9,982 research outputs found

### Purposive discovery of operations

The Generate, Prune & Prove (GPP) methodology for discovering definitions of mathematical operators is introduced. GPP is a task within the IL exploration discovery system. We developed GPP for use in the discovery of mathematical operators with a wider class of representations than was possible with the previous methods by Lenat and by Shen. GPP utilizes the purpose for which an operator is created to prune the possible definitions. The relevant search spaces are immense and there exists insufficient information for a complete evaluation of the purpose constraint, so it is necessary to perform a partial evaluation of the purpose (i.e., pruning) constraint. The constraint is first transformed so that it is operational with respect to the partial information, and then it is applied to examples in order to test the generated candidates for an operator's definition. In the GPP process, once a candidate definition survives this empirical prune, it is passed on to a theorem prover for formal verification. We describe the application of this methodology to the (re)discovery of the definition of multiplication for Conway numbers, a discovery which is difficult for human mathematicians. We successfully model this discovery process utilizing information which was reasonably available at the time of Conway's original discovery. As part of this discovery process, we reduce the size of the search space from a computationally intractable size to 3468 elements

### Simplicity of algebras associated to \'etale groupoids

We prove that the C*-algebra of a second-countable, \'etale, amenable
groupoid is simple if and only if the groupoid is topologically principal and
minimal. We also show that if G has totally disconnected unit space, then the
associated complex *-algebra introduced by Steinberg is simple if and only if
the interior of the isotropy subgroupoid of G is equal to the unit space and G
is minimal.Comment: The introduction has been updated and minor changes have been made
throughout. To appear in Semigroup Foru

### Effects of 3-d and 4-d-transition metal substitutional impurities on the electronic properties of CrO2

We present first-principles based density functional theory calculations of
the electronic and magnetic structure of CrO2 with 3d (Ti through Cu) and 4d
(Zr through Ag) substitutional impurities. We find that the half-metallicity of
CrO2 remains intact for all of the calculated substitutions. We also observe
two periodic trends as a function of the number of valence electrons: if the
substituted atom has six or fewer valence electrons (Ti-Cr or Zr-Mo), the
number of down spin electrons associated with the impurity ion is zero,
resulting in ferromagnetic (FM) alignment of the impurity magnetic moment with
the magnetization of the CrO2 host. For substituent atoms with eight to ten
(Fe-Ni or Ru-Pd with the exception of Ni), the number of down spin electrons
contributed by the impurity ion remains fixed at three as the number
contributed to the majority increases from one to three resulting in
antiferromagnetic (AFM) alignment between impurity moment and host
magnetization. The origin of this variation is the grouping of the impurity
states into 3 states with approximate "t2g" symmetry and 2 states with
approximate "eg" symmetry. Ni is an exception to the rule because a
Jahn-Teller-like distortion causes a splitting of the Ni eg states. For Mn and
Tc, which have 8 valence electrons, the zero down spin and 3 down spin
configurations are very close in energy. For Cu and Ag atoms, which have 11
valence electrons, the energy is minimized when the substituent ion contributes
5 Abstract down-spin electrons. We find that the interatomic exchange
interactions are reduced for all substitutions except for the case of Fe for
which a modest enhancement is calculated for interactions along certain
crystallographic directions.Comment: 26 pages, 10 figures, 2 table

### Thermal acoustic oscillations, volume 2

A number of thermal acoustic oscillation phenomena and their effects on cryogenic systems were studied. The conditions which cause or suppress oscillations, the frequency, amplitude and intensity of oscillations when they exist, and the heat loss they induce are discussed. Methods of numerical analysis utilizing the digital computer were developed for use in cryogenic systems design. In addition, an experimental verification program was conducted to study oscillation wave characteristics and boiloff rate. The data were then reduced and compared with the analytical predictions

### Femtosecond probing of bimolecular reactions: The collision complex

Progress has been made in probing the femtosecond
dynamics of transition states of chemical reactions.(1) The
"half-collision" case of unimolecular reactions has been
experimentally investigated for a number of systems and
much theoretical work has already been developed.(2) For
bimolecular reactions, the case of full collision, the zero of
time is a problem which makes the femtosecond temporal
resolution of the dynamics a difficult task

### Femtosecond real-time probing of reactions. VIII. The bimolecular reaction Br+I2

In this paper, we discuss the experimental technique for real-time measurement of the lifetimes of the collision complex of bimolecular reactions. An application to the atomâ€“molecule Br+I_2 reaction at two collision energies is made. Building on our earlier Communication [J. Chem. Phys. 95, 7763 (1991)], we report on the observed transients and lifetimes for the collision complex, the nature of the transition state, and the dynamics near threshold. Classical trajectory calculations provide a framework for deriving the global nature of the reactive potential energy surface, and for discussing the real-time, scattering, and asymptotic (product-state distribution) aspects of the dynamics. These experimental and theoretical results are compared with the extensive array of kinetic, crossed beam, and theoretical studies found in the literature for halogen radicalâ€“halogen molecule exchange reactions

### Theoretical investigation into the possibility of very large moments in Fe16N2

We examine the mystery of the disputed high-magnetization \alpha"-Fe16N2
phase, employing the Heyd-Scuseria-Ernzerhof screened hybrid functional method,
perturbative many-body corrections through the GW approximation, and onsite
Coulomb correlations through the GGA+U method. We present a first-principles
computation of the effective on-site Coulomb interaction (Hubbard U) between
localized 3d electrons employing the constrained random-phase approximation
(cRPA), finding only somewhat stronger on-site correlations than in bcc Fe. We
find that the hybrid functional method, the GW approximation, and the GGA+U
method (using parameters computed from cRPA) yield an average spin moment of
2.9, 2.6 - 2.7, and 2.7 \mu_B per Fe, respectively.Comment: 8 pages, 3 figure

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