A Note on PIN Polynomials and PRIN Rational Functions

This brief presents a necessary and sufficient condition for testing positive, real, imaginary, and negative rational functions. A related term, the positive, imaginary, and negative polynomial, is defined and two necessary and sufficient conditions for testing it are given.     

Cooling and Solidification of Melted Drops in an Immiscible Cooling Medium

The cooling and solidification of melted drops during their movement in an immiscible cooling medium is widely employed for granulation in the chemical industry, and a study of these processes to provides a basis for the design of the granulation tower height and the temperature of the cooling medium is reported. A physical model of the cooling and solidification of the drop is established and the numerical calculation is performed. The influences of the key factors in the solidification, i.e., Bi number, drop diameter, temperature of the cooling medium, etc. are presented. The cooling and solidification during wax granulation in a water‐cooling tower and during urea granulation in an air‐cooling tower (spraying tower) are described in detail. Characteristics of the solidification and temperature distribution within the particle at different times are shown. The model and calculations can be used for structure design of the granulation tower and optimization of the operation parameters.     

Continuous precipitation of calcium sulfate dihydrate from waste sulfuric acid and lime

Precipitation of calcium sulfate dihydrate, gypsum, from (i) a pure sulfuric acid/lime suspension and (ii) a waste sulfuric acid/lime suspension in a continuous pilot plant in the temperature range from 40 °C to 80 °C was studied. It was observed that in the case of waste sulfuric acid with a high content of Mg²⁺ and Fe²⁺ ions, several hours after the beginning of the precipitation, partial dissolution of the product and modification of the crystals from needle‐ and plate‐like to agglomerated structures occurred. It is suggested that the secondary changes occur due to the increased concentration of Mg²⁺ and Fe²⁺ ions in the reactor. Below 60 °C, and above 70 °C plate‐like and needle‐like single crystals respectively were formed. The mean size (d₅₀) of the crystals was found to increase with increasing temperature and decrease with the initial concentration of lime. Gypsum produced between 70 °C and 80 °C is suitable for further processing for construction plaster. In a precipitation process with pure sulfuric acid only single perfect needle‐like crystals occurred. Copyright © 2005 Society of Chemical Industry     

A general framework for debugging

The state of the art of debugging is examined. A debugged process model that serves as the basis of a general debugging framework is described. The relationship of the model to traditional debugging processes and support tools is discussed. A minimal set of requirements for a general debugging framework is described in terms of both the theory behind debugging methodologies and the support tools. An execution monitor, Eden, that serves as a debugging tool within this general framework is described     

A comparison of the3He melting curve,T c(P) curve,and the susceptibility of lanthanum-diluted cerium magnesium nitrate below 50 mK

The ac susceptibility of lanthanum-diluted cerium magnesium nitrate has been compared to the temperature scales as derived from the (P, T) relation determined by Halperin and that was measured recently by Greywall. It is found that the susceptibility does not obey a simple Curie-Weiss law over the temperature range between 1 and 50 mK. The results of these calibrations are also used to determine the temperatures for the second-order phase transitions into the superfluid phases of³He at several pressures. TheseT _c(P) values are compared to results of earlier experiments that used thermometry based on the susceptibility of platinum as well as other thermometry techniques.     

Low-thermal expansion polycrystalline tantalum tungstate ceramics

The synthesis of thermal-shock-resistant materials from the system Ta₂O₅WO₃ was investigated. Ta₂WO₈ had a very low unit-cell thermal expansion coefficient (+0.5 X 10^–6° C^–1). Ta₃₀W₂O₈₁ also had a relatively low coefficient (+4.0 X 10^–6 ° C^–1) and a thermal durability over 1600° C. The thermal expansion curves of these polycrystalline ceramics were lowered because of microcracks caused by the large thermal expansion anisotropy of the crystal axes and were accompanied by hysteresis loops. The densification of Ta₂WO₈ ceramic was promoted by the addition of some metal oxides, and the strong ceramic of Ta₃₀W₂O₈₁ was obtained by controlling grain growth.     

Effects of alloy additions on the microstructures and tensile properties of cast Co-Cr-Mo alloy used for surgical implants

The composition of the Co-Cr-Mo alloy has been modified by additions of nickel and some trace elements aluminium, titanium and boron. In this paper, the first part of the present study, the effects of alloy additions on the microstructures and tensile properties of the as-cast Co-Cr-Mo alloy are discussed. The effects of alloy additions on the fatigue behaviour of the alloy will be discussed in the second part of the present study. It is found that alloy additions do not seem to result in changes in the nature of the casting structure. A directional, coarse dendritic cast structure is produced in the modified alloys as in the base alloY. However, the alloy additions affect the carbide precipitations and the formation of some fine details of the microstructure such as dislocations, stacking faults and twins produced during the solidification. A considerable improvement in the transient mechanical properties, especially in the tensile ductility, is achieved by modifying the base alloy with alloy additions.     

Theoretical analysis of RAIM in the occurrence of simultaneous two-satellite faults

Most algorithms on receiver autonomous integrity monitoring (RAIM) are under the assumption of a single-satellite fault, because there is an extremely small probability that significant simultaneous multiple-satellite faults may occur. However, after the implementation of the Galileo system in a few years, there will be more satellites in view for the user to utilise together with GPS satellites, and a combination of them will bring better performance for RAIM. On the other hand, with the help of wide area augmentation system and the use of dual-frequency operation, pseudo-range errors will be reduced greatly. Thus, tighter alert limits are required for RAIM, and formerly `small' errors should not be neglected. All of those factors make it necessary to consider simultaneous multiple-satellite faults. A detailed theoretical analysis of RAIM under the condition of two-satellite faults for both vertical and horizontal directions is presented. The characteristic/max slopes for every pair of satellites are then deduced in order to calculate the tighter vertical/horizontal protection level for RAIM     

LLDPE’s grown with Metallocene and Ziegler–Natta catalysts: events in the melt and FTIR analysis

LLDPE samples synthesized with Ziegler–Natta (ZN) and Metallocene (MT) catalysts have been analyzed to investigate a potential catalyst-dependent morphology and to find an explanation for the difficult processing of MT. Slow calorimetry at v = 0.02 K/min and IR at RT and in the melt are used. The differences between MT and ZN are assigned to their different composition, MT not having the linear segments, which are present in ZN. Slow calorimetry is effectively a drawing process of the melt with chain orientation followed by decay. The later event, characterized by an endotherm, ΔH _network, occurs at higher temperatures for MT, the presence of a regular distribution of methyl groups slowing down the process. The rocking, gauche, bending and stretching regions of the IR spectra are analyzed. The nascent MT has more strained bands in the rocking region. The wagging region reveals the more homogeneous environment of MT through the maximum absorbance at 1,368 cm⁻¹. Decomposition of bands is made for the rocking and wagging regions. The orthorhombic crystallinity, α_c (FTIR), measures the sum of long- and short-range orthorhombic order, the latter being obtained by α_c (FTIR)-α_c (X-rays). The values of α_c (FTIR) for MT and ZN are very similar in conditions of equilibrium. The justifications for the molecular origin of ΔH _network are presented: (i) the slow relaxation of long chains strained and oriented in the melt measured by other techniques, (ii) The correlation, for gels of a linear sample, made in different solvents, between the maximum drawability, λ_max, and ΔH _network in a slow T-ramp. The range is 80–270 for λ_max and 40–120 J/g for ΔH _network. (iii) The comparison of two traces of the same sample, between 140 °C and 270 °C, show that comparable events in the melt appear in the integrated absorbance and in the slow calorimetry signal. Analysis on thin films of the little-studied CH₂ stretching region reveals that their extinction coefficient, ε, and the shape of the bands are highly sensitive to the sample history, ε diminishing by a large factor in slowly crystallized samples. Events in the slow T-ramp, followed by a fast crystallization, on the other hand, leads to materials with standard characteristics. Slow calorimetry traces display more events (endothermic and exothermic) for MT than for ZN, a finding consistent with more flow irregularities during processing. Equilibrium conditions and better processing could be reached for MT by extending time in the melt or using higher temperatures.