Minimal set of generators for the derivation module of certain monomial curves

Let K be a field of characteristic zero and let m(0),..., m(e-1) be a sequence of positive integers. Let C be an algebroid monomial curve in the affine e-space A(K)(e) defined parametrically by X-0 = T-m0,..., Xe-1 = Tme-1 and let A be the coordinate ring of C. In this paper, we assume that some e - 1 terms of m(0),..., m(e-1) form an arithmetic sequence and construct a minimal set of generators for the derivation module Der(K)(A) of A and write an explicit formula for mu (Der(K)(A)).

Diaphragmless shock wave generators for industrial applications of shock waves

The prime focus of this study is to design a 50 mm internal diameter diaphragmless shock tube that can be used in an industrial facility for repeated loading of shock waves. The instantaneous rise in pressure and temperature of a medium can be used in a variety of industrial applications. We designed, fabricated and tested three different shock wave generators of which one system employs a highly elastic rubber membrane and the other systems use a fast acting pneumatic valve instead of conventional metal diaphragms. The valve opening speed is obtained with the help of a high speed camera. For shock generation systems with a pneumatic cylinder, it ranges from 0.325 to 1.15 m/s while it is around 8.3 m/s for the rubber membrane. Experiments are conducted using the three diaphragmless systems and the results obtained are analyzed carefully to obtain a relation between the opening speed of the valve and the amount of gas that is actually utilized in the generation of the shock wave for each system. The rubber membrane is not suitable for industrial applications because it needs to be replaced regularly and cannot withstand high driver pressures. The maximum shock Mach number obtained using the new diaphragmless system that uses the pneumatic valve is 2.125 +/- 0.2%. This system shows much promise for automation in an industrial environment.

Fuzzy logic intelligent system for gas turbine module and system fault isolation

A fuzzy logic intelligent system is developed for gas-turbine fault isolation. The gas path measurements used for fault isolation are exhaust gas temperature, low and high rotor speed, and fuel flow. These four measurements are also called the cockpit parameters and are typically found in almost all older and newer jet engines. The fuzzy logic system uses rules developed from a model of performance influence coefficients to isolate engine faults while accounting for uncertainty in gas path measurements. It automates the reasoning process of an experienced powerplant engineer. Tests with simulated data show that the fuzzy system isolates faults with an accuracy of 89% with only the four cockpit measurements. However, if additional pressure and temperature probes between the compressors and before the burner, which are often found in newer jet engines, are considered, the fault isolation accuracy rises to as high as 98%. In addition, the additional sensors are useful in keeping the fault isolation system robust as quality of the measured data deteriorates.

Interdiffusion and the vacancy wind effect in Ni-Pt and Co-Pt systems

In this study, bulk and multifoil diffusion couple experiments were conducted to examine the interdiffusion process in Ni-Pt and Co-Pt binary alloy systems. Inter-, intrinsic-, and tracer-diffusion coefficients at different temperatures, and as a function of the composition, were estimated by using the experimental data. Results show that in both the alloy systems, Pt is the slower diffusing species, and hence the interdiffusion process is controlled by either Ni or Co. The thermodynamic driving force makes the intrinsic diffusion coefficients of Co and Ni higher in the range of 30-70 at.%. The low activation energy for Co and Ni impurity diffusion in Pt compared with Pt in Ni and Co indicates that the size of the atoms plays an important role. The vacancy wind effects on the diffusion process are examined in detail, and it was demonstrated that its contribution falls within the experimental scatter and hence can be neglected.

Bases and Ideal Generators for Projective Monomial Curves

In this article we study bases for projective monomial curves and the relationship between the basis and the set of generators for the defining ideal of the curve. We understand this relationship best for curves in P-3 and for curves defined by an arithmetic progression. We are able to prove that the latter are set theoretic complete intersections.

Vacancy wind effect on interdiffusion in a dilute Cu(Sn) solid solution

A study has been conducted on a Cu(Sn) solid solution to examine the role of the vacancy wind effect on interdiffusion. First, the interdiffusion and the intrinsic diffusion coefficients are calculated. The trend of the interdiffusion coefficients is explained with the help of the driving force. Following this, the tracer diffusion coefficients of the species are calculated with and without consideration of the vacancy wind effect. We found that the role of the vacancy wind is negligible on the minor element in a dilute solid solution, which is the faster diffusing species in this system and controls the interdiffusion process. However, consideration of this effect is important to understand the diffusion rate of the major element, which is the slower diffusing species in this system.