Algebraic Geometry over Free Metabelian Lie Algebra I: U-Algebras and Universal Classes

This paper is the first in a series of three, the aim of which is to lay the foundations of algebraic geometry over the free metabelian Lie algebra $F$. In the current paper we introduce the notion of a metabelian Lie $U$-algebra and establish connections between metabelian Lie $U$-algebras and special matrix Lie algebras. We define the $\Delta$-localisation of a metabelian Lie $U$-algebra $A$ and the direct module extension of the Fitting's radical of $A$ and show that these algebras lie in the universal closure of $A$.Comment: 34 page

Annular flow of viscoelastic fluids: Analytical and numerical solutions

This work provides analytical and numerical solutions for the linear, quadratic and exponential Phan–Thien–Tanner (PTT) viscoelastic models, for axial and helical annular fully-developed flows under no slip and slip boundary conditions, the latter given by the linear and nonlinear Navier slip laws. The rheology of the three PTT model functions is discussed together with the influence of the slip velocity upon the flow velocity and stress fields. For the linear PTT model, full analytical solutions for the inverse problem (unknown velocity) are devised for the linear Navier slip law and two different slip exponents. For the linear PTT model with other values of the slip exponent and for the quadratic PTT model, the polynomial equation for the radial location (β) of the null shear stress must be solved numerically. For both models, the solution of the direct problem is given by an iterative procedure involving three nonlinear equations, one for β, other for the pressure gradient and another for the torque per unit length. For the exponential PTT model we devise a numerical procedure that can easily compute the numerical solution of the pure axial flow problemCOMPETE, FEDER and Fundação para a Ciência e a Tecnologia (FCT) through projects PEst-C/CTM/LA0025/2013 (Strategic Project – LA 25 – 2013-2014), PTDC/EQU-FTT/113811/2009 and PTDC/EME-MFE/113988/2009. LLF and AMA would also like to thank FCT for financial support through the scholarships SFRH/BD/37586/2007 and SFRH/BPD/75436/2010, respectively

Проблема острых ингаляционных воздействий аммиака при промышленных авариях

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Melt fracture behaviour of molten polypropylenes

Experiments were carried out in both sliding plate and capillary I rheometers with two polypropylene resins to determine the conditions for the onset of slip, surface and gross melt fracture. It was found that there was no distinction between surface and gross melt fracture, which is commonly observed in the case of polyethylenes. Furthermore, the flow curves determined by using capillaries having various diameters are diameter independent, implying the absence of slip. However, performing experiments with slit dies having rough surfaces suggested the presence of wall slip. Further analysis has shown that the effect of viscous heating masks the detection of slip from the diameter dependency of the flow curves. The effect of presence of a thin layer of fluoropolymer (Teflon® PA and Viton®, DuPont) on the critical shear stress for the onset of wall slip and melt fracture as well as on the relationship between the wall slip and the shear stress were also examined. It was found that the presence of such layers increases the slip velocity while decreases the critical shear stress for the onset of slip. Surprisingly, this reduction in the wall shear stress had no effect on the critical shear rate for the onset of melt fracture.Applied Science, Faculty ofChemical and Biological Engineering, Department ofGraduat

Surgical treatment of enuresis in case of urinary bladder extrophy in children

Available from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio

Influence of molecular structure on rheological and processing behaviour of molten polymers

The primary focus of this work was to study the effect of molecular characteristics of polymers on their rheological and processing behaviour. In particular, the melt fracture and wall slip phenomena have been extensively studied using various rheological tools and techniques. In order to study the effects of the two key molecular characteristics, the weight average molecular weight and the molecular weight distribution, two series of polyethylene resins have been specially selected. A new method of interpretation of the large-amplitude oscillatory shear (LAOS) data has been proposed. It provides an easier and more convenient way for the data analysis suitable for use as a non-linear viscoelastic polymer characterisation technique. In addition, this method has been shown to offer an alternative way for determination of the damping function. Furthermore, a criterion for melt fracture performance has been developed and it was found to be related to a characteristic relaxation time of polymers. Additional experiments have been carried out with two metallocene polyethylene resins, which exhibited unusually long start-up transients during their capillary extrusion. This phenomenon has been investigated in detail and the results are explained in terms of a qualitative molecular model based on the two mechanisms of slip, namely flow-induced chain detachment and disentanglement. A multimode dynamic slip model has also been developed and a procedure for the determination of its parameters is proposed. The model has been found to provide better predictions compared to a static and a single-mode slip models for the flow of molten polymers in transient experiments under slip conditions. Finally, a flow visualisation apparatus has been developed using a quartz capillary and interrupted laser beam. It allowed the measurement of the velocity profiles at high temperatures and shear stresses. Using this apparatus, the effect of processing aids on the flow profile and melt fracture behaviour of molten polypropylene has been studied.Applied Science, Faculty ofChemical and Biological Engineering, Department ofGraduat