Interdigital transducers deposited on glass were used to couple acoustic waves in the 10–50-MHz f... more Interdigital transducers deposited on glass were used to couple acoustic waves in the 10–50-MHz frequency range into a b-cut (010) TGS plate from room temperature to slightly above the ferroelectric phase transition temperature, Tc = 49.1°C. The coupling peaked near Tc. Two major modes were observed. Evidence is given identifying the higher frequency mode with a longitudinal bulk wave and the lower frequency mode with a bulk shear wave. The velocities of the upper and lower frequency modes for temperatures near Tc were found from their resonant frequencies to be (4.18±0.06)×105 and (2.56±0.06)×105 cm∕sec, respectively. Data on the temperature variation of the velocity of the low frequency mode are given. Estimates of the effective piezoelectric coupling constants for the two modes are deduced from the data.
We generalise to abstract many-sorted algebras the classical proof-theoretic result due to Parson... more We generalise to abstract many-sorted algebras the classical proof-theoretic result due to Parsons and Mints that an assertion " x $ y P(x,y){\forall} x {\exists} y {\it P}(x,y) (where P is ∑01^{\rm 0}_{\rm 1}), provable in Peano arithmetic with ∑01^{\rm 0}_{\rm 1} induction, has a primitive recursive selection function. This involves a corresponding generalisation to such algebras of the notion of primitive recursiveness. The main difficulty encountered in carrying out this generalisation turns out to be the fact that equality over these algebras may not be computable, and hence atomic formulae in their signatures may not be decidable. The solution given here is to develop an appropriate concept of realisability of existential assertions over such algebras, and to work in an intuitionistic proof system. This investigation gives some insight into the relationship between verifiable specifications and computability on topological data types such as the reals, where the atomic fo...
Functional Programming, Concurrency, Simulation and …, 1993
... Remark ~. To correlate this semantic definition with the one in the following paper, we can u... more ... Remark ~. To correlate this semantic definition with the one in the following paper, we can use the notation [p] (See Remark 1 in ~3, loc. cir.) Remark $. ... 3 Fixed point characterizations We first define some notation. ... 4 Safety, Liveness and Fairness Properties ...
Interdigital transducers deposited on glass were used to couple acoustic waves in the 10–50-MHz f... more Interdigital transducers deposited on glass were used to couple acoustic waves in the 10–50-MHz frequency range into a b-cut (010) TGS plate from room temperature to slightly above the ferroelectric phase transition temperature, Tc = 49.1°C. The coupling peaked near Tc. Two major modes were observed. Evidence is given identifying the higher frequency mode with a longitudinal bulk wave and the lower frequency mode with a bulk shear wave. The velocities of the upper and lower frequency modes for temperatures near Tc were found from their resonant frequencies to be (4.18±0.06)×105 and (2.56±0.06)×105 cm∕sec, respectively. Data on the temperature variation of the velocity of the low frequency mode are given. Estimates of the effective piezoelectric coupling constants for the two modes are deduced from the data.
We generalise to abstract many-sorted algebras the classical proof-theoretic result due to Parson... more We generalise to abstract many-sorted algebras the classical proof-theoretic result due to Parsons and Mints that an assertion " x $ y P(x,y){\forall} x {\exists} y {\it P}(x,y) (where P is ∑01^{\rm 0}_{\rm 1}), provable in Peano arithmetic with ∑01^{\rm 0}_{\rm 1} induction, has a primitive recursive selection function. This involves a corresponding generalisation to such algebras of the notion of primitive recursiveness. The main difficulty encountered in carrying out this generalisation turns out to be the fact that equality over these algebras may not be computable, and hence atomic formulae in their signatures may not be decidable. The solution given here is to develop an appropriate concept of realisability of existential assertions over such algebras, and to work in an intuitionistic proof system. This investigation gives some insight into the relationship between verifiable specifications and computability on topological data types such as the reals, where the atomic fo...
Functional Programming, Concurrency, Simulation and …, 1993
... Remark ~. To correlate this semantic definition with the one in the following paper, we can u... more ... Remark ~. To correlate this semantic definition with the one in the following paper, we can use the notation [p] (See Remark 1 in ~3, loc. cir.) Remark $. ... 3 Fixed point characterizations We first define some notation. ... 4 Safety, Liveness and Fairness Properties ...
Uploads