Differential equations for the cuspoid canonical integrals

Differential equations satisfied by the cuspoid canonical integrals I_n(a) are obtained for arbitrary values of n≥2, where n−1 is the codimension of the singularity and a=(ɑ_1,ɑ_2,...,ɑ_(n−1)). A set of linear coupled ordinary differential equations is derived for each step in the sequence I_n(0,0,...,0,0) →I_n(0,0,...,0,ɑ_(n−1)) →I_n(0,0,...,ɑ_(n−2),ɑ_(n−1)) →...→I_n(0,ɑ_2,...,ɑ_(n−2),ɑ_(n−1)) →I_n(ɑ_1,ɑ_2,...,ɑ_n−2,ɑ_(n−1)). The initial conditions for a given step are obtained from the solutions of the previous step. As examples of the formalism, the differential equations for n=2 (fold), n=3 (cusp), n=4 (swallowtail), and n=5 (butterfly) are given explicitly. In addition, iterative and algebraic methods are described for determining the parameters a that are required in the uniform asymptotic cuspoid approximation for oscillating integrals with many coalescing saddle points. The results in this paper unify and generalize previous researches on the properties of the cuspoid canonical integrals and their partial derivatives

Contraception and the Contralife Will

Father Connor received his Ph.D. in philosophy from the Lateran University in Rome. He points out that “Intending the good is a subjective operation deriving from an intellectual objective perception of being. The being that I perceive is the esse of my personal self which is thrusting to fulfillment through acts. The person and his/her acts are the grounding of what I mean by “good” or “bad”. The evil of contraception, then is not an intention against the life of a future child, but the nonconformity of the will with the double structure (love-making/life giving) of the coital act which is a manifestation of the intercoursing process. “The evident weakness of the contralife will shows in the inability to apply it uniformly throughout sexual morality. For example, in in vitro fertilization, the will is pro-life, yet the “manufacturing” of the child is evil. They then have recourse to other principles ad hoc.” </jats:p

Unified theory of the semi-collisional tearing mode and internal kink mode in a hot tokamak: implications for sawtooth modelling

In large hot tokamaks like JET, the width of the reconnecting layer for resistive modes is determined by semi-collisional electron dynamics and is much less than the ion Larmor radius. Firstly a dispersion relation valid in this regime is derived which provides a unified description of drift-tearing modes, kinetic Alfven waves and the internal kink mode at low beta. Tearing mode stability is investigated analytically recovering the stabilising ion orbit effect, obtained previously by Cowley et al. [Phys. Fluids (29) 3230 1986], which implies large values of the tearing mode stability parameter "Delta prime" are required for instability. Secondly, at high beta it is shown that the tearing mode interacts with the kinetic Alfven wave and that there is an absolute stabilisation for all "Delta prime" due to the shielding effects of the electron temperature gradients, extending the result of Drake et. al [Phys. Fluids (26) 2509 1983] to large ion orbits. The nature of the transition between these two limits at finite values of beta is then elucidated. The low beta formalism is also relevant to the m=n=1 tearing mode and the dissipative internal kink mode, thus extending the work of Pegoraro et al. [Phys. Fluids B (1) 364 1989] to a more realistic electron model incorporating temperature perturbations, but then the smallness of the dissipative internal kink mode frequency is exploited to obtain a new dispersion relation valid at arbitrary beta. A diagram describing the stability of both the tearing mode and dissipative internal kink mode, in the space of "Delta prime" and beta, is obtained. The trajectory of the evolution of the current profile during a sawtooth period can be plotted in this diagram, providing a model for the triggering of a sawtooth crash.Comment: 37 pages, updated version, accepted, to appear on Plasma Physics and Controlled Fusio

The Effect of Plasma Beta on High-n Ballooning Stability at Low Magnetic Shear

An explanation of the observed improvement in H-mode pedestal characteristics with increasing core plasma pressure or poloidal beta, as observed in MAST and JET, is sought in terms of the impact of the Shafranov shift, d', on ideal ballooning MHD stability.Comment: 18 pages, 5 figures. This is an author-created, un-copyedited version of an article submitted for publication in Plasma Physics and Controlled Fusion. IoP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from i

Impact reactivity of materials at very high oxygen pressure

The requirements for impact testing of materials in an oxygen atmosphere at pressures from 82.7 MPa (12,000 psi) to 172 MPa (25,000 psi) were evaluated. The impact tester system was evaluated for potential pressure increases from 69 MPa (10,000 psi) to 82.7 MPa (12,000 psi). The low pressure oxygen and nitrogen systems, the impact tower, the impact test cell, and the high pressure oxygen system were evaluated individually. Although the structural integrity of the impact test cell and the compressor were sufficient for operation at 82.7 MPa (12,000 psi), studies revealed possible material incompatibility at that pressure and above. It was recommended that if a component should be replaced for 82.7 MPa (12,000 psi) operation the replacement should meet the final objectives of 172 MPa (25,000 psi). Recommended changes in the system include; use of Monel 400 for pressures above 82.7 MPa (12,000 psi), use of bellows to replace the seal in the impact tester, use of a sapphire window attached to a fiber optic for event sensing, and use of a three diaphragm compressor

Exploring the Cost Effectiveness of Land Conservation Auctions and Payment Policies

Until recently public efforts to encourage conservation on private land in many countries has primarily been through uniform payment policies. Auctions are increasingly used as a payment mechanism to acquire public benefits such as conservation actions that provide environmental improvements on private land (e.g. the US Conservation Reserve Program (CRP). The economic rationale for use of auctions is that they create decentralised incentives to offer bids at close to the true landholder opportunity costs, even when the implementing agency holds little information about these opportunity costs. This paper assesses the cost of a case study auction relative to four payment policies that use varying levels of information strategically to reduce rent payment and to prioritise funding based on environmental value. The results suggest that the estimated cost savings achievable with the discriminant price auction for conservation contracts depends on the policy to which the auction outcomes are compared. Auction cost savings are likely to be greatest when compared to policy alternatives involving little effort to discriminate amongst offers based on differences in landholder opportunity costs. A further key finding is that, for this case study, most of the savings resulting from the discriminant price auction could be attributed to the use of the environmental benefits index in project ranking and selection.Land Economics/Use,

Internet authentication based on personal history - a feasibility test

On the Internet, there is an uneasy tension between the security and usability of authentication mechanisms. An easy three-part classification is: 'something you know' (e.g. password); 'something you hold' (e.g. device holding digital certificate), and 'who you are' (e.g. biometric assessment) [9]. Each of these has well-known problems; passwords are written down, guessable, or forgotten; devices are lost or stolen, and biometric assays alienate users. We have investigated a novel strategy of querying the user based on their personal history (a 'Rip van Winkle' approach.) The sum of this information is large and well-known only to the individual. The volume is too large for impostors to learn; our observation is that, in the emerging environment, it is possible to collate and automatically query such information as an authentication test. We report a proof of concept study based on the automatic generation of questions from electronic 'calendar' information. While users were, surprisingly, unable to answer randomly generated questions any better than impostors, if questions are categorized according to appropriate psychological parameters then significant results can be obtained. We thus demonstrate the potential viability of this concept

Thermal Radiation Analysis System (TRASYS)

A user's manual is presented for TRASYS, which is a digital software system with a generalized capability for solving radiation problems. Subroutines, file, and variable definitions are presented along with subroutine and function descriptions for the preprocessor. Definitions and descriptions of components of the processor are also presented