Fixed point theorems on ordered metric spaces and applications to nonlinear elastic beam equations

In this paper, we establish certain fixed point theorems in metric spaces with a partial ordering. Presented theorems extend and generalize several existing results in the literature. As application, we use the fixed point theorems obtained in this paper to study existence and uniqueness of solutions for fourth-order two-point boundary value problems for elastic beam equations.     

Ultrasonic characterization of a fluid layer using a broadband transducer

A measurement method is proposed for the ultrasonic characterization of a fluid layer, corresponding to the resin transfer molding (RTM) manufacturing process. The ultrasonic velocity and attenuation of the silicone oil are measured in three samples having different viscosities. The measurement method is established on the basis of the attenuation of ultrasonic waves in fluids. A correction of the beam diffraction is implemented to improve measurement precision. A single element transducer with central frequency of 15 MHz is used. The tested fluids simulate the industrial resin used to manufacture composite materials. When injecting this resin, its viscosity increases until it reaches a critical state of polymerization. In this paper we focus on ultrasonic characterization of three fluids representing three intermediate cases of fluid resin during its injection before reaching the polymerization state.     

Preparation of peri-annulated indoles from polynitro compounds

A novel peri-annulated heterocyclic system of 1,2-dihydrobenz[6,7]oxepino[4,3,2-cd]indole was prepared starting from TNT via 4,6-dinitro-1-tosylindoline as a key intermediate. Base-induced CC bond shift in 1,2-dihydrobenz[6,7]oxepino[4,3,2-cd]indoles affords isomeric 2,11-dihydrobenz[6,7]oxepino[4,3,2-cd]indoles.     

A second order self-consistent IMEX method for radiation hydrodynamics

We present a second order self-consistent implicit/explicit (methods that use the combination of implicit and explicit discretizations are often referred to as IMEX (implicit/explicit) methods ,  and ) time integration technique for solving radiation hydrodynamics problems. The operators of the radiation hydrodynamics are splitted as such that the hydrodynamics equations are solved explicitly making use of the capability of well-understood explicit schemes. On the other hand, the radiation diffusion part is solved implicitly. The idea of the self-consistent IMEX method is to hybridize the implicit and explicit time discretizations in a nonlinearly consistent way to achieve second order time convergent calculations. In our self-consistent IMEX method, we solve the hydrodynamics equations inside the implicit block as part of the nonlinear function evaluation making use of the Jacobian-free Newton Krylov (JFNK) method ,  and . This is done to avoid order reductions in time convergence due to the operator splitting. We present results from several test calculations in order to validate the numerical order of our scheme. For each test, we have established second order time convergence.     

Mineralogical and chemical investigation of Tunisian phosphate washing waste during calcination

Phosphate washing waste (PWW) is one of the wastes generated by the phosphate mine with a very high amount. This waste was investigated in this work to study the effect of the calcination of the PWW at four different temperatures 600 °C, 700 °C, 800 °C and 900 °C on its mineralogical and chemical composition. The samples were investigated by X-ray powder diffraction, Fourier transform infrared, differential scanning calorimetry and thermogravimetric analysis, solid-state magic angle spinning nuclear magnetic resonance of ²⁹Si, ²⁷Al and ³¹P and scanning electron microscope. The results show that the PWW presents a complex system and it suffers a significant change on its mineralogical and chemical composition after calcination. It reveals the presence of carbonate, natural zeolite, fluorapatite, quartz and clay. After calcination, the waste shows the disappearance of some of these phases and the appearance of others and some other phases remain steady.

     

Synthesis of heterocyclic systems with a carbohydrate fragment

The reactions of levoglucosenone with urea, thiourea andN-cyano- andN-nitroguanidines result in pyrimidine systems fused with a carbohydrate fragment. In all cases, the cyclization occurs stereospecifically. The structures of different products of conversion of levoglucosenone were established on the basis of NMR and X-ray diffraction data.     

Synthesis of 2-amino-5-nitro-4H-pyran-3-carbonitriles

Reaction of 2-carbomethoxy-ω-nitroacetophenone with arylmethylenemalononitriles gives the previously unknown 2-amino-4-aryl-5-nitro-6-(2-carbomethoxyphenyl)-4H-pyran-3-carbonitriles. N. D. Zelinskii Institute of Organic Chemistry, Russian Academy of Sciences, Moscow 117913. E-mail: muskat@cacr.ioc.ac.ru. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 12, pp. 1661–1663, December, 1998.