Search results for "Levels"
showing 10 items of 521 documents
Learning with belief levels
2008
AbstractWe study learning of predicate logics formulas from “elementary facts,” i.e. from the values of the predicates in the given model. Several models of learning are considered, but most of our attention is paid to learning with belief levels. We propose an axiom system which describes what we consider to be a human scientist's natural behavior when trying to explore these elementary facts. It is proved that no such system can be complete. However we believe that our axiom system is “practically” complete. Theorems presented in the paper in some sense confirm our hypothesis.
On regularity up to the boundary of solutions to a system of degenerate nonlinear elliptic fourth-order equations
2008
Under some hypotheses on weighted functions, using the interior regularity results established in (Kovalevsky, A. and Nicolosi, F., 2005, Existence and regularity of solutions to a system of degenerate nonlinear fourth-order equations. Nonlinear Analysis, 61, 281–307) and estimating the oscillation of solutions near the boundary of Ω, we establish results on regularity up to the boundary of a solutions of the system (1.1).
Theoretical study of degenerate Boulton-Katritzky rearrangements. Semiempirical and ab initio procedures
1998
Abstract A theoretical study of degenerate Boulton–Katritzky rearrangements concerning the anions of the 3-formylamino-1,2,4-oxadiazole, 3-formylmethyl-isoxazole and 3-hydroxy-iminomethyl-1,2,5-oxadiazole has been carried out by using semiempirical MNDO and ab initio Hartree–Fock procedures. Different transition structures and reactive pathways were obtained in the two cases. Semiempirical treatment shows asymmetrical transition states and non-concerted processes via symmetrical intermediates. By contrast, ab initio procedures describe concerted and synchronous processes involving symmetrically-located transition states. Some comments and criticisms on the theoretical treatment of these typ…
Iterative pairs and multitape automata
1996
In this paper we prove that if every iterative k-tuple of a language L recognized by a k-tape automaton is very degenerate, then L is recognizable. Moreover, we prove that if L is an aperiodic langnage recognized by a deterministic k-tape automaton, then L is recognizable.
Weakly Interacting Bose-Einstein Condensates under Rotation: Mean-Field versus Exact Solutions
2000
We consider a weakly-interacting, harmonically-trapped Bose-Einstein condensed gas under rotation and investigate the connection between the energies obtained from mean-field calculations and from exact diagonalizations in a subspace of degenerate states. From the latter we derive an approximation scheme valid in the thermodynamic limit of many particles. Mean-field results are shown to emerge as the correct leading-order approximation to exact calculations in the same subspace.
Pairing in a three-component Fermi gas
2006
We consider pairing in a three-component gas of degenerate fermions. In particular, we solve the finite temperature mean-field theory of an interacting gas for a system where both interaction strengths and fermion masses can be unequal. At zero temperature we find a a possibility of a quantum phase transition between states associated with pairing between different pairs of fermions. On the other hand, finite temperature behavior of the three-component system reveals some qualitative differences from the two-component gas: for a range of parameters it is possible to have two different critical temperatures. The lower one corresponds to a transition between different pairing channels, while …
Magnetic exchange interaction in a pair of orbitally degenerate ions: Magnetic anisotropy of [Ti2Cl9]−3
2001
The theory of the kinetic exchange in a pair of orbitally degenerate ions developed by the authors [J. Phys. Chem. A 102, 200 (1998)] is applied to the case of face-shared bioctahedral dimer (overall D3h-symmetry). The effective kinetic exchange Hamiltonian is found for a 2T2–2T2 system taking into account all relevant transfer pathways and charge-transfer crystal field states. The influence of different transfer integrals involved in the kinetic exchange on the energy pattern and magnetic properties of the system is examined. The role of other related interactions (trigonal crystal field, spin–orbit coupling) is also discussed in detail. Using the pseudoangular momentum representation and …
Orbitally dependent kinetic exchange in cobalt(II) pairs: origin of the magnetic anisotropy
2003
Abstract A comprehensive theoretical study of the magnetic exchange between Co 2+ ions is reported. Using the microscopic background we deduce the general Hamiltonian for a corner-shared bioctahedral system involving kinetic exchange, spin–orbit coupling and low-symmetry local crystal field. This Hamiltonian acting within orbitally degenerate ground manifold 4 ( T 1g ) A ⊗ 4 ( T 1g ) B of the cobalt pair is expressed in terms of orbital and spin operators. We elucidate the major electronic factors controlling the exchange anisotropy in the Co(II) pairs. The degree of the magnetic anisotropy is shown to depend on the strength of the cubic crystal field and on the relative efficiency of two k…
Magnetic Exchange between Orbitally Degenerate Metal Ions: The Problem of Magnetic Anisotropy
2001
Abstract In this paper we show that a strong magnetic anisotropy appears in exchange mixed–valence clusters containing orbitally degenerate metal ions. Combining an effective Hamiltonian approach with the technique of the irreducible tensor operators (ITO) and pseudoangular momentum representation we have solved the problem of magnetic exchange in localized and delocalized (mixed–valence) systems with different overall symmetries ( D 2 h , D 3 h , D 4 h ). The energy pattern as well as the character of the magnetic anisotropy is closely related to the ground term of the ions, electron transfer pathways, and overall symmetry of the system being affected also by the local crystal fields, spin…
Magnetic exchange between metal ions with unquenched orbital angular momenta: basic concepts and relevance to molecular magnetism
2010
This review article is a first attempt to give a systematic and comprehensive description (in the framework of the unified theoretical approach) of the exchange interactions in polynuclear systems based on orbitally degenerate metal ions in the context of their relevance to the modern molecular magnetism. Interest in these systems is related to the fundamental problems of magnetism and at the same time steered by a number of impressive potential applications of molecular magnets, like high-density memory storage units, nanoscale qubits, spintronics and photoswitchable devices. In the presence of orbital degeneracy, the conventional spin Hamiltonian (Heisenberg–Dirac–van Vleck model) becomes…