A unified study on human and Web granular reasoning

AbstractA unified study is undertaken of finitely generated varieties HSP () of distributive lattices with unary operations, extending work of Cornish. The generating algebra () is assusmed to be of the form (P; ∧, ∨, 0, 1, {fμ}), where each fμ is an endomorphism or dual endomorphism of (P; ∧, ∨, 0, 1), and the Priestly dual of this lattice is an ordered semigroup N whose elements act by left multiplication to give the maps dual to the operations fμ. Duality theory is fully developed within this framework, into which fit many varieties arising in algebraic logic. Conditions on N are given for the natural and Priestley dualities for HSP () to be essentially the same, so that, inter alia, coproducts in HSP () are enriched D-coproducts.

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On the problem of a unified study of HCP metals from a perturbative approach: A possible resolution

Physica B Condensed Matter ◽

10.1016/0921-4526(94)00926-m ◽

1995 ◽

Vol 210 (1) ◽

pp. 73-86 ◽

Cited By ~ 2

Author(s):

B Datta ◽

D Sen ◽

D Roy

Keyword(s):

Perturbative Approach ◽

Unified Study

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Variational Sets of Multivalued Mappings and a Unified Study of Optimality Conditions

Journal of Optimization Theory and Applications ◽

10.1007/s10957-008-9415-1 ◽

2008 ◽

Vol 139 (1) ◽

pp. 47-65 ◽

Cited By ~ 9

Author(s):

P. Q. Khanh ◽

N. D. Tuan

Keyword(s):

Optimality Conditions ◽

Multivalued Mappings ◽

Unified Study ◽

Variational Sets

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GENERALIZED BCS EQUATIONS: APPLICATIONS

International Journal of Modern Physics B ◽

10.1142/s0217979210055858 ◽

2010 ◽

Vol 24 (19) ◽

pp. 3701-3712 ◽

Cited By ~ 11

Author(s):

G. P. MALIK

Keyword(s):

Cooper Pair ◽

Energy Gap ◽

High Temperature Superconductors ◽

Bcs Theory ◽

Simple Extension ◽

Cooper Pairs ◽

Debye Temperatures ◽

Unified Study ◽

Interesting Candidate ◽

Composite Superconductors

Based on the concepts of a superpropagator, multiple Debye temperatures, and equivalence of the binding energy of a Cooper pair and the BCS energy gap, the set of generalized BCS equations obtained recently via a temperature-generalized Bethe–Salpeter equation is employed for a unified study of the following composite superconductors: MgB 2, Nb 3 Sn , and YBCO. In addition, we study the Nb – Al system in which Cooper pairs as resonances have recently been reported to have been observed. Our approach seems to suggest that a simple extension of the BCS theory that accommodates the concept of Cooper pairs bound via a more than one phonon exchange mechanism may be an interesting candidate for dealing with high-temperature superconductors.

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