title: Lie theory and separation of variables. 3. The equation ftt−fss =γ2f

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: Kalnins has related the 11 coordinate systems in which variables separate in the equation ftt−fss = γ 2f to 11 symmetric quadratic operators L in the enveloping algebra of the Lie algebra of the pseudo-Euclidean group in the plane E(1,1). There are, up to equivalence, only 12 such operators and one of them, LE, is not associated with a separation of variables. Corresponding to each faithful unitary irreducible representation of E(1,1) we compute the spectral resolution and matrix elements in an L basis for seven cases of interest and also give overlap functions between different bases: Of the remaining five operators three are related to Mathieu functions and two are related to exponential solutions corresponding to Cartesian type coordinates. We then use these results to derive addition and expansion theorems for special solutions of ftt−fss = 2f obtained via separation of variables, e.g., products of Bessel, Macdonald and Bessel, Airy and parabolic cylinder functions. The exceptional operator LE is also treated in detail.

text: Lie theory and separation of variables. 3. The equation ftt−fss =γ2f Kalnins has related the 11 coordinate systems in which variables separate in the equation ftt−fss = γ 2f to 11 symmetric quadratic operators L in the enveloping algebra of the Lie algebra of the pseudo-Euclidean group in the plane E(1,1). There are, up to equivalence, only 12 such operators and one of them, LE, is not associated with a separation of variables. Corresponding to each faithful unitary irreducible representation of E(1,1) we compute the spectral resolution and matrix elements in an L basis for seven cases of interest and also give overlap functions between different bases: Of the remaining five operators three are related to Mathieu functions and two are related to exponential solutions corresponding to Cartesian type coordinates. We then use these results to derive addition and expansion theorems for special solutions of ftt−fss = 2f obtained via separation of variables, e.g., products of Bessel, Macdonald and Bessel, Airy and parabolic cylinder functions. The exceptional operator LE is also treated in detail.

year: 1974-07

title: Removal of the water soluble binder components from titanium and titanium alloy powder compacts produced by MIM

authors: Ewart, Paul

subjects: Debinding

abstract: This work investigates the debinding process of powder compacts formed by metal injection moulding (MIM) of feedstocks comprised of HDH Ti or HDH Ti-6Al-4V powder mixed with a binder of a predetermined ratio of water soluble polyethylene and wax. The full debinding process has three stages: a solvent debinding process to leach the water soluble component, a drying phase allowing the removal rate to be measured and a thermal treatment step for removing the wax components, leaving the backbone components to retain part geometry prior to sintering. Leaching of the water soluble component was monitored and the results were consistent with the general correlation which predicts that binder removal time increases by a factor of 4 when the section thickness is doubled. Uniformity of binder removal, defect formation and particle surface degradation in Ti MIM parts are also discussed.

text: Removal of the water soluble binder components from titanium and titanium alloy powder compacts produced by MIM This work investigates the debinding process of powder compacts formed by metal injection moulding (MIM) of feedstocks comprised of HDH Ti or HDH Ti-6Al-4V powder mixed with a binder of a predetermined ratio of water soluble polyethylene and wax. The full debinding process has three stages: a solvent debinding process to leach the water soluble component, a drying phase allowing the removal rate to be measured and a thermal treatment step for removing the wax components, leaving the backbone components to retain part geometry prior to sintering. Leaching of the water soluble component was monitored and the results were consistent with the general correlation which predicts that binder removal time increases by a factor of 4 when the section thickness is doubled. Uniformity of binder removal, defect formation and particle surface degradation in Ti MIM parts are also discussed.

year: 2012

title: In your face: wearing Moko - Maori facial marking in today's world

authors: Nikora, Linda Waimarie

subjects: Moko

abstract: The early voyagers, missionaries, settlers all reacted to the pukanohi, to the marked
faces of the Maori people during the period of first contact, and the century following
it. Their accounts are vivid, judgemental, revealing, telling us as much about them, as
it does about the people they described. Curiosity and horror are mixed with a
genuine fascination; where sternly evangelizing words failed, armed confrontation
occurred; and we now live with the results, te ao hou, a new world.
In this world, today, wahine mau kauae, tangata mau moko, pukanohi - wearers - are
speaking for themselves, about themselves, and commenting on how others view
them. Unanimously, they insist the decision to take the marking is about continuity,
affirmation, identity, and commitment. It is also about wearing those ancestors,
carrying them into the future; as their moko become a companion, a salient being with
its own life force, its own integrity and power, beyond the face.

text: In your face: wearing Moko - Maori facial marking in today's world The early voyagers, missionaries, settlers all reacted to the pukanohi, to the marked
faces of the Maori people during the period of first contact, and the century following
it. Their accounts are vivid, judgemental, revealing, telling us as much about them, as
it does about the people they described. Curiosity and horror are mixed with a
genuine fascination; where sternly evangelizing words failed, armed confrontation
occurred; and we now live with the results, te ao hou, a new world.
In this world, today, wahine mau kauae, tangata mau moko, pukanohi - wearers - are
speaking for themselves, about themselves, and commenting on how others view
them. Unanimously, they insist the decision to take the marking is about continuity,
affirmation, identity, and commitment. It is also about wearing those ancestors,
carrying them into the future; as their moko become a companion, a salient being with
its own life force, its own integrity and power, beyond the face.

year: 2003-08-01