Intrinsic metric preserving maps on partially ordered groups

In [11] Pap proved that a surjective mapf from an abelian lattice ordered groupG ₁ onto an abelian Archimedean lattice ordered group G₂ which preserves non-zero intrinsic metricsd ₁, andd ₂ onG ₁ andG ₂, respectively (i.e.d ₁(x,y)=d₁(z, t) implies d₂(f(x)f(y))= d₂(f(z),f(t))) and satisfiesf(0)=0 is a homomorphism and put the question whether that assertion is true in the case that G₂ is a non-Archimedean lattice ordered group. In this paper it is proved that a surjective map from an abelian directedG ₁ onto a directed group G₂ such thatf(0)=0 is a homomorphism if ¦x –y ¦=¦z – t¦ implies ¦f(x) –f(y)¦=¦f(z) –f(t)¦ and it is shown that the answer to the question of Pap is positive.Presented by M. Henriksen.     

Measurement of electron distribution function by means of direct differentiation of probe characteristic

Conclusion Using the above described method we measured the electron distribution function in homogeneous positive column of a low-pressure discharge for different repetition frequencies and different time intervals of recording the probe characteristic. An example of the second derivative of the probe charecteristic measured at a repetition frequency of 1 kHz is shown in Fig. 3. The probe characteristic was recorded in 10 us intervals, i.e. 0.01 period.The method can be easily applied for measurements in a steady state as well as in a periodically changing discharge. Substantial advantage of this method lies in the possibility to measure the electron distribution function and its changes during short time intervals (of the order of several us), which enables to apply the method for measurements in unstable and extinguishing plasmas.Works on improving this method even further are presently under way; they are focussed in the first place on using this method for the measurements of the electron distribution function in an extinguishing plasma, where the maximum of electron distribution function lies at energies of the order of 0.1 eV. The method of superimposing a small harmonic signal on the probe bias is virtually impracticable for such low energies, because this method gives accurate results only for the probe voltages that are much higher than the amplitude of superimposed signal.The procedure for testing the correct operation of the apparatus and its accuracy in determining the second derivative, as described above, is applicable also for other methods used in differentiating the probe characteristic, where only indirect methods were used so far.     

Synthesis and Thermodynamic Investigation of 4-Amino-6-Hydroxy-2-Mercapto Pyrimidine (AHMP) Complexes with Some Selected Divalent Metal(II) Ions

The synthesis and characterization of zinc(II), cadmium(II), lead(II), mercury(II) and phenylmercury(II) complexes of 4-amino-6-hydroxy-2-mercapto pyrimidine (AHMP) are reported. The stoichiometry of the complexes was found to be 1:2 except for the phenylmercury(II) complex where the ratio is 1:1. Characterization of these complexes was carried out by means of elemental analyses, IR and ¹H NMR measurements. In these complexes the ligand is bonded to the metal through its sulfur atom. The potentiometric results showed the formation of 1:1 and 1:2 complexes and the corresponding stability constants were determined for both Zn(II) and Cd(II) ions. The high insolubility of mercury(II), phenylmercury(II) and lead(II) complexes prevented the determination of their stability constants. The concentration distribution of the complexes in solution was evaluated. The effect of temperature on the dissociation constant of AHMP and the formation constants of both the Zn-AHMP and Cd-AHMP complexes were studied and the thermodynamic parameters were calculated.     

Modeling and analysis of stick-slip and bit bounce in oil well drillstrings equipped with drag bits

Rotary drilling systems equipped with drag bits or fixed cutter bits (also called PDC), used for drilling deep boreholes for the production and the exploration of oil and natural gas, often suffer from severe vibrations. These vibrations are detrimental to the bit and the drillstring causing different failures of equipment (e.g., twist-off, abrasive wear of tubulars, bit damage), and inefficiencies in the drilling operation (reduction of the rate of penetration (ROP)). Despite extensive research conducted in the last several decades, there is still a need to develop a consistent model that adequately captures all phenomena related to drillstring vibrations such as nonlinear cutting and friction forces at the bit/rock formation interface, drive system characteristics and coupling between various motions. In this work, a physically consistent nonlinear model for the axial and torsional motions of a rotating drillstring equipped with a drag bit is proposed. A more realistic cutting and contact model is used to represent bit/rock formation interaction at the bit. The dynamics of both drive systems for rotary and translational motions of the drillstring, including the hoisting system are also considered. In this model, the rotational and translational motions of the bit are obtained as a result of the overall dynamic behavior rather than prescribed functions or constants. The dynamic behavior predicted by the proposed model qualitatively agree well with field observations and published theoretical results. The effects of various operational parameters on the dynamic behavior are investigated with the objective of achieving a smooth and efficient drilling. The results show that with proper choice of operational parameters, it may be possible to minimize the effects of stick-slip and bit-bounce and increase the ROP. Therefore, it is expected that the results will help reduce the time spent in drilling process and costs incurred due to severe vibrations and consequent damage to equipment.