over $2M and more than 16% ($21M) of overall maintenance cost reduction over 10 years of mine life, compared with the spreadsheet based approach used currently at the operation.     

Evolution of Structural and Magnetic Properties of BaFe12O19 with B2O3 Addition

We investigate the effects of B2O3 addition on structural and magnetic properties of hard magnetic BaFe12O19 particles. The conventional solid state reaction method is used as the synthesis route. Single phase BaFe12O19 could be synthesized with very small amounts of B2O3 addition and with calcination at low temperatures （850°C） in short times （1 h）. B2O3 addition also improves the magnetic parameters significantly. Remanence magnetization and specific magnetization at 1.5 T increase by ～40% in magnitude although no significant variations on coercivity is observed.     

一个解剖基人体下肢的生物动力模型--第一部分: 模型描述

建立一个完整的解剖基人体下肢二维（矢状面内）生物动力模型,该模型仿真了人体下肢的生物动力运动,并可用来计算人体下肢在冲击外载荷或肌肉活性力的作用下,下肢的重要承力部位－膝关节处的结构力（包括：膝关节的咬合接触力、膝关节处四个主要韧带张力等）和人体下肢的肌肉群力;同时本模型也可用来计算人体下肢在运动期间,膝关节处的咬合位移以及膝关节和髋关节的屈伸位移等。另外,模型还为研究人工关节、人工韧带和人工肌肉     

Effect of structural modifications of diaza-18-crown-6 on the extractability and selectivity of univalent metal picrates

The solvent extraction of univalent metal cations with N,N'-dibenzyl-1,4,10,13-tetraoxa-7,16 diaza-2,3,11,12-dibenzocycloocta deca-2,11-diene (L(1)), N,N' didodecyl-1,4,10,13-tetraoxa-7,16-diaza-2,3-benzocylooctadeca-2 ene (L(2)) and N,N'-dibenzyl-1,4,10,13-tetraoxa-7,16 diaza-2,3,11,12-dibenzocyclo octadeca-2,11-diene (L(3)) with picrate anion into dichloromethane has been studied at 25 degrees C by UV-visible spectroscopy. The extractability and selectivity of univalent metal picrates (Li(+), Na(+), Ag(+), PhCH(2)NH(3)(+), NH(4)(+)) was evaluated as a function of [ligand]/[metal cation]. L(2) showed the highest extractability and selectivity for Li(+) over the larger studied cations, and also exhibited the highest [Li(+)]/[NH(4)(+)] selectivity as L/M=1.     

On Intersection of Maximal Orthogonally k-Starshaped Polygons

Let F be a simply connected orthogonal polygon in R ² and let P denote the intersection of all maximal orthogonally k-starshaped polygons in F for any fixed integer k,k2. If P and for every x,y P which are joined in F by a staircase path having two segments there is a similar staircase path from x to y in P, then there exists a maximal orthogonally k-starshaped polygon Q in F such that the staircase k-kernel of Q is a subset of the staircase k-kernel of P. In particular, F is either an orthogonally k-starshaped simply connected polygon in F or empty.     

Carbon-13 Nuclear Magnetic Resonance Spectroscopy Study of the Glucose Stress of Human Lenses

The sorbitol theory in diabetic cataractogenesis was based on sorbitol accumulation under glucose stress. Sorbitol accumulation was examined by ¹³C nuclear magnetic resonance spectroscopy (NMR) for the first time in matched human lenses incubated in 5.5 mM and 35.5 mM C-1 ¹³C-enriched glucose up to 28 hours. The results showed that sorbitol and lactate in human tens can be detected at 35.5 mM, but not in 5.5 mM glucose solution. The glycolysis metabolic pathway of human lenses may be quite different from that of animals. The accumulation of metabolites can be traced and quantified by the intensities of ¹³C NMR peaks. Therefore, ¹³C NMR spectroscopy can be used as a valuable tool to investigate human lens carbohydrate metabolism non-interventionally.     

Electrochemical control of solid phase micro-extraction: conducting polymer coated film material applicable for preconcentration/analysis of neutral species

Exploitation of the physical, chemical and electrically conductive properties of poly(3-dodecylthiophene) (P3DDT) for the preconcentration and release in solid phase microextraction (SPME) of organometallic arsenobetaine (AsB) from aqueous media was investigated. Hydrophobic interactions between this neutral arsenic species and an undoped polythiophene (no applied potential) with n-substituted alkyl groups (n=12) in the three position were used for the diffusion-controlled preconcentration. After absorption into the polymer matrix, the chemical properties of this conductive polymer were changed by applying an external potential. This potential provides a sufficient driving force for desorption of the analyte from the extraction phase into an aqueous solution for subsequent analysis. The applied positive potential oxidizes the polymer to its charged hydrophilic state, which releases the neutral analyte. The concentration and speciation of the analyte from the sample matrix was analyzed by HPLC coupled to an ICP-MS. The diffusion-controlled uptake was fast (equilibrium attained within minutes) and did not require pretreatment of the analyte. The electrochemically-controlled release of the analyte is also very rapid (within minutes). This conducting polymer film system, therefore, can offer analytical applications for the convenient preconcentration and subsequent analysis of neutral environmental species.